The defroster of an automobile functions by discharging

The temperature distribution within a laminar thermal boundary layer associated with flow over an isothermal flat plate is shown in the sketch. The temperature distribution shown is located at x
x2 (a) Is the plate being heated or cooled by the fluid? (b) Carefully sketch the temperature distributions at x
x1 and x
x3. Based on your sketch, at which of the three x-locations is the local heat flux largest? At which location is the local heat flux smallest? (c) As the free stream velocity increases, the velocity and thermal boundary layers both become thinner. Carefully sketch the temperature distributions at x
x2 for (i) a low free stream velocity and (ii) a high free stream velocity. Based on your sketch, which velocity condition will induce the larger local convective heat flux?

In flow over a surface, velocity and temperature profiles are of the forms T(y)
D  Ey  Fy2 Gy3 u(y)
Ay  By2 Cy3 and where the coefficients A through G are constants. Obtain expressions for the friction coefficient Cf and the convection coefficient h in terms of u
, T
, and appropriate profile coefficients and fluid properties

In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as where y is the distance normal to the surface and the Prandtl number, Pr
cp/k
0.7, is a dimensionless fluid property. If T

400 K, Ts
300 K, and u
/
5000 m1 , what is the surface heat flux?

Water at a temperature of T

25 C flows over one of the surfaces of a steel wall (AISI 1010) whose temperature is Ts,1
40 C. The wall is 0.35 m thick, and its other surface temperature is Ts,2
100 C. For steadystate conditions what is the convection coefficient associated with the water flow? What is the temperature gradient in the wall and in the water that is in contact with the wall? Sketch the temperature distribution in the wall and in the adjoining water

For laminar flow over a flat plate, the local heat transfer coefficient hx is known to vary as x1/2, where x is the distance from the leading edge (x
0) of the plate. What is the ratio of the average coefficient between the leading edge and some location x on the plate to the local coefficient at x?

A flat plate is of planar dimension 1 m  0.75 m. For parallel laminar flow over the plate, calculate the ratio of the average heat transfer coefficients over the entire plate, L,1/ L,2, for two cases. In Case 1, flow is in the short direction (L
0.75 m); in Case 2, flow is in the long direction (L
1 m). Which orientation will result in the larger heat transfer rate? See Problem 6.5

Parallel flow of atmospheric air over a flat plate of length L
3 m is disrupted by an array of stationary rods placed in the flow path over the plate. Laboratory measurements of the local convection coeffi- cient at the surface of the plate are made for a prescribed value of V and Ts  T
. The results are correlated by an expression of the form hx
0.7  13.6x 3.4x2 , where hx has units of W/m2
K and x is in meters. Evaluate the average convection coefficient L for the entire plate and the ratio at the trailing edge.

For laminar free convection from a heated vertical surface, the local convection coefficient may be expressed as hx
Cx1/4, where hx is the coefficient at a distance x from the leading edge of the surface and the quantity C, which depends on the fluid properties, is independent of x. Obtain an expression for the ratio x/hx, where x is the average coefficient between the leading edge (x
0) and the x-location. Sketch the variation of hx and x with x.

A circular, hot gas jet at T
is directed normal to a circular plate that has radius ro and is maintained at a uniform temperature Ts. Gas flow over the plate is axisymmetric, causing the local convection coefficient to have a radial dependence of the form h(r)
a  brn , where a, b, and n are constants. Determine the rate of heat transfer to the plate, expressing your result in terms of T
, Ts, ro, a, b, and n.

Experiments have been conducted to determine local heat transfer coefficients for flow perpendicular to a long, isothermal bar of rectangular cross section. The bar is of width c parallel to the flow, and height d normal to the flow. For Reynolds numbers in the range 104  Red  5  104 , the face-averaged Nusselt numbers are well correlated by an expression of the form The values of C and m for the front face, side faces, and back face of the rectangular rod are found to be the following: Face c/d Cm Front 0.33  c/d  1.33 0.674 1/2 Side 0.33 0.153 2/3 Side 1.33 0.107 2/3 Back 0.33 0.174 2/3 Back 1.33 0.153 2/3 Determine the value of the average heat transfer coeffi- cient for the entire exposed surface (that is, averaged over all four faces) of a c
40-mm-wide, d
30-mm-tall rectangular rod. The rod is exposed to air in cross flow at V
10 m/s, T

