A 5-m-long, twin-tube, counterflow heat exchanger,such as

In a fire-tube boiler, hot products of combustion flow-ing through an array of thin-walled tubes are used toboil water flowing over the tubes. At the time of instal-lation, the overall heat transfer coefficient was400 W/m2?K. After 1 year of use, the inner and outertube surfaces are fouled, with corresponding foulingfactors of R?,i?0.0015 and R?,o?0.0005 m2?K/W,respectively. Should the boiler be scheduled for clean-ing of the tube surfaces?

A type-302 stainless steel tube of inner and outer diam-eters Di?22 mm and Do?27 mm, respectively, isused in a cross-flow heat exchanger. The fouling fac-tors, R?, for the inner and outer surfaces are estimatedto be 0.0004 and 0.0002 m2?K/W, respectively. a) Determine the overall heat transfer coefficient basedon the outside area of the tube, Uo. Compare the hermal resistances due to convection, tube wallconduction, and fouling.(b) Instead of air flowing over the tube, consider a situ- ation for which the cross-flow fluid is water at 15?Cwith a velocity of Vo?1 m/s. Determine the overallheat transfer coefficient based on the outside area ofthe tube, Uo. Compare the thermal resistances due toconvection, tube wall conduction, and fouling.(c) For the waterair conditions of part (a) and meanvelocities, um,i, of 0.2, 0.5, and 1.0 m/s, plot theoverall heat transfer coefficient as a function of the cross-flow velocity for 5?Vo?30 m/s.(d) For the waterwater conditions of part (b) andcross-flow velocities, Vo, of 1, 3, and 8 m/s, plot theoverall heat transfer coefficient as a function of the mean velocity for 0.5?um,i2? .5 m/s.

A shell-and-tube heat exchanger is to heat an acidic liquidthat flows in unfinned tubes of inside and outside diame-ters Di?10 mm and Do?11 mm, respectively. A hotgas flows on the shell side. To avoid corrosion of the tubematerial, the engineer may specify either a Ni-Cr-Mo corrosion-resistant metal alloy (?m?8900 kg/m3, km?8W/m?K) or a polyvinylidene fluoride (PVDF) plastic(?p?1780 kg/m3, kp?0.17 W/m?K). The inner andouter heat transfer coefficients are hi?1500 W/m2?Kand ho?200 W/m2?K, respectively.(a) Determine the ratio of plastic to metal tube surfaceareas needed to transfer the same amount of heat.(b) Determine the ratio of plastic to metal mass associ-ated with the two heat exchanger designs.(c) The cost of the metal alloy per unit mass is threetimes that of the plastic. Determine which tubematerial should be specified on the basis of cost

A steel tube (k?50 W/m?K) of inner and outer diame-ters Di?20 mm and Do?26 mm, respectively, is usedto transfer heat from hot gases flowing over the tube(hh?200 W/m2?K) to cold water flowing through thetube (hc?8000 W/m2?K). What is the cold-side overallheat transfer coefficient Uc? To enhance heat transfer, 16 straight fins of rectangular profile are installed longi-tudinally along the outer surface of the tube. The finsare equally spaced around the circumference of thetube, each having a thickness of 2 mm and a length of15 mm. What is the corresponding overall heat transfercoefficient Uc?

A heat recovery device involves transferring energyfrom the hot flue gases passing through an annularregion to pressurized water flowing through the innertube of the annulus. The inner tube has inner and outer diameters of 24 and 30 mm and is connected by eightstruts to an insulated outer tube of 60-mm diameter.Each strut is 3 mm thick and is integrally fabricatedwith the inner tube from carbon steel (k?50 W/m?K).Consider conditions for which water at 300 Kflows through the inner tube at 0.161 kg/s while fluegases at 800 K flow through the annulus, maintaining aconvection coefficient of 100 W/m2?K on both thestruts and the outer surface of the inner tube. What isthe rate of heat transfer per unit length of tube from gasto the water?

A novel design for a condenser consists of a tube ofthermal conductivity 200 W/m?K with longitudinal finssnugly fitted into a larger tube. Condensing refrigerantat 45?C flows axially through the inner tube, while waterat a flow rate of 0.012 kg/s passes through the six chan-nels around the inner tube. The pertinent diameters areD1?10 mm, D2?14 mm, and D3?50 mm, while thefin thickness is t?2 mm. Assume that the convectioncoefficient associated with the condensing refrigerant isextremely large.Determine the heat removal rate per unit tube length ina section of the tube for which the water is at 15?C.

The condenser of a steam power plant containsN?1000 brass tubes (kt?110 W/m?K), each ofinner and outer diameters, Di?25 mm and Do? 28 mm, respectively. Steam condensation on the outersurfaces of the tubes is characterized by a convectioncoefficient of ho?10,000 W/m2?K.(a) If cooling water from a large lake is pumpedthrough the condenser tubes at , whatis the overall heat transfer coefficient Uobased on the outer surface area of a tube? Properties ofthe water may be approximated as ??9.60, and Pr?6.6.(b) If, after extended operation, fouling provides aresistance of at the innersurface, what is the value of Uo?(c) If water is extracted from the lake at and 10 kg/s of steam at 0.0622 bars are to be con-densed, what is the corresponding temperature ofthe water leaving the condenser? The specific heatof the water is 4180 .

Thin-walled aluminum tubes of diameter D?10 mmare used in the condenser of an air conditioner. Undernormal operating conditions, a convection coefficientof hi?5000 W/m2?K is associated with condensationon the inner surface of the tubes, while a coefficient ofho?100 W/m2?K is maintained by airflow over thetubes.(a) What is the overall heat transfer coefficient if thetubes are unfinned?(b) What is the overall heat transfer coefficient based on the inner surface, Ui, if aluminum annu-lar fins of thickness t?1.5 mm, outer diameterDo?20 mm, and pitch S?3.5 mm are added to the outer surface? Base your calculations on a1-m-long section of tube. Subject to the require-ments that t?1 mm and (S?t)?1.5 mm, explorethe effect of variations in tand Son Ui. What com-bination of tand Swould yield the best heattransfer performance?

A finned-tube, cross-flow heat exchanger is to use theexhaust of a gas turbine to heat pressurized water. Labo-ratory measurements are performed on a prototype ver-sion of the exchanger, which has a surface area of 10 m2,to determine the overall heat transfer coefficient as afunction of operating conditions. Measurements madeunder particular conditions, for which h?2 kg/s,Th,i?325?C, c?0.5 kg/s, and Tc,i?25?C, reveal awater outlet temperature of Tc,o?150?C. What is theoverall heat transfer coefficient of the exchanger?

Water at a rate of 45,500 kg/h is heated from 80 to150C in a heat exchanger having two shell passes and eight tube passes with a total surface area of 925 m2.Hot exhaust gases having approximately the same thermophysical properties as air enter at 350C and exit at 175C. Determine the overall heat transfer coefficient.

A novel heat exchanger concept consists of a largenumber of extruded polypropylene sheets (k?0.17W/m?K), each having a fin-like geometry, that aresubsequently stacked and melted together to form theheat exchanger core. Besides being inexpensive, the heatexchanger can be easily recycled at the end of its life.Carbon dioxide at a mean temperature of 10?C andpressure of 2 atm flows in the cool channels at a meanvelocity of um?0.1 m/s. Air at 30?C and 2 atm flowsat 0.2 m/s in the warm channels. Neglecting the thermal contact resistance at the welded interface,determine the product of the overall heat transfercoefficient and heat transfer area, UA, for a heatexchanger core consisting of 200 cool channels and200 warm channels.

The properties and flow rates for the hot and cold flu-ids of a heat exchanger are shown in the followingtable. Which fluid limits the heat transfer rate of theexchanger? Explain your choice.Hot flui Cold fluiDensity, kg/m3997 1247Specific heat, 4179 2564Thermal conductivity, 0.613 0.287Viscosity, N?s/m28.5510?41.6810?4Flow rate, m3/h141

A process fluid having a specific heat of 3500 J/kg?Kand flowing at 2 kg/s is to be cooled from 80?C to50?C with chilled water, which is supplied at a temper-ature of 15?C and a flow rate of 2.5 kg/s. Assuming anoverall heat transfer coefficient of 2000 W/m2?K, cal-culate the required heat transfer areas for the followin exchanger configurations: (a) parallel flow, (b) counter-flow, (c) shell-and-tube, one shell pass and two tubepasses, and (d) cross-flow, single pass, both fluidsunmixed. Compare the results of your analysis. Yourwork can be reduced by using IHT

A shell-and-tube exchanger (two shells, four tube passes)is used to heat 10,000 kg/h of pressurized water from35 to 120C with 5000 kg/h pressurized water enteringthe exchanger at 300C. If the overall heat transfercoefficient is 1500 W/m2?K, determine the requiredheat exchanger area.

