The role of surface tension in bubble formation can

Show that, for water at 1-atm pressure with Ts?Tsat?10?C, the Jakob number is much less than unity. Whatis the physical significance of this result? Verify thatthis conclusion applies to other fluids.

The surface of a horizontal, 7-mm-diameter cylinder ismaintained at an excess temperature of 5?C in saturatedwater at 1 atm. Estimate the heat flux using an appro-priate free convection correlation and compare yourresult to the boiling curve of Figure 10.4. Repeat thecalculation for a horizontal, 7-?m- diameter wire at the same excess temperature. What can you say about thegeneral applicability of Figure 10.4 to all situationsinvolving boiling of water at 1 atm?

The role of surface tension in bubble formation can bedemonstrated by considering a spherical bubble of puresaturated vapor in mechanicaland thermalequilibriumwith its superheated liquid.(a) Beginning with an appropriate free-body diagramof the bubble, perform a force balance to obtain anexpression of the bubble radius,where psatis the pressure of the saturated vapor andplis the pressure of the superheated liquid outsidethe bubble.(b) On a pvdiagram, represent the bubble and liquidstates. Discuss what changes in these conditionswill cause the bubble to grow or collapse.(c) Calculate the bubble size under equilibrium condi-tions for which the vapor is saturated at 101?C andthe liquid pressure corresponds to a saturation tem-perature of 100C ? .

Estimate the heat transfer coefficient, h, associated with Points A, B, C, D, and Ein Figure 10.4. Which point isassociated with the largest value of h? Which point cor-responds to the smallest value of h? Determine thethickness of the vapor blanket at the Leidenfrost point,neglecting radiation heat transfer through the blanket.Assume the solid is a flat surface.

A long, 1-mm-diameter wire passes an electrical currentdissipating 3150 W/m and reaches a surface temperatureof 126?C when submerged in water at 1 atm. What is theboiling heat transfer coefficient? Estimate the value ofthe correlation coefficient Cs,f

Estimate the nucleate pool boiling heat transfercoefficient for water boiling at atmospheric pressureon the outer surface of a platinum-plated 10-mm-diameter tube maintained 10C above the saturation temperature.

Plot the nucleate boiling heat flux for saturated water atatmospheric pressure on a large, horizontal polishedcopper plate, over the excess temperature range 5?C??Te?30?C. Compare your results with Figure 10.4.Also find the excess temperature corresponding to thecritical heat flux.

A simple expression to account for the effect of pres-sure on the nucleate boiling convection coefficient inwater (W/m2?K) iswhere pand paare the system pressure and standardatmospheric pressure, respectively. For a horizontal plate and the range 15q?s235 kW/m2, C?5.56and n?3. Units of ?Teare kelvins. Compare pre-dictions from this expression with the Rohsenow cor-relation (Cs,f?0.013, n?1) for pressures of 2 and 5 bars with?Te?10?C.

In Example 10.1 we considered conditions for whichvigorous boiling occurs in a pan of water, and wedetermined the electric power (heat rate) required tomaintain a prescribed temperature for the bottom ofthe pan. However, the electric power is, in fact, thecontrol (independent) variable, from which the tem-perature of the pan follows.(a) For nucleate boiling in the copper pan of Exam-ple 10.1, compute and plot the temperature ofthe pan as a function of the heat rate for 1?q?100 kW.(b) If the water is initially at room temperature, itmust, of course, be heated for a period of timebefore it will boil. Consider conditions shortlyafter heating is initiated and the water is at 20?C.Estimate the temperature of the pan bottom for aheat rate of 8 kW

Calculate the critical heat flux on a large horizontal sur-face for the following fluids at 1 atm: mercury, ethanol,and refrigerant R-134a. Compare these results to thecritical heat flux for water at 1 atm.

Water at atmospheric pressure boils on the surface of alarge horizontal copper tube. The heat flux is 90% ofthe critical value. The tube surface is initially scored;however, over time the effects of scoring diminish andthe boiling eventually exhibits behavior similar to thatassociated with a polished surface. Determine the tubesurface temperature immediately after installation andafter prolonged service.

The bottom of a copper pan, 150 mm in diameter, ismaintained at 115C by the heating element of an electric range. Estimate the power required to boil thewater in this pan. Determine the evaporation rate.What is the ratio of the surface heat flux to the criticalheat flux? What pan temperature is required to achievethe critical heat flux?