300 K. Provide a plausible explanation of the relative values of the face-averaged heat transfer coefficients on the front, side, and back faces

A concentrating solar collector consists of a parabolic reflector and a collector tube of diameter D, through Nud
hd/k
CRem d Pr1/3 h h h hL/hL h 406 Chapter 6
Introduction to Convection CH006.qxd 4/14/11 9:37 AM Page 406 which flows a working fluid that is heated with concentrated solar irradiation. Throughout the day, the reflector is slowly repositioned to track the sun. For wind conditions characterized by a steady, horizontal flow normal to the tube axis, the local heat transfer coeffi- cient on the tube surface varies, as shown in the schematic for various reflector positions. (a) Estimate the value of the average heat transfer coefficient over the entire collector tube surface for each of the three cases. (b) Assuming the tube receives the same amount of solar irradiation in each case, which case would have the highest collector efficiency?

Air at a free stream temperature of T

20 C is in parallel flow over a flat plate of length L
5 m and temperature Ts
90 C. However, obstacles placed in the flow intensify mixing with increasing distance x from the leading edge, and the spatial variation of temperatures measured in the boundary layer is correlated by an expression of the form T( C)
20  70 exp (600xy), where x and y are in meters. Determine and plot the manner in which the local convection coefficient h varies with x. Evaluate the average convection coefficient for the plate.

The heat transfer rate per unit width (normal to the page) from a longitudinal section, x2 x1, can be expressed as q 12
12(x2 x1)(Ts T
), where 12 is the average coefficient for the section of length (x2 x1). Consider laminar flow over a flat plate with a uniform temperature Ts. The spatial variation of the local convection coeffi- cient is of the form hx
Cx1/2, where C is a constant. (a) Beginning with the convection rate equation in the form dq
hx dx(Ts T
), derive an expression for 12 in terms of C, x1, and x2. (b) Derive an expression for 12 in terms of x1, x2, and the average coefficients 1 and 2, corresponding to lengths x1 and x2, respectively. 6.1

Experiments to determine the local convection heat transfer coefficient for uniform flow normal to a heated circular disk have yielded a radial Nusselt number distribution of the form where both n and a are positive. The Nusselt number at the stagnation point is correlated in terms of the Reynolds (ReD
VD/) and Prandtl numbers V T D ro Ts L Nuo
h(r
0)D k
0.814 ReD 1/2 Pr0.36 Obtain an expression for the average Nusselt number, D
D/k, corresponding to heat transfer from an isothermal disk. Typically, boundary layer development from a stagnation point yields a decaying convection coefficient with increasing distance from the stagnation point. Provide a plausible explanation for why the opposite trend is observed for the disk

An experimental procedure for validating results of Problem 6.14 involves preheating a copper disk to an initial elevated temperature Ti and recording its temperature history T(t) as it is subsequently cooled by the impinging flow to a final temperature Tf . The measured temperature decay may then be compared with predictions based on the correlation for . Assume that values of a
0.30 and n
2 are associated with the correlation. Consider experimental conditions for which a disk of diameter D
50 mm and length L
25 mm is preheated to Ti
1000 K and cooled to Tf
400 K by an impinging airflow at T

300 K. The cooled surface of the disk has an emissivity of
0.8 and is exposed to large, isothermal surroundings for which Tsur
T
. The remaining surfaces of the disk are well insulated, and heat transfer through the supporting rod may be neglected. Using results from Problem 6.14, compute and plot temperature histories corresponding to air velocities of V
4, 20, and 50 m/s. Constant properties may be assumed for the copper (
8933 kg/m3 , cp
425 J/kg
K, k
386 W/m
K) and air (
38.8  106 m2 /s, k
0.0407 W/m
K, Pr
0.684).

If laminar flow is induced at the surface of a disk due to rotation about its axis, the local convection coefficient is known to be a constant, h
C, independent of radius. Consider conditions for which a disk of radius ro
100 mm is rotating in stagnant air at T

20 C and a value of C
20 W/m2
K is maintained. If an embedded electric heater maintains a surface temperature of Ts
50 C, what is the local heat flux at Support tube r ro Connections to electric heate the top surface of the disk? What is the total electric power requirement? What can you say about the nature of boundary layer development on the disk?