Consider the heat exchanger of Problem 11.14. Afterseveral years of operation, it is observed that the outlettemperature of the cold water reaches only 95C ratherthan the desired 120C for the same flow rates andinlet temperatures of the fluids. Determine the cumula-tive (inner and outer surface) fouling factor that is thecause of the poorer performance.

The hot and cold inlet temperatures to a concentrictube heat exchanger are Th,i?200?C, Tc,i?100?C,respectively. The outlet temperatures are Th,o?110?Cand Tc,o?125?C. Is the heat exchanger operating in aparallel flow or in a counterflow configuration? Whatis the heat exchanger effectiveness? What is the NTU?Phase change does not occur in either fluid

A concentric tube heat exchanger of length L?2m isused to thermally process a pharmaceutical productflowing at a mean velocity of um,c?0.1 m/s with aninlet temperature of Tc,i?20?C. The inner tube ofdiameter Di?10 mm is thin walled, and the exteriorof the outer tube (Do?20 mm) is well insulated.Water flows in the annular region between the tubes ata mean velocity of um,h?0.2 m/s with an inlet temper-ature of Th,i?60?C. Properties of the pharmaceuticalproduct are ??1010?6m2/s, k?0.25 W/m?K,??1100 kg/m3, and cp?2460 J/kg?K. Evaluate waterproperties at Th?50?C.(a) Determine the value of the overall heat transfercoefficient U.(b) Determine the mean outlet temperature of thepharmaceutical product when the exchanger oper-ates in the counterflow mode.(c) Determine the mean outlet temperature of thepharmaceutical product when the exchanger oper-ates in the parallel-flow mode

A counterflow, concentric tube heat exchanger isdesigned to heat water from 20 to 80?C using hot oil,which is supplied to the annulus at 160?C and dis-charged at 140?C. The thin-walled inner tube has adiameter of Di?20 mm, and the overall heat transfer coefficient is 500 W/m2?K. The design condition callsfor a total heat transfer rate of 3000 W.(a) What is the length of the heat exchanger?(b) After 3 years of operation, performance isdegraded by fouling on the water side of theexchanger, and the water outlet temperature isonly 65?C for the same fluid flow rates and inlettemperatures. What are the corresponding valuesof the heat transfer rate, the outlet temperature ofthe oil, the overall heat transfer coefficient, and thewater-side fouling factor, ?

Consider the counterflow, concentric tube heatexchanger of Example 11.1. The designer wishes toconsider the effect of the cooling water flow rate onthe tube length. All other conditions, including theoutlet oil temperature of 60?C, remain the same.(a) From the analysis of Example 11.1, we saw thatthe overall coefficient Uis dominated by the hot-side convection coefficient. Assuming the waterproperties are independent of temperature, calcu-late Uas a function of the water flow rate. Justify aconstant value of Uin the calculations of part (b).(b) Calculate and plot the required exchanger tubelength Land the water outlet temperature Tc,oas a function of the cooling water flow rate for.

Consider a concentric tube heat exchanger with an areaof 50 m2operating under the following conditions:Hot flui Cold fluiHeat capacity rate, kW/K 63Inlet temperature, 60 30Outlet temperature, 54(a) Determine the outlet temperature of the hot fluid.(b) Is the heat exchanger operating in counterflow orparallel flow, or cant you tell from the availableinformation?(c) Calculate the overall heat transfer coefficient.(d) Calculate the effectiveness of this exchanger.(e) What would be the effectiveness of this exchangerif its length were made very large?

As part of a senior project, a student was given theassignment to design a heat exchanger that meets the following specifications:Hot water28 90 Like many real-world situations, the customer hasntrevealed, or doesnt know, additional requirements thatwould allow you to proceed directly to a final configu-ration. At the outset, it is helpful to make a first-cutdesign based upon simplifying assumptions, which canbe evaluated to determine what additional requirementsand trade-offs should be considered by the customer.(a) Design a heat exchanger to meet the foregoing spec-ifications. List and explain your assumptions. Hint:Begin by finding the required value for UAandusing representative values of Uto determine A.(b) Evaluate your design by identifying what featuresand configurations could be explored with yourcustomer in order to develop more complete spec-ifications.

A shell-and-tube heat exchanger must be designed toheat 2.5 kg/s of water from 15 to 85?C. The heating isto be accomplished by passing hot engine oil, which is available at 160?C, through the shell side of theexchanger. The oil is known to provide an averageconvection coefficient of ho?400 W/m2?K on theoutside of the tubes. Ten tubes pass the water throughthe shell. Each tube is thin walled, of diameterD?25 mm, and makes eight passes through the shell.If the oil leaves the exchanger at 100?C, what is itsflow rate? How long must the tubes be to accomplishthe desired heating?

A concentric tube heat exchanger for cooling lubri-cating oil is comprised of a thin-walled inner tube of25-mm diameter carrying water and an outer tube of45-mm diameter carrying the oil. The exchangeroperates in counterflow with an overall heat transfercoefficient of 60 W/m2?K and the tabulated averageproperties.PropertiesWaterOil?(kg/m3)1000800cp(J/kg?K)42001900?(m2/s)710?7110?5k(W/m?K)0. 640.134Pr4.7140WaterOilmw= 0.1 kg/sTo,outTw,outTw,in = 30CTo,in = 100Cmo = 0.1 kg/sL(a) If the outlet temperature of the oil is 60?C, deter-mine the total heat transfer and the outlet tempera-ture of the water.(b) Determine the length required for the heatexchanger.

A counterflow, concentric tube heat exchanger usedfor engine cooling has been in service for an extendedperiod of time. The heat transfer surface area of theexchanger is 5 m2, and the design valueof the overallconvection coefficient is 38 W/m2?K. During a testrun, engine oil flowing at 0.1 kg/s is cooled from110?C to 66?C by water supplied at a temperature of25?C and a flow rate of 0.2 kg/s. Determine whetherfouling has occurred during the service period. If so,calculate the fouling factor, .

An automobile radiator may be viewed as a cross-flowheat exchanger with both fluids unmixed. Water,which has a flow rate of 0.05 kg/s, enters the radiatorat 400 K and is to leave at 330 K. The water is cooledby air that enters at 0.75 kg/s and 300 K.(a) If the overall heat transfer coefficient is 200 W/ m2?K,what is the required heat transfer surface area?(b) A manufacturing engineer claims ridges can bestamped on the finned surface of the exchanger,which could greatly increase the overall heattransfer coefficient. With all other conditionsremaining the same and the heat transfer surfacearea determined from part (a), generate a plot ofthe air and water outlet temperatures as a functionof Ufor 200?U?400 W/m2?K. What benefitsresult from increasing the overall convection coef- ficient for this application?

Hot air for a large-scale drying operation is to be pro-duced by routing the air over a tube bank (unmixed),while products of combustion are routed through the tubes. The surface area of the cross- flow heatexchanger is A?25 m2, and for the proposed operat-ing conditions, the manufacturer specifies an overallheat transfer coefficient of U?35 W/m2?K. The airand the combustion gases may each be assumed tohave a specific heat of cp?1040 J/kg?K. Considerconditions for which combustion gases flowing at1 kg/s enter the heat exchanger at 800 K, while air at 5 kg/s has an inlet temperature of 300 K.(a) What are the air and gas outlet temperatures?(b) After extended operation, deposits on the innertube surfaces are expected to provide a foulingresistance of . Should opera-tion be suspended in order to clean the tubes?(c) The heat exchanger performance may be im-proved by increasing the surface area and/or overall heat transfer coefficient. Explore the effectof such changes on the air outlet temperature for500U ? A?2500 W/K.

