question_answer

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and\[2K\]and thickness\[x\]and\[4x,\]respectively are\[{{T}_{2}},\]and\[{{T}_{1}}({{T}_{2}}>{{T}_{1}})\]. The rate of heat transfer through the slab, in a steady state is\[\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f,\]with f equals                                                [AIEEE 2004]

A)  1       

B)       1/2    

C)  2/3      

D)       1/3

Correct Answer: D

Solution :

[d] Let the temperature of common interface be Rate of heat flow

And

In steady state, the rate of heat flow should be same in whole system i.e.,

Hence, heat flow from composite slab is

.(i)

[from Eq. (i)]

Accordingly,

(iii)

By comparing Eqs. (ii) and (iii), we get