A nickel-coated heater element with a thickness of15 mm and a thermal conductivity of 50 W/m?K isexposed to saturated water at atmospheric pressure. Athermocouple is attached to the back surface, which iswell insulated. Measurements at a particular operatingcondition yield an electrical power dissipation in theheater element of 6.950?107W/m3and a tempera-ture of To?266.4?C (a) From the foregoing data, calculate the surface tem-perature, Ts, and the heat flux at the exposed surface.(b) Using the surface heat flux determined in part (a),estimate the surface temperature by applying anappropriate boiling correlation

Advances in very large scale integration (VLSI) of elec-tronic devices on a chip are often restricted by the abil-ity to cool the chip. For mainframe computers, an arrayof several hundred chips, each of area 25 mm2, may bemounted on a ceramic substrate. A method of coolingthe array is by immersion in a low boiling point fluidsuch as refrigerant R-134a. At 1 atm and 247 K, proper-ties of the saturated liquid are ??1.46?10?4N?s/m2,cp?1551 J/kg?K, and Pr?3.2. Assume values ofCs,f?0.004 and n?1.7.(a) Estimate the power dissipated by a single chip if itis operating at 50% of the critical heat flux. Whatis the corresponding value of the chip temperature?(b) Compute and plot the chip temperature as a functionof surface heat flux for 0.25?q?s/q?max? .90.

Saturated ethylene glycol at 1 atm is heated by a hori-zontal chromium-plated surface which has a diameter of200 mm and is maintained at 480 K. Estimate the heat-ing power requirement and the rate of evaporation. Whatfraction is the power requirement of the maximumpower associated with the critical heat flux? At 470 K,properties of the saturated liquid are ??0.38?10?3N?s/m2, cp?3280 J/kg?K, and Pr?8.7. The saturatedvapor density is ??1.66 kg/m3. Assume nucleate boil-ing constants of Cs,f?0.01 and n?1.0.

Copper tubes 25 mm in diameter and 0.75 m long areused to boil saturated water at 1 atm.(a) If the tubes are operated at 75% of the critical heatflux, how many tubes are needed to provide avapor production rate of 750 kg/h? What is thecorresponding tube surface temperature?(b) Compute and plot the tube surface temperature asa function of heat flux for 0.25?q?s/q?max0.90.On the same graph, plot the corresponding num-ber of tubes needed to provide the prescribedvapor production rate.

Consider a gas-fired boiler in which five coiled, thin-walled, copper tubes of 25-mm diameter and 8- mlength are submerged in pressurized water at 4.37 bars.The walls of the tubes are scored and may be assumedto be isothermal. Combustion gases enter each of thetubes at a temperature of Tm,i?700?C and a flow rateof , respectively.(a) Determine the tube wall temperature Tsand the gasoutlet temperature Tm,ofor the prescribed conditions.As a first approximation, the properties of the com- bustion gases may be taken as those of air at 700 K.(b) Over time the effects of scoring diminish, leadingto behavior similar to that of a polished coppersurface. Determine the wall temperature and gasoutlet temperature for the aged condition

Estimate the current at which a 1-mm-diameter nickelwire will burn out when submerged in water at atmos-pheric pressure. The electrical resistance of the wire is0.129 ?/m

Estimate the power (W/m2) required to maintain abrass plate at ?Te?15?C while boiling saturatedwater at 1 atm. What is the power requirement if thewater is pressurized to 10 atm? At what fraction of thecritical heat flux is the plate operating

A dielectric fluid at atmospheric pressure is heated witha 0.5-mm-diameter, horizontal platinum wire. Determinethe temperature of the wire when the wire is heated at 50%of the critical heat flux. The properties of the fluid arecp,l?1300 J/kg?K, hfg?142 kJ/kg, kl?0.075 W/m?K,?l?0.32?10?6m2/s, ?l?1400 kg/m3, ?v?7.2 kg/m3,??12.4?10?3N/m, Tsat?34?C. Assume the nucleateboiling constants are Cs,f?0.005 and n?1.7. For smallhorizontal cylinders, the critical heat flux is found by mul-tiplying the value associated with large horizontal cylin-ders by a correction factor F, where F?0.892.27exp(?3.44Co?1/2). The Confinement number is based onthe radius of the cylinder, and the range of applicability forthe correction factor is 1.3? o?6.7 [11]

It has been demonstrated experimentally that the criti-cal heat flux is highly dependent on pressure, primarily through the pressure dependence of the fluid surfacetension and latent heat of vaporization. Using Equation10.6, calculate values of for water on a large hori-zontal surface as a function of pressure. Demonstratethat the peak critical heat flux occurs at approximatelyone-third the critical pressure (pc?221 bars). Since allcommon fluids have this characteristic, suggest whatcoordinates should be used to plot critical heatfluxpressure values to obtain a universal curve

In applying dimensional analysis, Kutateladze [9] pos-tulated that the critical heat flux varies with the heat ofvaporization, vapor density, surface tension, and thebubble diameter parameter given in Equation 10.4a.Verify that dimensional analysis would yield the fol-lowing expression for the critical heat flux:

A silicon chip of thickness L?2.5 mm and thermalconductivity ks?135 W/m?K is cooled by boiling asaturated fluorocarbon liquid (Tsat?57?C) on its sur-face. The electronic circuits on the bottom of the chipproduce a uniform heat flux of ,while the sides of the chip are perfectly insulated.Properties of the saturated fluorocarbon are cp,l?1100 J/kg?K, hg?84,400 J/kg, ?l?1619.2 kg/m3, ?v?13.4 kg/m3, ??8.1?10?3N/m, ?l?440?10?6kg/m?s, and Prl?9.01. In addition, the nucleate boilingconstants are Cs,?0.005 and n?1.7.(a) What is the steady-state temperature Toat the bottom of the chip? If, during testing of the chip,q?ois increased to 90% of the critical heat flux,what is the new steady-state value of To?(b) Compute and plot the chip surface temperatures(top and bottom) as a function of heat flux for0.20?q?o/q?max?0.90. If the maximum allowablechip temperature is 80?C, what is the maximumallowable value of q?o?

What is the critical heat flux for boiling water at 1 atmon a large horizontal surface on the surface of themoon, where the gravitational acceleration is one-sixththat of the earth?

A heater for boiling a saturated liquid consists of twoconcentric stainless steel tubes packed with dense boron nitride powder. Electrical current is passed through theinner tube, creating uniform volumetric heating (W/m3). The exposed surface of the outer tube is in con-tact with the liquid and the boiling heat flux is given asIt is feared that under high-power operation the stain-less steel tubes would severely oxidize if temperaturesexceed Tss,xor that the boron nitride would deteriorateif its temperature exceeds Tbn,x. Presuming that the sat-uration temperature of the liquid (Tsat) and the boilingsurface temperature (Ts) are prescribed, derive expres-sions for the maximum temperatures in the stainlesssteel (ss) tubes and in the boron nitride (bn). Expressyour results in terms of geometric parameters (r1, r2,r3, r4), thermal conductivities (kss, kbn), and the boilingparameters (C, Tsat, Ts).

A device for performing boiling experiments consists of acopper bar (k?400 W/m?K), which is exposed to a boil-ing liquid at one end, encapsulates an electrical heater atthe other end, and is well insulated from its surroundingsat all but the exposed surface. Thermocouples inserted inthe bar are used to measure temperatures at distances ofx1?10 mm and x2?25 mm from the surface.Copper bar, k Electrical heater (a) An experiment is performed to determine the boil-ing characteristics of a special coating applied tothe exposed surface. Under steady-state condi-tions, nucleate boiling is maintained in saturatedwater at atmospheric pressure, and values ofT1?133.7?C and T2?158.6?C are recorded. Ifn?1, what value of the coefficient Cs,fis associ-ated with the Rohsenow correlation?(b) Assuming applicability of the Rohsenow correla-tion with the value of Cs,fdetermined from part(a), compute and plot the excess temperature ?Teas a function of the boiling heat flux for105?q?s?106W/m2. What are the correspondingvalues of T1and T2for q?s?106W/m2? If q?swereincreased to 1.5?106W/m2, could the foregoingresults be extrapolated to infer the correspondingvalues of ?Te, T1, and T2?

A small copper sphere, initially at a uniform, elevatedtemperature T(0)?Ti, is suddenly immersed in alarge fluid bath maintained at Tsat. The initial tempera-ture of the sphere exceeds the Leidenfrost point corre-sponding to the temperature TDof Figure 10.4.(a) Sketch the variation of the average sphere temper-ature, , with time during the quenching process.Indicate on this sketch the temperatures Ti, TD, andTsat, as well as the regimes of film, transition, andnucleate boiling and the regime of single-phaseconvection. Identify key features of the tempera-ture history.(b) At what time(s) in this cooling process do youexpect the surface temperature of the sphere todeviate most from its center temperature? Explainyour answer.

A sphere made of aluminum alloy 2024 with a diame-ter of 20 mm and a uniform temperature of 500C issuddenly immersed in a saturated water bath main-tained at atmospheric pressure. The surface of thesphere has an emissivity of 0.25.(a) Calculate the total heat transfer coefficient for theinitial condition. What fraction of the total coeffi-cient is contributed by radiation?(b) Estimate the temperature of the sphere 30 s after itis immersed in the bath.

A disk-shaped turbine rotor is heat-treated by quench-ing in water at p?1 atm. Initially, the rotor is at auniform temperature of Ti?1100?C and the water isat its boiling point as the rotor is lowered into thequenching bath by a harness. (a) Assuming lumped-capacitance behavior and con-stant properties for the rotor, carefully plot therotor temperature versus time, pointing out impor-tant features of your T(t) curve. The rotor is inOrientation A.(b) If the rotor is reoriented so that its large surfacesare horizontal (Orientation B), would the rotortemperature decrease more rapidly or less rapidlyrelative to Orientation A?