Consider the rotating disk of Problem 6.16. A diskshaped, stationary plate is placed a short distance away from the rotating disk, forming a gap of width g. The stationary plate and ambient air are at T

20 C. If the flow is laminar and the gap-to-radius ratio, G
g/ro, is small, the local radial Nusselt number distribution is of the form where Rer
r 2 / [Pelle J., and S. Harmand, Exp. Thermal Fluid Science, 31, 165, 2007]. Determine the value of the average Nusselt number, where D
2ro. If the rotating disk temperature is Ts
50 C, what is the total heat flux from the disks top surface for g
1 mm, 
150 rad/s? What is the total electric power requirement? What can you say about the nature of the flow between the disks?

Consider airflow over a flat plate of length L
1 m under conditions for which transition occurs at xc
0.5 m based on the critical Reynolds number, Rex,c
5  105 . (a) Evaluating the thermophysical properties of air at 350 K, determine the air velocity. (b) In the laminar and turbulent regions, the local convection coefficients are, respectively, where, at T
350 K, Clam
8.845 W/m3/2
K, Cturb
49.75 W/m1.8
K, and x has units of m. Develop an expression for the average convection coefficient, lam(x), as a function of distance from the leading edge, x, for the laminar region, 0  x  xc. (c) Develop an expression for the average convection coefficient, turb(x), as a function of distance from the leading edge, x, for the turbulent region, xc  x  L. (d) On the same coordinates, plot the local and average convection coefficients, hx and , respectively, as a function of x for 0  x  L

A fan that can provide air speeds up to 50 m/s is to be used in a low-speed wind tunnel with atmospheric air at 25 C. If one wishes to use the wind tunnel to study flatplate boundary layer behavior up to Reynolds numbers of Rex
108 , what is the minimum plate length that should be used? At what distance from the leading edge would transition occur if the critical Reynolds number were Rex,c
5  105 ?

Consider the flow conditions of Example 6.2 for two situations, one in which the flow is completely laminar, and the second for flow that is tripped to turbulence at the leading edge of the plate. Determine whether there is a plate length L for which the average convection coefficient for laminar flow is the same as the average convection coefficient for turbulent flow. Assume a water temperature of 300 K.

Assuming a transition Reynolds number of 5  105 , determine the distance from the leading edge of a flat plate at which transition will occur for each of the following fluids when u

1 m/s: atmospheric air, engine oil, and mercury. In each case, calculate the transition location for fluid temperatures of 27 C and 77 C

To a good approximation, the dynamic viscosity , the thermal conductivity k, and the specific heat cp are independent of pressure. In what manner do the kinematic viscosity  and thermal diffusivity  vary with pressure for an incompressible liquid and an ideal gas? Determine  of air at 350 K for pressures of 1, 5, and 10 atm. Assuming a transition Reynolds number of 5  105 , determine the distance from the leading edge of a flat plate at which transition will occur for air at 350 K at pressures of 1, 5, and 10 atm with u

2 m/s.

For the situation described in Example 6.2, the boundary layer can be tripped into a turbulent state by applying roughness to the surface of the flat plate at a particular x-location. Hence the location where transition occurs, xc, can be moved upstream relative to the transition location associated with the smooth plate of the example. Calculate and plot the average convection coefficient over the entire plate for roughness applied over the range 0  xr  L. What values of xr provide the minimum and maximum values of ? Assume the water temperature is 300 K.

Consider a laminar boundary layer developing over a flat plate. The flow is incompressible. (a) Substitute Equations 6.18 and 6.19 into Equation 6.23 to determine the boundary conditions in dimensional form associated with flow over a flat plate of length L. (b) Substitute Equations 6.18, 6.19, as well as the defi- nition of ReL into Equation 6.21, and compare the resulting expression with Equation 6.16. Note that for a flat plate, dp/dx
0 and u

V

Consider a laminar boundary layer developing over an isothermal flat plate. The flow is incompressible, and viscous dissipation is negligible. (a) Substitute Equations 6.18 and 6.20 into Equation 6.24 to determine the thermal boundary conditions in dimensional form associated with flow over a flat plate of length L and temperature Ts. (b) Substitute Equations 6.18, 6.19, and 6.20, as well as the definitions of ReL and Pr, into Equation 6.22, and compare the resulting dimensional expression with Equation 6.17

6 Experiments have shown that the transition from laminar to turbulent conditions for flow normal to the axis of a long cylinder occurs at a critical Reynolds number of ReD,c 2  105 , where D is the cylinder diameter. Moreover, the transition from incompressible to compressible flow occurs at a critical Mach number of Mac 0.3. For air at a pressure of p
1 atm and temperature T
27 C, determine the critical cylinder diameter Dc below which, if the flow is turbulent, compressibility effects are likely to be important.