In a dairy operation, milk at a flow rate of 250 L /h anda cow-bodytemperature of 38.6?C must be chilled to asafe-to-store temperature of 13?C or less. Groundwater at 10?C is available at a flow rate of 0.72 m3/h.The density and specific heat of milk are 1030 kg/m3and 3860 J/kg?K, respectively.(a) Determine the UAproduct of a counterflow heatexchanger required for the chilling process. Deter- mine the length of the exchanger if the inner pipehas a 50-mm diameter and the overall heat trans-fer coefficient is U?1000 W/m2?K.(b) Determine the outlet temperature of the water.(c) Using the value of UAfound in part (a), determinethe milk outlet temperature if the water flow rateis doubled. What is the outlet temperature if theflow rate is halved?

A shell-and-tube heat exchanger with one shell passand two tube passes is used as a regenerator,to pre-heat milk before it is pasteurized. Cold milk enters theregenerator at Tc,i?5?C, while hot milk, which hascompleted the pasteurization process, enters at Th,i?70?C. After leaving the regenerator, the heated milkenters a second heat exchanger, which raises its tem-perature from Tc,oto 70?C.(a) A regenerator is to be used in a pasteurizationprocess for which the flow rate of the milk is. For this flow rate, the manufac-turer of the regenerator specifies an overall heattransfer coefficient of 2000 W/m2?K. If the desiredeffectiveness of the regenerator is 0.5, what is therequisite heat transfer area? What are the corre-sponding rate of heat recovery and the fluid outlettemperatures? Refer to Problem 11.27 for theproperties of milk.(b) If the hot fluid in the secondary heat exchangerderives its energy from the combustion of naturalm c?m h?5 kg/sPasteurizer withsecondary heat exchangerRegeneratorTh,omc,Tc,imh = mc,Th,iTc,ogas and the burner has an efficiency of 90%, whatwould be the annual savings in energy and fuel costsassociated with installation of the regenerator? Thefacility operates continuously throughout the year,and the cost of natural gas is Cng$? 0.02/MJ.

A twin-tube, counterflow heat exchanger operates withbalanced flow rates of 0.003 kg/s for the hot and coldairstreams. The cold stream enters at 280 K and mustbe heated to 340 K using hot air at 360 K. The averagepressure of the airstreams is 1 atm and the maximumallowable pressure drop for the cold air is 10 kPa. Thetube walls may be assumed to act as fins, each with anefficiency of 100%.(a) Determine the tube diameter Dand length Lthatsatisfy the prescribed heat transfer and pressuredrop requirements.(b) For the diameter Dand length Lfound in part (a),generate plots of the cold stream outlet tempera-ture, the heat transfer rate, and pressure drop as afunction of balanced flow rates in the range from0.002 to 0.004 kg/s. Comment on your results.

A 5-m-long, twin-tube, counterflow heat exchanger,such as that illustrated in Problem 11.29, is used to heatair for a drying operation. Each tube is made from plaincarbon steel (k?60 W/m?K) and has an inner diameterand wall thickness of 50 mm and 4 mm, respectively.The thermal resistance per unit length of the brazedjoint connecting the tubes is . Con-sider conditions for which air enters one tube at a pres-sure of 5 atm, a temperature of 17?C, and flow rate of0.030 kg/s, while saturated steam at 2.455 bar con-denses in the other tube. The convection coefficient forcondensation may be approximated as 5000 W/m2?K.What is the air outlet temperature? What is the mass rateat which condensate leaves the system? Hint: Accountfor the effects of circumferential conduction in the tubesby treating them as extended surfaces

Hot water for an industrial washing operation is pro-duced by recovering heat from the flue gases of a fur-nace. A cross-flow heat exchanger is used, with thegases passing over the tubes and the water making asingle pass through the tubes. The steel tubes(k?60 W/m?K) have inner and outer diameters ofDi?15 mm and Do?20 mm, while the staggeredtube array has longitudinal and transverse pitches ofST?SL?40 mm. The plenum in which the array isinstalled has a width (corresponding to the tube length)of W?2 m and a height (normal to the tube axis) ofH?1.2 m. The number of tubes in the transverseplane is therefore NT?H/ST?30. The gas propertiesmay be approximated as those of atmospheric air, andthe convection coefficient associated with water flow in the tubes may be approximated as 3000 W/m2?K.(a) If 50 kg/s of water are to be heated from 290 to350 K by 40 kg/s of flue gases entering theexchanger at 700 K, what is the gas outlet temper-ature and how many tube rows NLare required?(b) The water outlet temperature may be controlled byvarying the gas flow rate and/or inlet temperature.For the value of NLdetermined in part (a) and theprescribed values of H, W, ST, , and Tc,i, com-pute and plot Tc,oas a function of hover therange 20?h?40 kg/s for values of Th,i?500,600, and 700 K. Also plot the corresponding vari-ations of Th,o. If Th,omust not drop below 400 K toprevent condensation of corrosive vapors on theheat exchanger surfaces, are there any constraintson hand Th,i?

A single-pass, cross-flow heat exchanger uses hotexhaust gases (mixed) to heat water (unmixed) from30 to 80?C at a rate of 3 kg/s. The exhaust gases, hav-ing thermophysical properties similar to air, enter andexit the exchanger at 225 and 100?C, respectively. Ifthe overall heat transfer coefficient is 200 W/m2K ? ,estimate the required surface area.

Consider the fluid conditions and overall heat transfercoefficient of Problem 11.32 for a concentric tube heatexchanger operating in parallel flow. The thin-walledseparator tube has a diameter of 100 mm.(a) Determine the required length for the exchanger.(b) Assuming water flow inside the separator tube tobe fully developed, estimate the convection heattransfer coefficient.(c) Using the overall coefficient and the inlet temper-atures from Problem 11.32, plot the heat transferrate and fluid outlet temperatures as a function ofthe tube length for 60?L?400 m and the parallel-flow configuration.m m m m c(d) If the exchanger were operated in counterflow withthe same overall coefficient and inlet temperatures,what would be the reduction in the required lengthrelative to the value found in part (a)?(e) For the counterflow configuration, plot the effec-tiveness and fluid outlet temperatures as a functionof the tube length for 60?L?400 m.

The compartment heater of an automobile exchangesheat between warm radiator fluid and cooler outsideair. The flow rate of water is large compared to the air,and the effectiveness, ?, of the heater is known todepend on the flow rate of air according to the rela-tion, ? .(a) If the fan is switched to high and airis doubled,determine the percentage increase in the heatadded to the car, if fluid inlet temperatures remainthe same.(b) For the low-speed fan condition, the heater warmsoutdoor air from 0 to 30?C. When the fan is turnedto medium, the airflow rate increases 50% and theheat transfer increases 20%. Find the new outlettemperature.

A counterflow, twin-tube heat exchanger is made bybrazing two circular nickel tubes, each 40 m long,together as shown below. Hot water flows through thesmaller tube of 10-mm diameter and air at atmos-pheric pressure flows through the larger tube of 30-mm diameter. Both tubes have a wall thickness of2 mm. The thermal contact conductance per unitlength of the brazed joint is 100 W/m?K. The massflow rates of the water and air are 0.04 and 0.12 kg/s,respectively. The inlet temperatures of the water andair are 85 and 23?C, respectively.Employ the ?NTU method to determine the out-let temperature of the air. Hint:Account for the effectsof circumferential conduction in the walls of the tubesby treating them as extended surfaces.

Consider a coupledshell-in-tube heat exchange deviceconsisting of two identical heat exchangers A and B. Air flows on the shell side of heat exchanger A, enter-ing at Th,i,A?520 K and . Ammoniaflows in the shell of heat exchanger B, entering atTc,i,B?280 K, . The tube-side flow iscommon to both heat exchangers and consists of waterat a flow rate with two tube passes. TheUAproduct increases with water flow rate for heatexchanger A as expressed by the relation UAA?a?bm.c,Awhere a?6000 W/K and b?100 J/kg?K. Forheat exchanger B, UAB?1.2UAA.(a) For , determine the outlet airand ammonia temperatures, as well as the heattransfer rate.(b) The plant engineer wishes to fine-tune the heatexchanger performance by installing a variable-speed pump to allow adjustment of the water flowrate. Plot the outlet air and outlet ammonia tem-peratures versus the water flow rate over the range0 kg/s .

Consider Problem 11.36.(a) For , determine the outlet airand ammonia temperatures, as well as the heattransfer rate.(b) Plot the outlet air and outlet ammonia tempera-tures versus the water flow rate over the range 5 kg/s.

