A hot 5x5-cm² surface at base temperature Tb = 100°C is to be cooled by attaching 3-cm-long pin fins of parabolic profile with the base diameter of 5 mm. The fin is made of aluminum (k=200 W/mK) and there are 25 fins installed. The temperature of the surrounding medium is 20°C, and the convective heat transfer coefficient is assumed to be 100 W/m²K. a. Determine the overall effectiveness of the heat sink design. Please show all calculations. b. Calculate the effectiveness when the base temperature is changed to 60°C. What is the heat transfer by the heat sink? What can you conclude? c. Using Tb = 100°C, study the effect of changing the fin length (say to 4, 5, 6, 7, 8, and 9 cm) to the effectiveness. You do not need to show calculation here and you may use Excel or EES to perform the calculations. Plot the effectiveness and heat transfer by the heat sink versus fins length. What can you conclude? d. Using Tb = 100°C and fin length of 3 cm, study the effect of changing the thermal conductivity (say from 100 W/mK to 250 W/mK with interval of 50 W/mK) to the effectiveness. You do not need to show calculation here and you may use Excel or EES to perform the calculations. Plot the effectiveness and heat transfer by the heat sink versus thermal conductivity. What can you conclude?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:A hot 5x5-cm² surface at base temperature Tb = 100°C is to be cooled by attaching 3-cm-long pin fins of parabolic profile with the base diameter of 5 mm. The fin is made of aluminum (k=200 W/mK) and there are 25 fins installed. The temperature of the surrounding medium is 20°C, and the convective heat transfer coefficient is assumed to be 100 W/m²K. a. Determine the overall effectiveness of the heat sink design. Please show all calculations. b. Calculate the effectiveness when the base temperature is changed to 60°C. What is the heat transfer by the heat sink? What can you conclude? c. Using Tb = 100°C, study the effect of changing the fin length (say to 4, 5, 6, 7, 8, and 9 cm) to the effectiveness. You do not need to show calculation here and you may use Excel or EES to perform the calculations. Plot the effectiveness and heat transfer by the heat sink versus fins length. What can you conclude? d. Using Tb = 100°C and fin length of 3 cm, study the effect of changing the thermal conductivity (say from 100 W/mK to 250 W/mK with interval of 50 W/mK) to the effectiveness. You do not need to show calculation here and you may use Excel or EES to perform the calculations. Plot the effectiveness and heat transfer by the heat sink versus thermal conductivity. What can you conclude?

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