# Kraus and Bar-Cohen Sample Problem 15.7 Comparison

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1 Kraus and Bar-Cohen Sample Problem 15.7 Comparison Compare the results of sample problem 15.7 of Allan Kraus and Avram Bar-Cohen book Thermal Analysis and Control of Electronic Equipment to COLDPLATE results. Below is a list of input parameters for their sample problem. Length L is 8 inches Width W is 4 inches Fin height H is.25 inches Fins are to be.006 inches thick Fin type is rectangular 11.1 The fin density is 11.1 fins/inch Cover plate is.01 inches Base plate is.01 inches thick The inlet fluid temperature is 71C The inlet fluid pressure is 14.7 PSI Cooling fluid is air Mass flow rate is 1.35 lb/min 400 Watts, 200 Watts on both sides, uniformly distributed Base, fins and cover are made of aluminum, K = 5.14 W/(in-C)

2 Input the geometry on this tab sheet.

3 Input the base plate, cover and fin conductivity on this tab sheet.

4 Input the temperature, pressure, flow rate and air as the fluid on this tab sheet.

5 Input the power dissipation on this tab sheet. (Note that we are inputting power on both One Side Only and Both Sides which will result in 2 runs to show the difference in results)

6 Here are the results with power on both sides ************************* VARIABLE INPUTS ************************** THE TYPE OF FINS SPECIFIED ARE: PLANE FIN 11.1 FIN HEIGHT, INCHES BASE THICKNESS, INCHES FIN THICKNESS, INCHES FIN DENSITY, FINS PER INCH 11.1 STATIC INLET FLUID TEMPERATURE, DEG C 71.0 INLET PRESSURE, LBS/IN MASS FLOWRATE, LBS/MIN 1.35 THE POWER APPLIED TO BOTH SIDES, WATTS TOP THE COOLING FLUID IS: BOTTOM AIR **************** INTERMEDIATE CALCULATED PARAMETERS **************** FREE FLOW CROSS SECTIONAL AREA, IN HYDRAULIC DIAMETER, INCHES COLDPLATE WEIGHT, LBS 0.12 TOTAL VOL FLOWRATE, [GAL/MIN] FT3/MIN [ ] COLDPLATE VOL FLOWRATE, [GAL/MIN] FT3/MIN [ ] COLDPLATE VELOCITY, FT/SEC AVERAGE DENSITY, LB/FT AVERAGE CONDUCTIVITY, W/(IN-C) AVERAGE SPECIFIC HEAT, W-MIN/(LB-C) AVERAGE DYNAMIC VISCOSITY, LB/(MIN-IN) PRANDTL NUMBER REYNOLDS NUMBER EQUIVALENT FRICTION LOSS COEFFICIENT, KFRICTION 3.01 INLET LOSS COEFFICIENT, KINLET 0.26 EXIT LOSS COEFFICIENT, KEXIT FILM COEFFICIENT, [BTU/(HR-FT2-F)] W/(IN2-C) [ 16.28] *************************** PRESSURE ******************************* INLET PRESSURE, [LB/IN2] INCHES-H2O [ ] INLET PRESSURE DROP, INCHES-H2O ACCELERATION PRESSURE DROP, INCHES-H2O FRICTIONAL PRESSURE DROP, INCHES-H2O EXIT PRESSURE DROP, INCHES-H2O TOTAL PRESSURE DROP, INCHES-H2O EXIT PRESSURE, [LB/IN2] INCHES-H2O [ ] DENSITY RATIO TIMES PRESSURE DROP, INCHES-H ************************ THERMAL RESISTANCE ************************ THERMAL RESISTANCE FROM INLET FLUID TO COLDPLATE, C/W TOP BOTTOM THERMAL RESISTANCE FROM LOCAL FLUID TO COLDPLATE, C/W TOP BOTTOM ************************** TEMPERATURES **************************** STATIC INLET FLUID TEMPERATURE, DEG C 71.0 STAGNATION FLUID TEMP RISE ALONG COLDPLATE, DEG C 38.8 TOTAL STAGNATION FLUID TEMP RISE, DEG C 38.8 STATIC EXIT FLUID TEMPERATURE, DEG C ISOTHERMAL COLDPLATE TEMPERATURE, DEG C TOP BOTTOM MAXIMUM COLDPLATE TEMPERATURE, DEG C TOP BOTTOM 138.2