A steel bar, 20 mm in diameter and 200 mm long, withan emissivity of 0.9, is removed from a furnace at 455C and suddenly submerged horizontally in a waterbath under atmospheric pressure. Estimate the initialheat transfer rate from the bar.

Electrical current passes through a horizontal, 2-mm-diameter conductor of emissivity 0.5 when immersedin water under atmospheric pressure.(a) Estimate the power dissipation per unit length ofthe conductor required to maintain the surfacetemperature at 555?C.(b) For conductor diameters of 1.5, 2.0, and 2.5 mm,compute and plot the power dissipation per unitlength as a function of surface temperature for250?Ts?650?C. On a separate figure, plot thepercentage contribution of radiation as a functionof Ts

Consider a horizontal, D?1-mm-diameter platinumwire suspended in saturated water at atmosphericpressure. The wire is heated by an electrical current.Determine the heat flux from the wire at the instantwhen the surface of the wire reaches its melting point.Determine the corresponding centerline temperatureof the wire. Due to oxidation at very high tempera-ture, the wire emissivity is ??0.80 when it burns out.The water vapor properties at the film temperature of1209 K are ?v?0.189 kg/m3, cp,v?2404 J/kg?K,?v?23? 0?6m2/s, kv? .113 W/m?K

A heater element of 5-mm diameter is maintainedat a surface temperature of 350C when immerse horizontally in water under atmospheric pressure.The element sheath is stainless steel with a mechanically polished finish having an emissivity of 0.25.(a) Calculate the electrical power dissipation and therate of vapor production per unit heater length.(b) If the heater were operated at the same powerdissipation rate in the nucleate boiling regime,what temperature would the surface achieve? Calculate the rate of vapor production per unit lengthfor this operating condition.(c) Sketch the boiling curve and represent the two operating conditions of parts (a) and (b). Compare theresults of your analysis. If the heater element isoperated in the power-controlled mode, explain howyou would achieve these two operating conditionsbeginning with a cold element.

The thermal energy generated by a silicon chipincreases in proportion to its clock speed. The sili-con chip of Problem 10.23 is designed to operate in the nucleate boiling regime at approximately 30% of the critical heat flux. A sudden surge in thechips clock speed triggers film boiling, after whichthe clock speed and power dissipation return to theirdesign values.(a) In which boiling regime does the chip operate afterthe power dissipation returns to its design value?(b) To return to the nucleate boiling regime, how muchmust the clock speed be reduced relative to thedesign value?

A cylinder of 120-mm diameter at 1000 K is quenchedin saturated water at 1 atm. Describe the quenchingprocess and estimate the maximum heat removal rateper unit length during the process

A 1-mm-diameter horizontal platinum wire of emis-sivity ??0.25 is operated in saturated water at 1- atmpressure.(a) What is the surface heat flux if the surface temper-ature is Ts?800 K?(b) For emissivities of 0.1, 0.25, and 0.95, generate aloglog plot of the heat flux as a function of sur-face excess temperature, ?Te?Ts?Tsat, for150??Te?550 K. Show the critical heat fluxand the Leidenfrost point on your plot. Separately,plot the percentage contribution of radiation to thetotal heat flux for 150??Te?550 K.

As strip steel leaves the last set of rollers in a hotrolling mill, it is quenched by planar water jets beforebeing coiled. Due to the large plate temperatures, filmboiling is achieved shortly downstream of the jetimpingement region. Consider conditions for which the strip steel beneaththe vapor blanket is at a temperature of 907 K and has an emissivity of 0.35. Neglecting the effects of thestrip and jet motions and assuming boiling within the film to be approximated by that associated with alarge horizontal cylinder of 1-m diameter, estimate therate of heat transfer per unit surface area from the stripto the wall jet.

A polished copper sphere of 10-mm diameter, initiallyat a prescribed elevated temperature Ti, is quenched in asaturated (1 atm) water bath. Using the lumped capaci-tance method of Section 5.3.3, estimate the time for thesphere to cool (a) from Ti?130?C to 110?C and (b)from Ti?550?C to 220?C. Make use of the averagesphere temperatures in evaluating properties. Plot thetemperature history for each quenching process.

A tube of 2-mm diameter is used to heat saturatedwater at 1 atm, which is in cross flow over the tube.Calculate and plot the critical heat flux as a function ofwater velocity over the range 0 to 2 m/s. On your plot,identify the pool boiling region and the transitionregion between the low- and high- velocity ranges.Hint:Problem 10.20 contains relevant information forpool boiling on small-diameter cylinders.

Saturated water at 1 atm and velocity 2 m/s flows over acylindrical heating element of diameter 5 mm. What isthe maximum heating rate (W/m) for nucleate boiling?