For health reasons, public spaces require the continu-ous exchange of a specified mass of stale indoor airwith fresh outdoor air. To conserve energy during theheating season, it is expedient to recover the thermalenergy in the exhausted, warm indoor air and transferit to the incoming, cold fresh air. A coupledsingle-pass, cross-flow heat exchanger with both fluidsunmixed is installed in the intake and return ducts of aheating system as shown in the schematic. Water con-taining an anti-freeze agent is used as the workingfluid in the coupled heat exchange device, which iscomposed of individual heat exchangers A and B.Hence, heat is transferred from the warm stale air tothe cold fresh air by way of the pumped water.?m c,A?m h,B ?50kg/sm c,A?m h,B?10kg/s?m c,A?m h,B ?2kg/sm c,A?m h,B?1kg/sABAirTh,i,A = 520 Kmh,A = 10 kg/sAmmoniaTc,i,B = 280 Kmc,B = 5 kg/sWatermc,A = mh,B = 1 kg/sPumpm c,A?m h,Bm c,B?5kg/sm h,A?10kg/sConsider a specified air mass flow rate (in each duct) of ?1.50 kg/s, an overall heat transfercoefficientarea product of UA?2500 W/K (for each heat exchanger), an outdoor temperature of Tc,i,A??4?C and an indoor temperature of Th,i,B?23?C. Since the warm air has been humidified, exces-sive heat transfer can result in unwanted condensationin the ductwork. What water flow rate is necessary to maximize heat transfer while ensuring the outlettemperature associated with heat exchanger B does notfall below the dew point temperature, Th,o,B?Tdp?13?C? Hint: Assume the maximum heat capacity rateis associated with the air.

A cross-flow heat exchanger used in a cardiopulmonarybypass procedure cools blood flowing at 5 L/min from a body temperature of 37?C to 25?C in order to inducebody hypothermia, which reduces metabolic andoxygen requirements. The coolant is ice water at 0?C,and its flow rate is adjusted to provide an outlet tem-perature of 15?C. The heat exchanger operates withboth fluids unmixed, and the overall heat transfercoefficient is 750 W/m2?K. The density and specificheat of the blood are 1050 kg/m3and 3740 J/kg?K,respectively.(a) Determine the heat transfer rate for the exchanger.(b) Calculate the water flow rate.(c) What is the surface area of the heat exchanger?(d) Calculate and plot the blood and water outlet tem-peratures as a function of the water flow rate for therange 2 to 4 L/min, assuming all other parametersremain unchanged. Comment on how the changesin the outlet temperatures are affected by changes inthe water flow rate. Explain this behavior and whyit is an advantage for this application.

Saturated steam at 0.14 bar is condensed in a shell-and-tube heat exchanger with one shell pass and two tubepasses consisting of 130 brass tubes, each with a lengthper pass of 2 m. The tubes have inner and outer diame-ters of 13.4 and 15.9 mm, respectively. Cooling waterenters the tubes at 20?C with a mean velocity of 1.25 m/s. The heat transfer coefficient for condensationon the outer surfaces of the tubes is 13,500 W/m2?K.(a) Determine the overall heat transfer coefficient, thecooling water outlet temperature, and the steamcondensation rate.(b) With all other conditions remaining the same, butaccounting for changes in the overall coefficient,plot the cooling water outlet temperature and thesteam condensation rate as a function of the waterflow rate for 10?.

A feedwater heater that supplies a boiler consists of ashell-and-tube heat exchanger with one shell pass andtwo tube passes. One hundred thin-walled tubes eachhave a diameter of 20 mm and a length (per pass) of2 m. Under normal operating conditions water entersthe tubes at 10 kg/s and 290 K and is heated by con-densing saturated steam at 1 atm on the outer surfaceof the tubes. The convection coefficient of the satu-rated steam is 10,000 W/m2?K.(a) Determine the water outlet temperature.(b) With all other conditions remaining the same, butaccounting for changes in the overall heat transfercoefficient, plot the water outlet temperature as afunction of the water flow rate for 5?c?20 kg/s.(c) On the plot of part (b), generate two additionalcurves for the water outlet temperature as a func-tion of flow rate for fouling factors of and 0.0005 m2?K/W.

Saturated steam at 110?C is condensed in a shell-and-tube heat exchanger (1 shell pass; 2, 4,...tubepasses) with a UAvalue of 2.5 kW/K. Cooling waterenters at 40?C.(a) Calculate the cooling water flow rate required tomaintain a heat rate of 150 kW.(b) Assuming that UAis independent of flow rate, cal-culate and plot the water flow rate required to pro-vide heat rates over the range from 130 to 160 kW.Comment on the validity of your assumption.

A shell-and-tube heat exchanger (1 shell pass, 2 tubepasses) is to be used to condense 2.73 kg/s of saturatedsteam at 340 K. Condensation occurs on the outer tubesurfaces, and the corresponding convection coefficientis 10,000 W/m2?K. The temperature of the coolingwater entering the tubes is 15?C, and the exit tempera-ture is not to exceed 30?C. Thin-walled tubes of 19-mmdiameter are specified, and the mean velocity of waterflow through the tubes is to be maintained at 0.5 m/s.(a) What is the minimum number of tubes that shouldbe used, and what is the corresponding tube lengthper pass?R?f?0.0002m m c?30kg/s(b) To reduce the size of the heat exchanger, it is pro-posed to increase the water-side convection coeffi-cient by inserting a wire mesh in the tubes. If themesh increases the convection coefficient by afactor of two, what is the required tube length perpass?

Saturated water vapor leaves a steam turbine at a flowrate of 1.5 kg/s and a pressure of 0.51 bar. The vapor isto be completely condensed to saturated liquid in ashell-and-tube heat exchanger that uses city water asthe cold fluid. The water enters the thin-walled tubesat 17?C and is to leave at 57?C. Assuming an overallheat transfer coefficient of 2000 W/m2?K, determinethe required heat exchanger surface area and the waterflow rate. After extended operation, fouling causes the overall heat transfer coefficient to decrease to1000 W/m2?K, and to completely condense the vapor,there must be an attendant reduction in the vapor flowrate. For the same water inlet temperature and flowrate, what is the new vapor flow rate required for com-plete condensation?

A two-fluid heat exchanger has inlet and outlet tem-peratures of 65 and 40?C for the hot fluid and 15 and30?C for the cold fluid. Can you tell whether thisexchanger is operating under counterflow or parallel-flow conditions? Determine the effectiveness of theheat exchanger.

The human brain is especially sensitive to elevatedtemperatures. The cool blood in the veins leaving theface and neck and returning to the heart may contributeto thermal regulation of the brain by cooling the arte-rial blood flowing to the brain. Consider a vein andartery running between the chest and the base of theskull for a distance L?250 mm, with mass flow ratesof 310?3kg/s in opposite directions in the two ves-sels. The vessels are of diameter D?5 mm and areseparated by a distance w?7 mm. The thermal con-ductivity of the surrounding tissue is kt?0.5 W/m?K.If the arterial blood enters at 37?C and the venousblood enters at 27?C, at what temperature will the arte-rial blood exit? If the arterial blood becomes over-heated, and the body responds by halving the bloodflow rate, how much hotter can the entering arterialblood be and still maintain its exit temperature below37?C? Hint:If we assume that all the heat leaving the artery enters the vein, then heat transfer between thetwo vessels can be modeled using a relationship foundin Table 4.1. Approximate the blood properties asthose of water.

Consider a very long,concentric tube heat exchangerhaving hot and cold water inlet temperatures of 85 and15?C. The flow rate of the hot water is twice that of the cold water. Assuming equivalent hot and cold waterspecific heats, determine the hot water outlet tempera-ture for the following modes of operation: (a) counter-flow and (b) parallel flow.

A plate-fin heat exchanger is used to condense a satu-rated refrigerant vapor in an air-conditioning system.The vapor has a saturation temperature of 45?C, and acondensation rate of 0.015 kg/s is dictated by systemperformance requirements. The frontal area of thecondenser is fixed at Afr?0.25 m2by installationrequirements, and a value of hfg?135 kJ/kg may beassumed for the refrigerant.(a) The condenser design is to be based on a nominalair inlet temperature of Tc,i?30?C and nominal airinlet velocity of V?2 m/s for which the manufac-turer of the heat exchanger core indicates an over-all coefficient of U?50 W/m2?K. What is thecorresponding value of the heat transfer surfacearea required to achieve the prescribed condensa-tion rate? What is the air outlet temperature?(b) From the manufacturer of the heat exchangercore, it is also known that U?V0.7. During daily operation the air inlet temperature is notcontrollable and may vary from 27 to 38?C. If the heat exchanger area is fixed by the result ofpart (a), what is the range of air velocities neededto maintain the prescribed condensation rate? Plot the velocity as a function of the air inlet temperature.