7 Here are the results with power on the base plate only FINNED MODEL WITH HEATING ON ONE SIDE ONLY ************************* VARIABLE INPUTS ************************** THE TYPE OF FINS SPECIFIED ARE: PLANE FIN 11.1 FIN HEIGHT, INCHES BASE THICKNESS, INCHES FIN THICKNESS, INCHES FIN DENSITY, FINS PER INCH 11.1 STATIC INLET FLUID TEMPERATURE, DEG C 71.0 INLET PRESSURE, LBS/IN MASS FLOWRATE, LBS/MIN 1.35 THE POWER APPLIED TO ONE SIDE ONLY, WATTS THE COOLING FLUID IS: AIR **************** INTERMEDIATE CALCULATED PARAMETERS **************** FREE FLOW CROSS SECTIONAL AREA, IN HYDRAULIC DIAMETER, INCHES COLDPLATE WEIGHT, LBS 0.12 TOTAL VOL FLOWRATE, [GAL/MIN] FT3/MIN [ ] COLDPLATE VOL FLOWRATE, [GAL/MIN] FT3/MIN [ ] COLDPLATE VELOCITY, FT/SEC AVERAGE DENSITY, LB/FT AVERAGE CONDUCTIVITY, W/(IN-C) AVERAGE SPECIFIC HEAT, W-MIN/(LB-C) AVERAGE DYNAMIC VISCOSITY, LB/(MIN-IN) PRANDTL NUMBER REYNOLDS NUMBER EQUIVALENT FRICTION LOSS COEFFICIENT, KFRICTION 3.01 INLET LOSS COEFFICIENT, KINLET 0.26 EXIT LOSS COEFFICIENT, KEXIT FILM COEFFICIENT, [BTU/(HR-FT2-F)] W/(IN2-C) [ 16.28] THE FIN EFFICIENCY WITH HEAT ON ONE SIDE ONLY IS *************************** PRESSURE ******************************* INLET PRESSURE, [LB/IN2] INCHES-H2O [ ] INLET PRESSURE DROP, INCHES-H2O ACCELERATION PRESSURE DROP, INCHES-H2O FRICTIONAL PRESSURE DROP, INCHES-H2O EXIT PRESSURE DROP, INCHES-H2O TOTAL PRESSURE DROP, INCHES-H2O EXIT PRESSURE, [LB/IN2] INCHES-H2O [ ] DENSITY RATIO TIMES PRESSURE DROP, INCHES-H ************************ THERMAL RESISTANCE ************************ THERMAL RESISTANCE FROM INLET FLUID TO COLDPLATE, C/W THERMAL RESISTANCE FROM LOCAL FLUID TO COLDPLATE, C/W ************************** TEMPERATURES **************************** STATIC INLET FLUID TEMPERATURE, DEG C 71.0 STAGNATION FLUID TEMP RISE ALONG COLDPLATE, DEG C 38.8 TOTAL STAGNATION FLUID TEMP RISE, DEG C 38.8 STATIC EXIT FLUID TEMPERATURE, DEG C ISOTHERMAL COLDPLATE TEMPERATURE, DEG C MAXIMUM COLDPLATE TEMPERATURE, DEG C 140.9

8 Comparison of results between Kraus and Bar-Cohen, and COLDPLATE: Kraus and Bar-Cohen COLDPLATE: Both Side Heating COLDPLATE: Single Side Heating Isothermal Temp C Pressure Drop in H2O 2.09* * Note that Kraus and Bar-Cohen used their Entrance and exit loss coefficient Figure 10.8 which is for triangular fins rather than the correct Figure 10.9 which is for rectangular fins. This accounts for the difference in their results versus COLDPLATE.

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