An object of irregular shape has a characteristic length of L
1 m and is maintained at a uniform surface temperature of Ts
400 K. When placed in atmospheric air at a temperature of T

300 K and moving with a velocity of V
100 m/s, the average heat flux from the surface to the air is 20,000 W/m2 . If a second object of the same shape, but with a characteristic length of L
5 m, is maintained at a surface temperature of Ts
400 K and is placed in atmospheric air at T

300 K, what will the value of the average convection coefficient be if the air velocity is V
20 m/s?

Experiments have shown that, for airflow at T

35 C and V1
100 m/s, the rate of heat transfer from a turbine blade of characteristic length L1
0.15 m and surface temperature Ts,1
300 C is q1
1500 W. What would be the heat transfer rate from a second turbine blade of characteristic length L2
0.3 m operating at Ts,2
400 C in airflow of T

35 C and V2
50 m/s? The surface area of the blade may be assumed to be directly proportional to its characteristic length

Experimental measurements of the convection heat transfer coefficient for a square bar in cross flow yielded the following values: h2
40 W/m2
K when V2
15 m/s h1
50 W/m2
K when V1
20 m/ Assume that the functional form of the Nusselt number is , where C, m, and n are constants. (a) What will be the convection heat transfer coefficient for a similar bar with L
1 m when V
15 m/s? (b) What will be the convection heat transfer coefficient for a similar bar with L
1 m when V
30 m/s? (c) Would your results be the same if the side of the bar, rather than its diagonal, were used as the characteristic length?

To assess the efficacy of different liquids for cooling an object of given size and shape by forced convection, it is convenient to introduce a figure of merit, FF, which combines the influence of all pertinent fluid properties on the convection coefficient. If the Nusselt number is governed by an expression of the form, , obtain the corresponding relationship between FF and the fluid properties. For representative values of m
0.80 and n
0.33, calculate values of FF for air (k
0.026 W/m
K, 
1.6  105 m2 /s, Pr
0.71), water (k
0.600 W/m
K, 
106 m2 /s, Pr
5.0), and a dielectric liquid (k
0.064 W/m
K, 
106 m2 /s, Pr
25). Which fluid is the most effective cooling agent? 6

Gases are often used instead of liquids to cool electronics in avionics applications because of weight considerations. The cooling systems are often closed so that coolants other than air may be used. Gases with high figures of merit (see Problem 6.30) are desired. For representative values of m
0.85 and n
0.33 in the expression of Problem 6.30, determine the figures of merit for air, pure helium, pure xenon (k
0.006 W/m
K,
24.14  10 6 N
s/m2 ), and an ideal He-Xe mixture containing 0.75 mole fraction of helium (k
0.0713 W/m
K,
25.95  10 6 N
s/m2 ). Evaluate properties at 300 K and atmospheric pressure. For monatomic gases such as helium and xenon and their mixtures, the specific heat at constant pressure is well described by the relation cp
(5/2)
/. 6.

Experimental results for heat transfer over a flat plate with an extremely rough surface were found to be correlated by an expression of the form where Nux is the local value of the Nusselt number at a position x measured from the leading edge of the plate Obtain an expression for the ratio of the average heat transfer coefficient to the local coefficient hx

Consider conditions for which a fluid with a free stream velocity of V
1 m/s flows over a surface with a characteristic length of L
1 m, providing an average convection heat transfer coefficient of . Calculate the dimensionless parameters , ReL, Pr, and for the following fluids: air, engine oil, mercury, and water. Assume the fluids to be at 300 K

Consider the nanofluid of Example 2.2. (a) Calculate the Prandtl numbers of the base fluid and nanofluid, using information provided in the example problem. (b) For a geometry of fixed characteristic dimension L, and a fixed characteristic velocity V, determine the ratio of the Reynolds numbers associated with the two fluids, Renf/Rebf. Calculate the ratio of the average Nusselt numbers, , that is associated with identical average heat transfer coefficients for the two fluids, . (c) The functional dependence of the average Nusselt number on the Reynolds and Prandtl numbers for a broad array of various geometries may be expressed in the general form where C and m are constants whose values depend on the geometry from or to which convection heat transfer occurs. Under most conditions the value of m is positive. For positive m, is it possible for the base fluid to provide greater convection heat transfer rates than the nanofluid, for conditions involving a fixed geometry, the same characteristic velocities, and identical surface and ambient temperatures?