A shell-and-tube heat exchanger is to heat 10,000 kg/hof water from 16 to 84?C by hot engine oil flowingthrough the shell. The oil makes a single shell pass,entering at 160?C and leaving at 94?C, with an averageheat transfer coefficient of 400 W/m2?K. The waterflows through 11 brass tubes of 22.9-mm inside diam-eter and 25.4-mm outside diameter, with each tubemaking four passes through the shell.(a) Assuming fully developed flow for the water,determine the required tube length per pass.VaporTc,oV, Tc,iAtmospheric airFrontal area, AfrRefrigerantmh,Tsat(b) For the tube length found in part (a), plot the effec-tiveness, fluid outlet temperatures, and water-sideconvection coefficient as a function of the waterflow rate for 5000?c?15,000 kg/h, with allother conditions remaining the same.

In a supercomputer, signal propagation delays arereduced by resorting to high-density circuit arrange-ments which are cooled by immersing them in a specialdielectric liquid. The fluid is pumped in a closed loopthrough the computer and an adjoining shell-and-tubeheat exchanger having one shell and two tube passes.During normal operation, heat generated within the com-puter is transferred to the dielectric fluid passing throughthe computer at a flow rate of . In turn, thefluid passes through the tubes of the heat exchanger and the heat is transferred to water passing over the tubes. Thedielectric fluid may be assumed to have constant proper-ties of cp?1040 J/kg?K, ??7.6510?4kg/s?m,k?0.058 W/m?K, and Pr?14. During normal opera-tion, chilled water at a flow rate of w?2.5 kg/s and aninlet temperature of Tw,i?5?C passes over the tubes. Thewater has a specific heat of 4200 J/kg?K and provides anaverage convection coefficient of 10,000 W/m2?K overthe outer surface of the tubes.(a) If the heat exchanger consists of 72 thin-walledtubes, each of 10-mm diameter, and fully devel-oped flow is assumed to exist within the tubes,what is the convection coefficient associated withflow through the tubes?(b) If the dielectric fluid enters the heat exchanger atTf,i?25?C and is to leave at Tf,o?15?C, what isthe required tube length per pass?(c) For the exchanger with the tube length per passdetermined in part (b), plot the outlet temperatureof the dielectric fluid as a function of its flow ratefor 4??6 kg/s. Account for correspondingchanges in the overall heat transfer coefficient, butassume all other conditions to remain the same.(d) The site specialist for the computer facilities isconcerned about changes in the performance of the water chiller supplying the cold water ( ,Tw,i) and their effect on the outlet temperature Tf,oof the dielectric fluid. With all other conditionsremaining the same, determine the effect ofa?10% change in the cold water flow rate on Tf,o.(e) Repeat the performance analysis of part (d) todetermine the effect of a?3?C change in thewater inlet temperature on Tf,o, with all other con-ditions remaining the same.

Untapped geothermal sites in the United States havethe estimated potential to deliver 100,000 MW (elec-tric) of new, clean energy. The key component in ageothermal power plant is a heat exchanger that trans-fers thermal energy from hot, geothermal brine to asecond fluid that is evaporated in the heat exchanger.The cooled brine is reinjected into the geothermal wellafter it exits the heat exchange, while the vapor exitingthe heat exchanger serves as the working fluid of aRankine cycle. Consider a geothermal power plantdesigned to deliver P?25 MW (electric) operating ata thermal efficiency of ??0.20. Pressurized hot brineat Th,i?200?C is sent to the tube side of a shell-and-tube heat exchanger, while the Rankine cycles work-ing fluid enters the shell side at Tc,i?45?C. The brineis reinjected into the well at Th,o?80?C.(a) Assuming the brine has the properties of water,determine the required brine flow rate, the requiredeffectiveness of the heat exchanger, and therequired heat transfer surface area. The overallheat transfer coefficient is U?4000 W/m2.(b) Over time, the brine fouls the heat transfer sur- faces, resulting in U?2000 W/m2. For the oper-ating conditions of part (a), determine the electricpower generated by the geothermal plant underfouled heat exchanger conditions.

An energy storage system is proposed to absorb ther-mal energy collected during the day with a solar col-lector and release thermal energy at night to heat abuilding. The key component of the system is a shell-and-tube heat exchanger with the shell side filled withn-octadecane (see Problem 8.47).(a) Warm water from the solar collector is delivered tothe heat exchanger at Th,i?40?C and ?2 kg/sthrough the tube bundle consisting of 50 tubes, two tube passes, and a tube length per pass ofLt?2 m. The thin-walled, metal tubes are of diam-eter D?25 mm. Free convection exists within themolten n- octadecane, providing an average heattransfer coefficient of ho?25 W/m2?K on the out-side of each tube. Determine the volume of n-octadecane that is melted over a 12-h period. If them m wtotal volume of n-octadecane is to be 50% greaterthan the volume melted over 12 h, determine thediameter of the Ls?2.2-m-long shell.(b) At night, water at Tc,i?15?C is supplied to theheat exchanger, increasing the water temperatureand solidifying the n-octadecane. Do you expectthe heat transfer rate to be the same, greater than,or less than the heat transfer rate in part (a)?Explain your reasoning.

A shell-and-tube heat exchanger consists of 135 thin-walled tubes in a double-pass arrangement, each of12.5-mm diameter with a total surface area of 47.5 m2.Water (the tube-side fluid) enters the heat exchanger at15?C and 6.5 kg/s and is heated by exhaust gas enteringat 200?C and 5 kg/s. The gas may be assumed to havethe properties of atmospheric air, and the overall heattransfer coefficient is approximately 200 W/m2?K.(a) What are the gas and water outlet temperatures?(b) Assuming fully developed flow, what is the tube-side convection coefficient?(c) With all other conditions remaining the same, plotthe effectiveness and fluid outlet temperatures as afunction of the water flow rate over the range from6 to 12 kg/s.(d) What gas inlet temperature is required for theexchanger to supply 10 kg/s of hot water at an out-let temperature of 42?C, all other conditionsremaining the same? What is the effectiveness forthis operating condition?

An ocean thermal energy conversion system is beingproposed for electric power generation. Such a systemis based on the standard power cycle for which theworking fluid is evaporated, passed through a turbine,and subsequently condensed. The system is to be usedin very special locations for which the oceanic watertemperature near the surface is approximately 300 K,while the temperature at reasonable depths is approxi-mately 280 K. The warmer water is used as a heatsource to evaporate the working fluid, while the colderwater is used as a heat sink for condensation of thefluid. Consider a power plant that is to generate 2 MWof electricity at an efficiency (electric power output perheat input) of 3%. The evaporator is a heat exchangerconsisting of a single shell with many tubes executingtwo passes. If the working fluid is evaporated at itsphase change temperature of 290 K, with ocean waterentering at 300 K and leaving at 292 K, what is the heatexchanger area required for the evaporator? What flowrate must be maintained for the water passing throughthe evaporator? The overall heat transfer coefficientmay be approximated as 1200 W/m

A single-pass, cross-flow heat exchanger with both flu-ids unmixed is being used to heat water (m.c?2 kg /s,cp?4200 J/kg?K) from 20?C to 100?C with hotexhaust gases (cp?1200 J/kg?K) entering at 320?C.What mass flow rate of exhaust gases is required?Assume that UAis equal to its design value of4700 W/K, independent of the gas mass flow rate.

Saturated process steam at 1 atm is condensed in ashell-and-tube heat exchanger (one shell, two tubepasses). Cooling water enters the tubes at 15?C with anaverage velocity of 3.5 m/s. The tubes are thin walledand made of copper with a diameter of 14 mm andlength of 0.5 m. The convective heat transfer coeffi-cient for condensation on the outer surface of the tubesis 21,800 W/m2?K.(a) Find the number of tubes/pass required to con-dense 2.3 kg/s of steam.(b) Find the outlet water temperature.(c) Find the maximum possible condensation rate thatcould be achieved with this heat exchanger usingthe same water flow rate and inlet temperature.(d) Using the heat transfer surface area found in part(a), plot the water outlet temperature and steamcondensation rate for water mean velocities in therange from 1 to 5 m/s. Assume that the shell-sideconvection coefficient remains unchanged.