A vertical steel tube carries water at a pressure of 10 bars. Saturated liquid water is pumped into theD?0.1-m-diameter tube at its bottom end (x?0)with a mean velocity of um?0.05 m/s. The tube isexposed to combusting pulverized coal, providing auniform heat flux of q??100,000 W/m2.(a) Determine the tube wall temperature and the qualityof the flowing water at x?15 m. Assume Gs,f?1.(b) Determine the tube wall temperature at a locationbeyond x?15 m where single-phase flow of the apor exists at a mean temperature of Tsat. Assumethe vapor at this location is also at a pressure of10 bars.(c) Plot the tube wall temperature in the range?5m?x?30 m.

Consider refrigerant R-134a flowing in a smooth, hori-zontal, 10-mm-inner-diameter tube of wall thickness2 mm. The refrigerant is at a saturation temperature of15?C (for which ?v,sat?23.75 kg/m3) and flows at arate of 0.01 kg/s. Determine the maximum wall tem-perature associated with a heat flux of 105W/m2at the inner wall at a location 0.4 m downstream from theonset of boiling for tubes fabricated of (a) pure copperand (b) AISI 316 stainless steel.

Determine the tube diameter associated with p = 1 atm and a critical Confinement number of 0.5 for ethanol,mercury, water, R-134a, and the dielectric fluid ofProblem 10.23.

Saturated steam at 0.1 bar condenses with a convec-tion coefficient of 6800 W/m2?K on the outside of abrass tube having inner and outer diameters of 16.5and 19 mm, respectively. The convection coefficientfor water flowing inside the tube is 5200 W/m2?K.Estimate the steam condensation rate per unit lengthof the tube when the mean water temperature is 30?C

Consider a container exposed to a saturated vapor, Tsat,having a cold bottom surface, TsTsat, and with insu-lated sidewalls.Assuming a linear temperature distribution for the liquid,perform a surface energy balance on the liquidvaporinterface to obtain the following expression for thegrowth rate of the liquid layer:Calculate the thickness of the liquid layer formed in1 h for a 200-mm2bottom surface maintained at 80?Cand exposed to saturated steam at 1 atm. Compare this result with the condensate formed by a verticalplate of the same dimensions for the same period of time.

Saturated steam at 1 atm condenses on the outersurface of a vertical, 100-mm-diameter pipe 1 m long,having a uniform surface temperature of 94C. Estimate the total condensation rate and the heat transferrate to the pipe.

Determine the total condensation rate and the heattransfer rate for Problem 10.46 when the steam is satu-rated at 1.5 bars.

Consider wave-free laminar condensation on a verticalisothermal plate of length L, providing an average heattransfer coefficient ofhL. If the plate is divided into Nsmaller plates, each of length LN?L/N, determine anexpression for the ratio of the heat transfer coefficientaveraged over the Nplates to the heat transfer coeffi-cient averaged over the single plate,

A vertical plate 500 mm high and 200 mm wide is tobe used to condense saturated steam at 1 atm.(a) At what surface temperature must the plate bemaintained to achieve a condensation rate of?25 kg/h?(b) Compute and plot the surface temperature as a func-tion of condensation rate for 15??50 kg/h.(c) On the same graph and for the same range of ,plot the surface temperature as a function of con-densation rate if the plate is 200 mm high and500 mm wide.

A 2 m?2 m vertical plate is exposed on one side tosaturated steam at atmospheric pressure and on theother side to cooling water that maintains a plate tem-perature of 50?C.(a) What is the rate of heat transfer to the coolant? Whatis the rate at which steam condenses on the plate?(b) For plates inclined at an angle from the vertical,the average convection coefficient for condensationon the upper surface, hL(incl), may be approxi-mated by an expression of the form, hL(incl)?(cos)1/4?hL(vert), where hL(vert)is the average coeffi-cient for the vertical orientation. If the 2 m?2mplate is inclined 45?from the normal, what are therates of heat transfer and condensation?

Saturated ethylene glycol vapor at 1 atm is exposed to a vertical plate 300 mm high and 100 mm wide having a uniform temperature of 420 K. Estimate the heattransfer rate to the plate and the condensation rate.Approximate the liquid properties as those corresponding to saturated conditions at 373 K (Table A.5).

A vertical plate 2.5 m high, maintained at a uniformtemperature of 54?C, is exposed to saturated steam atatmospheric pressure.(a) Estimate the condensation and heat transfer ratesper unit width of the plate.(b) If the plate height were halved, would the flowregime stay the same or change?(c) For 54?Ts?90?C, plot the condensation rate asa function of plate temperature for the two plateheights of parts (a) and (b)

Two configurations are being considered in thedesign of a condensing system for steam at 1 atmemploying a vertical plate maintained at 90?C. Thefirst configuration is a single vertical plate L?wandthe second consists of two vertical plates (L/2)?w,where Land ware the vertical and horizontal dimen-sions, respectively. Which configuration would youchoose?