For flow over a flat plate of length L, the local heat transfer coefficient hx is known to vary as x1/2, where x is the distance from the leading edge of the plate. What is the ratio of the average Nusselt number for the entire plate to the local Nusselt number at x
L (NuL)?

For laminar boundary layer flow over a flat plate with air at 20 C and 1 atm, the thermal boundary layer thickness
t is approximately 13% larger than the velocity boundary layer thickness
. Determine the ratio
/
t if the fluid is ethylene glycol under the same flow conditions.

Sketch the variation of the velocity and thermal boundary layer thicknesses with distance from the leading edge of a flat plate for the laminar flow of air, waterengine oil, and mercury. For each case assume a mean fluid temperature of 300 K.

Consider parallel flow over a flat plate for air at 300 K and engine oil at 380 K. The free stream velocity is u

2 m/s. The temperature difference between the surface and the free stream is the same in both cases, with Ts  T
. (a) Determine the location where transition to turbulence occurs, xc, for both fluids. (b) For laminar flow over a flat plate, the velocity boundary layer thickness is given by Calculate and plot the velocity boundary layer thickness
over the range 0  x  xc for each fluid. (c) Calculate and plot the thermal boundary layer thickness
t for the two fluids over the same range of x used in part (b). At an x-location where both fluids experience laminar flow conditions, explain which fluid has the largest temperature gradient at the plate surface, T/yy
0. Which fluid is associated with the largest local Nusselt number Nu? Which fluid is associated with the largest local heat transfer coefficient h?

Forced air at T

25 C and V
10 m/s is used to cool electronic elements on a circuit board. One such element is a chip, 4 mm  4 mm, located 120 mm from the leading edge of the board. Experiments have revealed that flow over the board is disturbed by the elements and that convection heat transfer is correlated by an expression of the form Estimate the surface temperature of the chip if it is dissipating 30 mW

Consider the electronic elements that are cooled by forced convection in Problem 6.39. The cooling system is designed and tested at sea level (p 1 atm), but the circuit board is sold to a customer in Mexico City, with an elevation of 2250 m and atmospheric pressure of 76.5 kPa. (a) Estimate the surface temperature of the chip located 120 mm from the leading edge of the board when the board is operated in Mexico City. The dependence of various thermophysical properties on pressure is noted in Problem 6.22. (b) It is desirable for the chip operating temperature to be independent of the location of the customer. What air velocity is required for operation in Mexico City if the chip temperature is to be the same as at sea level?

Consider the chip on the circuit board of Problem 6.39. To ensure reliable operation over extended periods, the chip temperature should not exceed 85 C. Assuming the availability of forced air at T

25 C and applicability of the prescribed heat transfer correlation, compute and plot the maximum allowable chip power dissipation Pc as a function of air velocity for 1  V  25 m/s. If the chip surface has an emissivity of 0.80 and the board is mounted in a large enclosure whose walls are at 25 C, what is the effect of radiation on the Pc V plot?

A major contributor to product defects in electronic modules relates to stresses induced during thermal cycling (intermittent heating and cooling). For example, in circuit cards having active and passive components with materials of different thermal expansion coefficients, thermal stresses are the principal source of failure in component joints, such as soldered and wired connections. Although concern is generally for fatigue failure resulting from numerous excursions during the life of a product, it is possible to identify defective joints by performing accelerated thermal stress tests before the product is released to the customer. In such cases, it is important to achieve rapid thermal cycling to minimize disruptions to production schedules. A manufacturer of circuit cards wishes to develop an apparatus for imposing rapid thermal transients on the cards by subjecting them to forced convection characterized by a relation of the form , where m
0.8 and n
0.33. However, he does not know whether to use air (k
0.026 W/m
K, 
1.6  105 m2 /s, Pr
0.71) or a dielectric liquid (k
0.064 W/m
K, 
106 m2 /s, Pr
25) as the working fluid. Assuming equivalent air and liquid velocities and validity of the lumped capacitance model for the components, obtain a quantitative estimate of the ratio of the thermal time constants for the two fluids. What fluid provides the faster thermal response?