The chief engineer at a university that is constructing alarge number of new student dormitories decides toinstall a counterflow concentric tube heat exchangeron each of the dormitory shower drains. The thin-walled copper drains are of diameter Di?50 mm.Wastewater from the shower enters the heat exchangerat Th,i?38?C while fresh water enters the dormitory atTc,i?10?C. The wastewater flows down the verticalwall of the drain in a thin, falling fil, providinghh?10,000 W/m2?K.Falling filmCopper tubeWarm fresh waterCold fresh waterAnnulusCool waste waterHot waste waterLdDTh,iTc,i, mcmh(a) If the annular gap is d?10 mm, the heatexchanger length is L?1 m, and the water flowrate is , determine the heat transferrate and the outlet temperature of the warmedfresh water.(b) If a helical spring is installed in the annular gap sothe fresh water is forced to follow a spiral pathfrom the inlet to the fresh water outlet, resulting inhc?9050 W/m2?K, determine the heat transferrate and the outlet temperature of the fresh water.(c) Based on the result for part (b), calculate the dailysavings if 15,000 students each take a 10-minuteshower per day and the cost of water heating is$0.07/kW?h.

A shell-and-tube heat exchanger with one shell passand 20 tube passes uses hot water on the tube side toheat oil on the shell side. The single copper tube hasinner and outer diameters of 20 and 24 mm and alength per pass of 3 m. The water enters at 87?C and0.2 kg/s and leaves at 27?C. Inlet and outlet tempera-tures of the oil are 7 and 37?C. What is the averageconvection coefficient for the tube outer surface?

The oil in an engine is cooled by air in a cross-flowheat exchanger where both fluids are unmixed. Atmos-pheric air enters at 30?C and 0.53 kg/s. Oil at0.026 kg/s enters at 75?C and flows through a tube of10-mm diameter. Assuming fully developed flow andconstant wall heat flux, estimate the oil-side heattransfer coefficient. If the overall convection coeffi-cient is 53 W/m2?K and the total heat transfer area is1m2, determine the effectiveness. What is the exittemperature of the oil?

A recuperator is a heat exchanger that heats the airused in a combustion process by extracting energyfrom the products of combustion (the flue gas). Con-sider using a single-pass, cross-flow heat exchanger asa recuperator.Eighty (80) silicon carbide ceramic tubes (k?20W/m?K) of inner and outer diameters equal to 55 and 80 mm, respectively, and of length L?1.4 m arearranged as an aligned tube bank of longitudinal andtransverse pitches SL?100 mm and ST?120 mm,respectively. Cold air is in cross flow over the tubebank with upstream conditions of V?1 m/s andTc,i?300 K, while hot flue gases of inlet temperatureTh,i?1400 K pass through the tubes. The tube outersurface is clean, while the inner surface is character-ized by a fouling factor of R?f?210?4m2?K/W.The air and flue gas flow rates are c?1.0 kg/s and, respectively. As first approximations,(1) evaluate all required air properties at 1 atm and300 K, (2) assume the flue gas to have the propertiesof air at 1 atm and 1400 K, and (3) assume the tubewall temperature to be at 800 K for the purpose oftreating the effect of variable properties on convectionheat transfer.(a) If there is a 1% fuel savings associated with each10?C increase in the temperature of the combus-tion air (Tc,o) above 300 K, what is the percentagefuel savings for the prescribed conditions?(b) The performance of the recuperator is stronglyinfluenced by the product of the overall heat trans-fer coefficient and the total surface area, UA. Com-pute and plot Tc,oand the percentage fuel savingsas a function of UAfor 300?UA?600 W/K.Without changing the flow rates, what measuresmay be taken to increase UA?

Consider operation of the furnacerecuperator combi-nation of Problem 11.60 under conditions for whichchemical energy is converted to thermal energy in thecombustor at a rate of qcomb?2.0106W and energyis transferred from the combustion gases to the load inthe furnace at a rate of qload?1.4106W. Assumingequivalent flow rates (m.c?m.h?1.0 kg/s) and specificheats (cp,c?cp,h?1200 J/kg?K) for the cold air andflue gases in the recuperator, determine Th,i, Th,o, andTc,owhen Tc,i?300 K and the recuperator has aneffectiveness of ??0.30. What value of the effective-ness would be needed to achieve a combustor air inlettemperature of 800 K?

It is proposed that the exhaust gas from a naturalgaspowered electric generation plant be used togenerate steam in a shell-and-tube heat exchangerwith one shell and one tube pass. The steel tubeshave a thermal conductivity of 40 W/m?K, an innerdiameter of 50 mm, and a wall thickness of 4 mm.The exhaust gas, whose flow rate is 2 kg/s, enters theheat exchanger at 400?C and must leave at 215?C. Tolimit the pressure drop within the tubes, the tube gasvelocity should not exceed 25 m/s. If saturated waterat 11.7 bar is supplied to the shell side of theexchanger, determine the required number of tubesm h?1.05kg/sm and their length. Assume that the properties of theexhaust gas can be approximated as those of atmos-pheric air and that the water-side thermal resistanceis negligible. However, account for fouling on thegas side of the tubes and use a fouling resistance of0.0015 m2?K/W.

A recuperator is a heat exchanger that heats air used ina combustion process by extracting energy from theproducts of combustion. It can be used to increase the efficiency of a gas turbine by increasing the tem-perature of air entering the combustor.Consider a system for which the recuperator is a cross-flow heat exchanger with both fluids unmixed and the flow rates associated with the turbine exhaust and theair are m.h?6.5 kg/s and m.c?6.2 kg/s, respectively.The corresponding value of the overall heat transfercoefficient is U?100 W/m2?K.(a) If the gas and air inlet temperatures areTh,i?700 K and Tc,i?300 K, respectively, whatheat transfer surface area is needed to provide an air outlet temperature of Tc,o?500 K? Boththe air and the products of combustion may beassumed to have a specific heat of 1040 J/kg?K.(b) For the prescribed conditions, compute and plotthe air outlet temperature as a function of the heattransfer surface area.

A concentric tube heat exchanger uses water, which isavailable at 15?C, to cool ethylene glycol from 100 to60?C. The water and glycol flow rates are each 0.5 kg/s.What are the maximum possible heat transfer rate andeffectiveness of the exchanger? Which is preferred, aparallel-flow or counterflow mode of operation?

Water is used for both fluids (unmixed) flowingthrough a single-pass, cross-flow heat exchanger. Thehot water enters at 90?C and 10,000 kg/h, while thecold water enters at 10?C and 20,000 kg/h. If the effec-tiveness of the exchanger is 60%, determine the coldwater exit temperature.

A cross-flow heat exchanger consists of a bundle of 32 tubes in a 0.6-m2duct. Hot water at 150?C and amean velocity of 0.5 m/s enters the tubes having inner and outer diameters of 10.2 and 12.5 mm. Atmosphericair at 10?C enters the exchanger with a volumetric flowrate of 1.0 m3/s. The convection heat transfer coefficienton the tube outer surfaces is 400 W/m2?K. Estimate thefluid outlet temperatures.

Exhaust gas from a furnace is used to preheat the com-bustion air supplied to the furnace burners. The gas,which has a flow rate of 15 kg/s and an inlet temperatureof 1100 K, passes through a bundle of tubes, while theair, which has a flow rate of 10 kg/s and an inlet tem-perature of 300 K, is in cross flow over the tubes. Thetubes are unfinned, and the overall heat transfer coeffi-cient is 100 W/m2?K. Determine the total tube surfacearea required to achieve an air outlet temperature of850 K. The exhaust gas and the air may each beassumed to have a specific heat of 1075 J/kg?K.

Derive Equation 11.35a. Hint: See Section 8.3.3.

A liquefied natural gas (LNG) regasification facilityutilizes a vertical heat exchanger or vaporizer that con-sists of a shell with a single-pass tube bundle used toconvert the fuel to its vapor form for subsequent deliv-ery through a land-based pipeline. Pressurized LNG isoff-loaded from an oceangoing tanker to the bottom ofthe vaporizer at Tc,i??155?C and ?150 kg/sand flows through the shell. The pressurized LNG hasa vaporization temperature of Tf??75?C and specificheat cp,l?4200 J/kg?K. The specific heat of the vapor-ized natural gas is cp,v?2210 J/kg?K while the gas has a latent heat of vaporization of hfg?575 kJ/kg.The LNG is heated with seawater flowing through the tubes, also introduced at the bottom of the vapor-izer, that is available at Th,i?20?C with a specific heatof cp,SW?3985 J/kg?K. If the gas is to leave the vapor-izer at Tc,o?8?C and the seawater is to exit the device atTh,o?10?C, determine the required vaporizer heat trans-fer area. Hint: Divide the vaporizer into three sections,as shown in the schematic, with UA?150 W/m2?K,UB?260 W/m2?K, and UC?40 W/m2?K.