The condenser of a steam power plant consists of asquare (in-line) array of 625 tubes, each of 25- mmdiameter. Consider conditions for which saturatedsteam at 0.105 bars condenses on the outer surface ofeach tube, while a tube wall temperature of 17C ismaintained by the flow of cooling water through thetubes. What is the rate of heat transfer to the water perunit length of the tube array? What is the correspond-ing condensation rate?

The condenser of a steam power plant consists of AISI302 stainless steel tubes (ks?15 W/m?K), each ofouter and inner diameters Do?30 mm and Di?26 mm, respectively. Saturated steam at 0.135 bar con- denses on the outer surface of a tube, while water at amean temperature of Tm?290 K is in fully developedflow through the tube.(a) For a water flow rate of ?0.25 kg /s, what is theouter surface temperature Ts,oof the tube and the rates of heat transfer and steam condensationper unit tube length? As a first estimate, you mayevaluate the properties of the liquid film at thesaturation temperature. If one wishes to increasethe transfer rates, what is the limiting factor thatshould be addressed?(b) Explore the effect of the water flow rate on Ts,oand the rate of heat transfer per unit length.

Saturated vapor from a chemical process condensesat a slow rate on the inner surface of a vertical, thin-walled cylindrical container of length L and diameterD. The container wall is maintained at a uniformtemperature Tsby flowing cold water across its outersurface. Derive an expression for the time, tf, required to fillthe container with condensate, assuming that the con-densate film is laminar. Express your result in terms ofD, L, (Tsat?Ts), g, and appropriate fluid properties.

Determine the total condensation rate and heat transferrate for the process of Problem 10.46 when the pipe isoriented at angles of ?0, 30, 45, and 60 from the horizontal.

A horizontal tube of 50-mm outer diameter, with asurface temperature of 34C, is exposed to steam at 0.2 bar. Estimate the condensation rate and heat trans-fer rate per unit length of the tube.

The tube of Problem 10.58 is modified by millingsharp-cornered grooves around its periphery, as inFigure 10.15. The 2-mm-deep grooves are each 2 mmwide with a pitch of S = 4 mm. Estimate the minimumcondensation and heat transfer rates per unit lengththat would be expected for the modified tube. Howmuch is the performance enhanced relative to the orig-inal tube of Problem 10.58?

A horizontal tube 1 m long with a surface temperatureof 70?C is used to condense saturated steam at 1 atm.(a) What diameter is required to achieve a condensa-tion rate of 125 kg/h?(b) Plot the condensation rate as a function of surfacetemperature for 70?Ts?90?C and tube diame-ters of 125, 150, 175 mm.

Saturated steam at a pressure of 0.1 bar is condensedover a square array of 100 tubes each of diameter 8 mm.(a) If the tube surfaces are maintained at 27C, estimate the condensation rate per unit tube length.(b) Subject to the requirement that the total number oftubes and the tube diameter are fixed at 100 and8 mm, respectively, what options are available forincreasing the condensation rate? Assess theseoptions quantitatively.

A thin-walled concentric tube heat exchanger of 0.19-m length is to be used to heat deionized waterfrom 40 to 60?C at a flow rate of 5 kg/s. The deionizedwater flows through the inner tube of 30- mm diameterwhile saturated steam at 1 atm is supplied to the annulusformed with the outer tube of 60-mm diameter. Thethermophysical properties of the deionized water are??982.3 kg/m3, cp?4181 J/kg?K, k?0.643 W/m?K,??548?10?6N?s/m2, and Pr?3.56. Estimate theconvection coefficients for both sides of the tube anddetermine the inner tube wall outlet temperature. Doescondensation provide a fairly uniform inner tube walltemperature equal approximately to the saturation tem-perature of the steam?

A technique for cooling a multichip module involvessubmerging the module in a saturated fluorocarbonliquid. Vapor generated due to boiling at the modulesurface is condensed on the outer surface of coppertubing suspended in the vapor space above the liquid.The thin-walled tubing is of diameter D?10 mm andis coiled in a horizontal plane. It is cooled by waterthat enters at 285 K and leaves at 315 K. All the heatdissipated by the chips within the module is transferredfrom a 100- mm?100-mm boiling surface, at whichthe flux is 105W/m2, to the fluorocarbon liquid, whichis at Tsat?57?C. Liquid properties are kl?0.0537W/m?K, cp,l?1100 J/kg?K, hfg?hg?84,400 J/kg,?l?1619.2 kg/m3, ?v?13.4 kg/m3, ??8.1?10?3N/m, ?l?440?10?6kg/m?s, and Prl?9. (a) For the prescribed heat dissipation, what is therequired condensation rate (kg/s) and water flowrate (kg/s)?(b) Assuming fully developed flow throughout thetube, determine the tube surface temperature at thecoil inlet and outlet.(c) Assuming a uniform tube surface temperature of Ts?53.0?C, determine the required length ofthe coil.

