Question

A parallel-sided slab is made of two different materials. The upper half of the slab is made of material X, of thermal conductivity l ; the lower half is made of material Y, of thermal conductivity 2l. In the steady state, the left hand face of the composite slab is at a higher, uniform temperature than the right-hand face, and the flow of heat through the slab is parallel to its shortest sides. What fraction of the total heat flow through the slab passes through material X ?

• A. 1/4
• B. 1/3
• C. 1/2
• D. 2/3

Answer 1

Answer: (B)

1/3

Answer 2

$\frac{\Delta Q}{\Delta t} = - \lambda A\frac{dT}{dx}$ Ž l_y = 2 l_x = 2l

Ž – A $\frac{dT}{dx}$ = constant = a, $\frac{\Delta Q_{x}}{\Delta t}$ = al

Ž $\frac{\Delta Q_{y}}{\Delta t}$ = 2al

Ž $\frac{\Delta Q}{\Delta t} = \frac{\Delta Q_{x}}{\Delta t} + \frac{\Delta Q_{y}}{\Delta t}$ = al + 2al = 3al

\ Fraction = $\frac{\Delta Q_{x}/\Delta t}{Q/\Delta t} = \frac{1}{3}$