Work Problem 11.69 for the situation where the sea-water is introduced to the top of the vaporizer, result-ing in counterflowing natural gas and seawater.

Cooling of outdoor electronic equipment such as intelecommunications towers is difficult due to seasonaland diurnal variations of the air temperature, and poten-tial fouling of heat exchange surfaces due to dust accu-mulation or insect nesting. A concept to provide a nearlyconstant sink temperature in a hermetically sealed envi-ronment is shown below. The cool surface is maintainedat nearly constant groundwater temperature (T1?5?C)while the hot surface is subjected to a constant heat loadfrom the electronic equipment (q2?50 W, T2). Con-necting the surfaces is a concentric tube of lengthL?10 m with Di?100 mm and Do?150 mm. A fanmoves air at a mass flow rate of m.?0.0325 kg/s anddissipates P?10 W of thermal energy. Heat transfer tothe cool surface is described by q?1?h1(Th,o?T1) whileheat transfer from the hot surface is described byq?2?h2(T2?Tf,o) where Tf,ois the fan outlet tempera-ture. The values of h1and h2are 40 and 60 W/m2?K,respectively. To isolate the electronics from ambienttemperature variations, the entire device is insulated atits outer surfaces. The design engineer is concerned thatconduction through the wall of the inner tube mayadversely affect the device performance. Determine thevalue of T2for the limiting cases of (i) no conductionresistance in the inner tube wall and (ii) infinite conduc-tion resistance in the inner tube wall. Does the proposeddevice maintain maximum temperatures below 80C ? ?

A shell-and-tube heat exchanger consisting of oneshell pass and two tube passes is used to transfer heatfrom an ethylene glycolwater solution (shell side) supplied from a rooftop solar collector to pure water(tube side) used for household purposes. The tubes areof inner and outer diameters Di?3.6 mm andDo?3.8 mm, respectively. Each of the 100 tubes is0.8 m long (0.4 m per pass), and the heat transfer coef-ficient associated with the ethylene glycolwater mix-ture is ho?11,000 W/m2?K.(a) For pure copper tubes, calculate the heat transferrate from the ethylene glycolwater solution(m.?2.5 kg/s, Th,i?80?C) to the pure water (m.?2.5 kg/s, Tc,i?20?C). Determine the outlet tem-peratures of both streams of fluid. The density andspecific heat of the ethylene glycolwater mixtureare 1040 kg/m3and 3660 J/kg?K, respectively.(b) It is proposed to replace the copper tube bundlewith a bundle composed of high-temperaturenylon tubes of the same diameter and tube wallthickness. The nylon is characterized by a thermalconductivity of kn?0.31 W/m?K. Determine thetube length required to transfer the same amountof energy as in part (a).

In analyzing thermodynamic cycles involving heatexchangers, it is useful to express the heat rate interms of an overall thermal resistance Rtand the inlettemperatures of the hot and cold fluids,The heat transfer rate can also be expressed in terms ofthe rate equations,(a) Derive a relation for Rlm/Rtfor a parallel-floheatexchanger in terms of a single dimensionless para-meter B, which does not involve any fluid temper-atures but only U, A, Ch, Cc(or Cmin, Cmax).(b) Calculate and plot Rlm/Rtfor values of B?0.1,1.0, and 5.0. What conclusions can be drawn fromthe plot?

The power needed to overcome wind and friction dragassociated with an automobile traveling at a constantvelocity of 25 m/s is 9 kW.(a) Determine the required heat transfer area of theradiator if the vehicle is equipped with an internalcombustion engine operating at an efficiency of21%. (Assume 79% of the energy generated bythe engine is in the form of waste heat removed by the radiator.) The inlet and outlet mean temper-atures of the water with respect to the radiator areq?UATlm?1RlmTlmq?(Th,i?Tc,i)RtTm,i?400 K and Tm,o?330 K, respectively. Cool-ing air is available at 3 kg/s and 300 K. The radia-tor may be analyzed as a cross-flow heat exchangerwith both fluids unmixed with an overall heattransfer coefficient of 400 W/m2?K.(b) Determine the required water mass flow rate andheat transfer area of the radiator if the vehicle isequipped with a fuel cell operating at 50% effi-ciency. The fuel cell operating temperature islimited to approximately 85?C, so the inlet andoutlet mean temperatures of the water with respectto the radiator are Tm,i?355 K and Tm,o?330 K,respectively. The air inlet temperature is as in part(a). Assume the flow rate of air is proportional tothe surface area of the radiator. Hint:Iteration isrequired.(c) Determine the required heat transfer area of the radi-ator and the outlet mean temperature of the waterfor the fuel cellequipped vehicle if the mass flowrate of the water is the same as in part (a).

An air conditioner operating between indoor and out-door temperatures of 23 and 43?C, respectively,removes 5 kW from a building. The air conditionercan be modeled as a reversed Carnot heat engine withrefrigerant as the working fluid. The efficiency of themotor for the compressor and fan is 80%, and 0.2 kWis required to operate the fan.(a) Assuming negligible thermal resistances (Problem11.73) between the refrigerant in the condenserand the outside air and between the refrigerant inthe evaporator and the inside air, calculate thepower required by the motor.(b) If the thermal resistances between the refrigerantand the air in the evaporator and condenser sectionsare the same, 310?3K/W, determine the temp-erature required by the refrigerant in each section.Calculate the power required by the motor.

In a Rankine power system, 1.5 kg/s of steam leaves theturbine as saturated vapor at 0.51 bar. The steam is con-densed to saturated liquid by passing it over the tubes ofa shell-and-tube heat exchanger, while liquid water,having an inlet temperature of Tc,i?280 K, is passedthrough the tubes. The condenser contains 100 thin-walled tubes, each of 10-mm diameter, and the totalwater flow rate through the tubes is 15 kg/s. The aver-age convection coefficient associated with condensationon the outer surface of the tubes may be approximatedas ?5000 W/m2?K. Appropriate property values forthe liquid water are cp?4178 J/kg?K, ??70010?6kg/s?m, k?0.628 W/m?K, and Pr?4.6. (a) What is the water outlet temperature?(b) What is the required tube length (per tube)?(c) After extended use, deposits accumulating on theinner and outer tube surfaces provide a cumulativefouling factor of 0.0003 m2?K/W. For the prescribedinlet conditions and the computed tube length, whatmass fraction of the vapor is condensed?(d) For the tube length computed in part (b) and thefouling factor prescribed in part (c), explore theextent to which the water flow rate and inlet tem-perature may be varied (within physically plausibleranges) to improve the condenser performance.Represent your results graphically, and draw appro-priate conclusions.

Consider a Rankine cycle with saturated steam leavingthe boiler at a pressure of 2 MPa and a condenser pres-sure of 10 kPa.(a) Calculate the thermal efficiency of the ideal Rankinecycle for these operating conditions.(b) If the net reversible work for the cycle is 0.5 MW,calculate the required flow rate of cooling watersupplied to the condenser at 15?C with an allow-able temperature rise of 10?C.(c) Design a shell-and-tube heat exchanger (one-shell,multiple-tube passes) that will meet the heat rateand temperature conditions required of the con-denser. Your design should specify the number oftubes and their diameter and length.

Consider the Rankine cycle of Problem 11.77, whichrejects 2.3 MW to the condenser, which is suppliedwith a cooling water flow rate of 70 kg/s at 15?C.(a) Calculate UA, a parameter that is indicative of thesize of the condenser required for this operatingcondition.(b) Consider now the situation where the overall heattransfer coefficient for the condenser, U, isreduced by 10% because of fouling. Determinethe reduction in the thermal efficiency of thecycle caused by fouling, assuming that the cool-ing water flow rate and water temperature remainthe same and that the condenser is operated at thesame steam pressure.WaterSteamfromboilerTc,iTc,oSaturatedliquidto pumpCondenserTurbine

Consider a concentric tube heat exchanger character-ized by a uniform overall heat transfer coefficient andoperating under the following conditions:cpTiTo(kg/s)(J/kg?K) (C) (C)Cold fluid 0.125 4200 40 95Hot fluid 0.125 2100 210 What is the maximum possible heat transfer rate?What is the heat exchanger effectiveness? Should theheat exchanger be operated in parallel flow or in coun-terflow? What is the ratio of the required areas forthese two flow conditions?