Determine the rate of condensation on a 100-mm-diameter sphere with a surface temperature of 150Cin saturated ethylene glycol vapor at 1 atm. Approxi-mate the liquid properties as those corresponding tosaturated conditions at 373 K (Table A.5).

A 10-mm-diameter copper sphere, initially at a uniform temperature of 50C, is placed in a large container filled with saturated steam at 1 atm. Using the lumped capacitance method, estimate the time required for the sphere to reach an equilibrium condition. How much condensate (kg) was formed during this period?

The Clean Air Act prohibited the production of chlo-rofluorocarbons (CFCs) in the United States as of1996. One widely used CFC, refrigerant R-12, hasbeen replaced by R-134a in many applications becauseof their similar properties, including a low boilingpoint at atmospheric pressure, Tsat?243 K and246.9 K for R-12 and R-134a, respectively. Comparethe performance of these two refrigerants under thefollowing conditions. The saturated refrigerant vaporat 310 K is condensed as it flows through a 30-mm-diameter, 0.8-m-long tube whose wall temperature ismaintained at 290 K. If vapor enters the tube at a flowrate of 0.010 kg/s, what is the rate of condensation andthe flow rate of vapor leaving the tube? The relevantproperties of R-12 at Tsat?310 K are ?v?50.1 kg/m3, hfg?160 kJ/kg, and ?v?150?10?7N?s/m2andthose of liquid R-12 at Tf?300 K are ?l?1306kg/m3, cp,l?978 J/kg?K, ?l?2.54 ?10?4N?s/m2,kl?0.072 W/m?K. The properties of the saturated R-134a vapor are ?v?46.1 kg/m3, hfg?166 kJ/kg,and ?v?136 ?10?7N?s/m2.

Saturated steam at 1.5 bars condenses inside a hori-zontal, 75-mm-diameter pipe whose surface is main-tained at 100C. Assuming low vapor velocities and film condensation, estimate the heat transfer coeffi-cient and the condensation rate per unit length of the pipe.

Consider the situation of Problem 10.67 at relativelyhigh vapor velocities, with a fluid mass flow rate of.(a) Determine the heat transfer coefficient and con-densation rate per unit length of tube for a massfraction of vapor of X?0.2.(b) Plot the heat transfer coefficient and the condensa-tion rate for 0.1? ? .3.

Refrigerant R-22 with a mass flow rate of ?8.75 ?10?3kg/s is condensed inside a 7-mm-diameter tube.Annular flow is observed. The saturation temperatureof the pressurized refrigerant is Tsat?45?C, and thewall temperature is Ts?40?C. Vapor properties are?v?77 kg/m3and ?v?15?10?6N?s/m2.(a) Determine the heat transfer coefficient and theheat transfer and condensation rates per unitlength at a quality of X?0.5.(b) Plot the condensation rate per unit length over therange 0.2X0.8

Consider Problem 10.44. In an effort to increase thecondensation rate, an engineer proposes to apply anL?100-?m-thick Teflon coating to the exteriorsurface of the brass tube to promote dropwisecondensation. Estimate the new condensation con-vection coefficient and the steam condensation rateper unit length of the tube after application of the coating. Comment on the proposed schemes effecton the condensation rate (the condensation rateper unit length in Problem 10.44 is approximately1?10?3kg/s)

Wetting of some metallic surfaces can be inhibited bymeans of ion implantation of the surface prior to itsuse, thereby promoting dropwise condensation. Thedegree of wetting inhibition and, in turn, the efficacyof the implantation process vary from metal to metal.Consider a vertical metal plate that is exposed to satu-rated steam at atmospheric pressure. The plate ist?1 mm thick, and its vertical and horizontal dimen-sions are L?250 mm and b?100 mm, respectively.The temperature of the plate surface that is exposed tothe steam is found to be Ts?90?C when the opposite surface of the metal plate is held at a cold tempera-ture, Tc.(a) Determine Tcfor 2024-T6 aluminum. Assume theion-implantation process does not promote drop-wise condensation for this metal.(b) Determine Tcfor AISI 302 stainless steel, assuming the ion-implantation process is effective inpromoting dropwise condensation.

A passive technique for cooling heat-dissipating integrated circuits involves submerging the ICs in a lowboiling point dielectric fluid. Vapor generated incooling the circuits is condensed on vertical platessuspended in the vapor cavity above the liquid. Thetemperature of the plates is maintained below the saturation temperature, and during steady-state opera-tion a balance is established between the rate of heattransfer to the condenser plates and the rate of heatdissipation by the ICs.Consider conditions for which the 25-mm2surface areaof each IC is submerged in a fluorocarbon liquid forwhich Tsat?50?C, ?l?1700 kg/m3, cp,l?1005 J/kg?K,?l?6.80?10?4kg/s?m, kl?0.062 W/m?K, Prl?11.0, ??0.013 N/m, hfg?1.05?105J/kg, Cs,f?0.004, and n?1.7. If the integrated circuits areoperated at a surface temperature of Ts?75?C, whatis the rate at which heat is dissipated by each circuit?If the condenser plates are of height H?50 mm andare maintained at a temperature of Tc?15?C by aninternal coolant, how much condenser surface areamust be provided to balance the heat generated by 500integrated circuits?

