Midterm quiz 151C Thermosciences
Convection heat transfer

• Quiz is open book and open notes. You must finish the problems independently. No
discussion is allowed.
• Quiz is due Midnight Thursday 05/07.
• Please define variables you use that are not in the problem statement, and clearly write
down all assumptions you make.

1. (30 points) Provide a brief answer to the following questions.
a. For internal pipe flow, how does Tb (bulk temperature) increase along the pipe
for: (i) constant wall heat flux, and (ii) constant wall temperature? Briefly explain.

b. Comparing convection heat transfer coefficient of air and water, which one is
usually higher and why?

c. What’s the difference between the Nusselt number and the Biot number?

2. (30 points) Computer CPU chips have highly integrated IC circuits that lead to excessive
heat generation during operation. Consider a 1 cm´1 cm CPU chip that generates a
constant heat flux of qw = 40 W/cm2. Suppose we want to cool the CPU by blowing air
over its surface using a fan. The air temperature is T∞ = 20 oC. The maximum air velocity
that the fan can generate is 10 m/s.
a. What is the average heat transfer coefficient over the CPU surface at the
maximum air velocity?
b. Is our proposed method sufficient to cool the CPU? The CPU chip will fail if it
exceeds a wall temperature of 120 oC.

The properties of air at 70 oC [/!] 1.03 " [/] 1009 [/] 0.029 [ ] 2.05´10-5 [#/] 2´10-5 [#/] 2.86´10-5 [−] 0.7

3. (40 points) A heat exchanger is formed from a section of thin-walled copper tubing (total
length = 12 m, diameter = 1.5 cm), which is used to reject heat from an internal water
flow (flow rate = 0.01 kg/s, inlet temperature = 70 oC) to the ambient (still air at T∞ = 20
oC). It is placed horizontally. The flow is hydrodynamically and thermally fully
developed.
a. Calculate the inside average heat transfer coefficient ℎ\$6666. You can assume that the
wall temperature is close to the fluid temperature of 70 oC, and evaluate the
properties at 340 K. This case is neither a constant wall temperature nor a
constant heat flux. For a rough approximation, we take the Nusselt number to be
the average of the constant temperature and constant flux situations.
b. Calculate the outside average heat transfer coefficient ℎ%666. Again, you can assume
that the wall temperature is approximately 70 oC.
c. What is the fluid temperature at the exit?
d. What is the total heat energy released from the water to the ambient? 