The floor space of any facility that houses shell-and-tube heat exchangers must be sufficiently large so the tube bundle can be serviced easily. A rule of thumbis that the floor space must be at least 2.5 times thelength of the tube bundle so that the bundle can be com-pletely removed from the shell (hence the absolute min-imum floor space is twice the tube bundle length) andsubsequently cleaned, repaired, or replaced easily (asso-ciated with the extra half bundle length floor space).The room in which the heat exchanger of Problem11.22 is to be installed is 8 m long and, therefore, the4.7-m-long heat exchanger is too large for the facility.Will a shell-and-tube heat exchanger with two shells,one above the other, be sufficiently small to fit into thefacility? Each shell has 10 tubes and 8 tube passes.

Consider the influence of a finite sheet thickness inExample 11.2, when there are 40 gaps.(a) Determine the exterior dimension, L, of the heatexchanger core for a sheet thickness of t?0.8 mmfor pure aluminum (kal?237 W/m?K) and poly-vinylidene fluoride (PVDF, kpv?0.17 W/m?K)sheets. Neglect the thickness of the top and bottomexterior plates.(b) Plot the heat exchanger core dimension as a func- tion of the sheet thickness for aluminum andPVDF over the range 0t ? ?1 mm.

Hot exhaust gases are used in a shell-and-tubeexchanger to heat 2.5 kg/s of water from 35 to 85?C.The gases, assumed to have the properties of air, enter at 200?C and leave at 93?C. The overallheat transfer coefficient is 180 W/m2?K. Using the effectivenessNTU method, calculate the area of theheat exchanger.

In open heart surgery under hypothermic conditions,the patients blood is cooled before the surgery and rewarmed afterward. It is proposed that a concentrictube, counterflow heat exchanger of length 0.5 m beused for this purpose, with the thin-walled inner tubehaving a diameter of 55 mm. The specific heat of the blood is 3500 J/kg?K.(a) If water at Th,i?60?C and m.h?0.10 kg/s is usedto heat blood entering the exchanger at Tc,i?18?Cand m.c?0.05 kg/s, what is the temperature of theblood leaving the exchanger? The overall heattransfer coefficient is 500 W/m2?K.(b) The surgeon may wish to control the heat rate qand the outlet temperature Tc,oof the blood byaltering the flow rate and/or inlet temperature ofthe water during the rewarming process. To assistin the development of an appropriate controller for the prescribed values of m.cand Tc,i, computeand plot qand Tc,oas a function of m.hfor0.05?m.h?0.20 kg/s and values of Th,i?50, 60,and 70?C. Since the dominant influence on theoverall heat transfer coefficient is associated withthe blood flow conditions, the value of Umay beassumed to remain at 500 W/m2K ? . Should cer-tain operating conditions be excluded?

Ethylene glycol and water, at 60 and 10?C, respec-tively, enter a shell-and-tube heat exchanger for whichthe total heat transfer area is 15 m2. With ethylene gly-col and water flow rates of 2 and 5 kg/s, respectively,the overall heat transfer coefficient is 800 W/m2?K.(a) Determine the rate of heat transfer and the fluidoutlet temperatures.(b) Assuming all other conditions to remain the same,plot the effectiveness and fluid outlet temperaturesas a function of the flow rate of ethylene glycol for0.5?m.h?5 kg/s.

A boiler used to generate saturated steam is in the formof an unfinned, cross-flow heat exchanger, with waterflowing through the tubes and a high-temperature gas incross flow over the tubes. The gas, which has a specificheat of 1120 J/kg?K and a mass flow rate of 10 kg/s,enters the heat exchanger at 1400 K. The water, whichhas a flow rate of 3 kg/s, enters as saturated liquid at450 K and leaves as saturated vapor at the same temper-ature. If the overall heat transfer coefficient is50 W/m2?K and there are 500 tubes, each of 0.025-mdiameter, what is the required tube length?

Waste heat from the exhaust gas of an industrial fur-nace is recovered by mounting a bank of unfinnedtubes in the furnace stack. Pressurized water at a flowrate of 0.025 kg/s makes a single pass through eachofthe tubes, while the exhaust gas, which has anupstream velocity of 5.0 m/s, moves in cross flow overthe tubes at 2.25 kg/s. The tube bank consists of asquare array of 100 thin-walled tubes (1010), each25 mm in diameter and 4 m long. The tubes arealigned with a transverse pitch of 50 mm. The inlettemperatures of the water and the exhaust gas are 300and 800 K, respectively. The water flow is fully devel-oped, and the gas properties may be assumed to bethose of atmospheric air.(a) What is the overall heat transfer coefficient?(b) What are the fluid outlet temperatures?(c) Operation of the heat exchanger may vary accordingto the demand for hot water. For the prescribed heatexchanger design and inlet conditions, compute andplot the rate of heat recovery and the fluid outlettemperatures as a function of water flow rate pertube for 0.02?m.c,1?0.20 kg/s.

A heat exchanger consists of a bank of 1200 thin-walled tubes with air in cross flow over the tubes. Thetubes are arranged in-line, with 40 longitudinal rows(along the direction of airflow) and 30 transverserows. The tubes are 0.07 m in diameter and 2 m long,with transverse and longitudinal pitches of 0.14 m.The hot fluid flowing through the tubes consists of sat-urated steam condensing at 400 K. The convectioncoefficient of the condensing steam is much largerthan that of the air.(a) If air enters the heat exchanger at m.c?12 kg/s,300 K, and 1 atm, what is its outlet temperature?(b) The condensation rate may be controlled by varyingthe airflow rate. Compute and plot the air outlet tem- perature, the heat rate, and the condensation rate as afunction of flow rate for 10?.

Derive the expression for the modified effectiveness?*, given in Comment 4 of Example 11.8.

Consider Problem 3.144a.(a) Using an appropriate correlation from Chapter 8,determine the air inlet velocity for each channel inthe heat sink. Assume laminar flow and evaluateair properties at T?300 K.(b) Accounting for the increase in air temperature asit flows through the heat sink, determine the chippower qcand the outlet temperature of the air exit-ing each channel. Assume the airflow along theouter surfaces provides a similar cooling effect asairflow in the channels.

Work Problem 7.29, taking into account the increasein temperature of the water as it flows through the heatsink. Properties of water are listed in Problem 7.29,along with ??995 kg/m3and cp?4178 J/kg?K. Hint:Assume the water does not escape through the uppersurface of the heat sink and that the boundary layerson each fin surface do not merge, allowing evaluationof the heat transfer coefficient using a correlation fromChapter 7. Also, see Problem 11.68.

The heat sink of Problem 7.29 is considered for an appli-cation in which the power dissipation is only 70 W, andthe engineer proposes to use air at T??20?C for cool-ing. Taking into account the increase in temperature ofthe air as it flows through the heat sink, plot the allow-able power dissipation and the air exit temperature as a function of the air velocity over the range1 m/s?u??5 m/s, with the constraint that the basetemperature not exceed Tb?70?C. Properties of theair may be approximated as k?0.027 W/m?K,??16.410?6m2/s, Pr?0.706, ??1.145 kg/m3,and cp?1007 J/kg?K. Hint: Assume the air does notescape through the upper surface of the heat sink, usea correlation for internal flow, and see Problem 11.68.

Solve Problem 8.109a using the effectiveness-NTUmethod.

Consider Problem 7.113. Estimate the heat transferrate to the air, accounting for both the increase in theair temperature as it flows through the foam and the thermal resistance associated with conduction in thefoam in the x-direction. Do you expect the actual heattransfer rate to the air to be equal to, less than, orgreater than the value you have calculated?

The metallic foam of Problem 7.113 is brazed to thesurface of a silicon chip of width W?25 mm on aside. The foam heat sink is L?10 mm tall. Air atTi?27?C, V?5 m/s impinges on the foam heat sinkwhile the chip surface is maintained at 70?C. Deter-mine the heat transfer rate from the chip. To calculatea conservative estimate of the heat transfer rate,neglect convection and radiation from the top andsides of the heat sink.