The defroster of an automobile functions by discharging warm air on the inner surface of the windshield. To prevent condensation of water vapor on the surface, the temperature of the air and the surface convection coeffi- cient ( , ) must be large enough to maintain a surface temperature Ts,i that is at least as high as the dewpoint (Ts,i  Tdp). Consider a windshield of length L
800 mm and thickness t
6 mm and driving conditions for which the vehicle moves at a velocity of V
70 mph in ambient air at T
,o
15 C. From laboratory experiments performed on a model of the vehicle, the average convection coefficient on the outer surface of the windshield is known to be correlated by an expression of the form , where ReL VL/. Air properties may be approximated as k
0.023 W/m
K, 
12.5  106 m2 /s, and Pr
0.71. If Tdp
10 C and
50 C, what is the smallest value of required to prevent condensation on the inner surface? 6

A microscale detector monitors a steady flow (T

27 C, V
10 m/s) of air for the possible presence of small, hazardous particulate matter that may be suspended in the room. The sensor is heated to a slightly higher temperature to induce a chemical reaction associated with certain substances of interest that might impinge on the sensors active surface. The active surface produces an electric current if such surface reactions occur; the electric current is then sent to an alarm. To maximize the sensor heads surface area and, in turn, the probability of capturing and detecting a particle, the sensor head is designed with a very complex shape. The value of the average heat transfer coefficient associated with the heated sensor must be known so that the required electrical power to the sensor can be determined. Consider a sensor with a characteristic dimension of Ls
80 m. A scale model of the sensor is placed in a recirculating (closed) wind tunnel using hydrogen as the working fluid. If the wind tunnel operates at a hydrogen absolute pressure of 0.5 atm and velocity of V
0.5 m/s, find the required hydrogen temperature and characteristic dimension of the scale model, Lm.

A thin, flat plate that is 0.2 m  0.2 m on a side is oriented parallel to an atmospheric airstream having a velocity of 40 m/s. The air is at a temperature of T

20 C, while the plate is maintained at Ts
120 C. The air flows over the top and bottom surfaces of the plate, and measurement of the drag force reveals a value of 0.075 N. What is the rate of heat transfer from both sides of the plate to the air?

Atmospheric air is in parallel flow (u

15 m/s, T

15 C) over a flat heater surface that is to be maintained at a temperature of 140 C. The heater surface area is 0.25 m2 , and the airflow is known to induce a drag force of 0.25 N on the heater. What is the electrical power needed to maintain the prescribed surface temperature?

Determine the drag force imparted to the top surface of the flat plate of Example 6.2 for water temperatures of 300 K and 350 K. Assume the plate dimension in the z-direction is W
1 m.

For flow over a flat plate with an extremely rough surface, convection heat transfer effects are known to be correlated by the expression of Problem 6.32. For airflow at 50 m/s, what is the surface shear stress at x
1 m from the leading edge of the plate? Assume the air to be at a temperature of 300 K.

A thin, flat plate that is 0.2 m  0.2 m on a side with rough top and bottom surfaces is placed in a wind tunnel so that its surfaces are parallel to an atmospheric airstream having a velocity of 30 m/s. The air is at a temperature of T

20 C while the plate is maintained at Ts
80 C. The plate is rotated 45 about its center point, as shown in the schematic. Air flows over the top and bottom surfaces of the plate, and measurement of the heat transfer rate is 2000 W. What is the drag force on the plate?

As a means of preventing ice formation on the wings of a small, private aircraft, it is proposed that electric resistance heating elements be installed within the wings. To determine representative power requirements, consider nominal flight conditions for which the plane moves at 100 m/s in air that is at a temperature of 23 C. If the characteristic length of the airfoil is L
2 m and wind tunnel measurements indicate an average friction coefficient of for the nominal conditions, what is the average heat flux needed to maintain a surface temperature of Ts
5 C?

A circuit board with a dense distribution of integrated circuits (ICs) and dimensions of 120 mm  120 mm on a side is cooled by the parallel flow of atmospheric air with a velocity of 2 m/s. Cf
0.0025 From wind tunnel tests under the same flow conditions, the average frictional shear stress on the upper surface is determined to be 0.0625 N/m2 . What is the allowable power dissipation from the upper surface of the board if the average surface temperature of the ICs must not exceed the ambient air temperature by more than 25 C? Evaluate the thermophysical properties of air at 300 K