A thermosyphon consists of a closed container thatabsorbs heat along its boiling section and rejects heatalong its condensation section. Consider a ther-mosyphon made from a thin-walled mechanicallypolished stainless steel cylinder of diameter D. Heatsupplied to the thermosyphon boils saturated water atatmospheric pressure on the surfaces of the lowerboiling section of length Lband is then rejected by condensing vapor into a thin film, which falls bygravity along the wall of the condensation section oflength Lcback into the boiling section. The two sec-tions are separated by an insulated section of length Li.The top surface of the condensation section may betreated as being insulated. The thermosyphon dimen-sions areD?20 mm, Lb?20 mm, Lc?40 mm, andLi?40 mm.(a) Find the mean surface temperature, Ts,b, of theboiling surface if the nucleate boiling heat fluxis to be maintained at 30% of the critical heatflux.(b) Find the total condensation flow rate, , and themean surface temperature of the condensation sec-tion, Ts,c.

A novel scheme for cooling computer chips uses athermosyphon containing a saturated fluorocarbon.The chip is brazed to the bottom of a cuplike con-tainer, within which heat is dissipated by boilingand subsequently transferred to an external coolant(water) via condensation on the inner surface of a thin-walled tube . The nucleate boiling constants and the properties ofthe fluorocarbon are provided in Problem 10.23. Inaddition, kl?0.054 W/m?K.(a) If the chip operates under steady-state conditionsand its surface heat flux is maintained at 90% ofthe critical heat flux, what is its temperature T?What is the total power dissipation if the chipwidth is Lc?20 mm on a side?(b) If the tube diameter is D?30 mm and its surfaceis maintained at Ts?25?C by the water, whattube length Lis required to maintain the desig-nated conditions?

A condenserboiler section contains a 2-m?2-mcopper plate operating at a uniform temperature ofTs?100?C and separating saturated steam, which iscondensing, from a saturated liquid-X, which experi-ences nucleate pool boiling. A portion of the boilingcurve for liquid-X is shown as follows. Both saturatedsteam and saturated liquid-X are supplied to the system,while water condensate and vapor- X are removed bymeans not shown in the sketch. At a pressure of 1 bar,fluid-X has a saturation temperature and a latent heat ofvaporization of Tsat?80?C and hfg?700,000 J/kg,respectively. (a) Estimate the rates of evaporation and condensa-tion (kg/s) for the two fluids.(b) Determine the saturation temperature Tsatandpressure pfor the steam, assuming that film con-densation occurs.

A thin-walled cylindrical container of diameter Dandheight Lis filled to a height ywith a low boiling pointliquid (A) at Tsat,A. The container is located in a largechamber filled with the vapor of a high boiling pointfluid (B). Vapor-B condenses into a laminar film on theouter surface of the cylindrical container, extendingfrom the location of the liquid-A free surface. The con-densation process sustains nucleate boiling in liquid-Aalong the container wall according to the relation q??C(Ts?Tsat)3, where Cis a known empirical constant. (a) For the portion of the wall covered with the con-densate film, derive an equation for the averagetemperature of the container wall, Ts. Assume thatthe properties of fluids A and B are known.(b) At what rate is heat supplied to liquid-A?(c) Assuming the container is initially filled com-pletely with liquid, that is, y?L, derive anexpression for the time required to evaporate allthe liquid in the container.

It has been proposed that the very hot air trapped insidethe attic of a house in the summer may be used as theenergy source for a passivewater heater installed in theattic. Energy costs associated with heating the coolwater and air conditioning the house are both reduced.Ten thermosyphons, similar to that of Problem 10.73,are inserted in the bottom of a well-insulated water heater. Each thermosyphon has a condensing sectionthat is Lc?50 mm long, an insulated section that is oflength Li?40 mm, and a boiling section that isLb?30 mm long. The diameter of each thermosyphonis D?20 mm. The working fluid within the thermo-syphons is water at a pressure of p?0.047 bars. (a) Determine the heating rate delivered by the 10thermosyphons when boiling occurs at 25% of theCHF. What are the mean temperatures of the boil-ing and condensing sections?(b) At night the attic air temperature drops below thetemperature of the water. Estimate the heat lossfrom the hot water tank to the cool attic, assuminglosses through the tank insulation are negligibleand the stainless steel tube wall thickness of eachthermosyphon is very small.