3. a. Two metal cubes, one copper (Cu) and one aluminum (Al), with 4 cm edges ar

Question

3. a. Two metal cubes, one copper (Cu) and one aluminum (Al), with 4 cm edges are arranged as shown in Figure 1. Find (j) the thermal resistance of each cube, (ii) the thermal resistance of the two-cube system, (iii) the thermal current I and (iv) the temperature at the interface of the two cubes. b. The same cubes are now arranged as shown in Figure 2. Find (j) the thermal current carried by each cube from one side to the other, (ii) the total thermal current, and (iii) the equivalent thermal resistance of the two-cube system.

Explanation / Answer

The thermal current is given by

(Q/t)=K*A*(T2-T1)/L

as A=L^2

(Q/t)=K*L*(T2-T1)

for Aluminum

(Q/t)Al=238*4X10^(-2)*(100-20)=0.76 KW

for Copper

(Q/t)cu=397*4X10^(-2)*(100-20)=1.27 KW

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total thermal current (3-b)

I=(Q/t)Al +(Q/t)cu=2.03 KW

thermal resistance of the combination (3-b)

R=(L/KAl)+(L/Kcu)=4X10^(-2)*(1/KAl+1/Kcu)

R=4X10^(-2)*(1/238 + 1/397)

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