Transmission Of Heat Question 130
Question: 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 T2 and T1 (T2 > T1). The rate of heat transfer through the slab, in a steady state is $ ( \frac{A(T _{2}-T _{1})K}{x} )f $ , with ¦ which equal to
[AIEEE 2004]
Options:
A) 1
B) $ \frac{1}{2} $
C) $ \frac{2}{3} $
D) $ \frac{1}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
Equation of thermal conductivity of the given combination $ K _{eq}=\frac{l _{1}+l _{2}}{\frac{l _{1}}{K _{1}}+\frac{l _{2}}{K _{2}}}=\frac{x+4x}{\frac{x}{K}+\frac{4x}{2K}}=\frac{5}{3}K $ . Hence rate of flow of heat through the given combination is $ \frac{Q}{t}=\frac{K _{eq}.A(T _{2}-T _{1})}{(x+4x)}=\frac{\frac{5}{3}K,A,(T _{2}-T _{1})}{5x} $ =$ \frac{\frac{1}{3}K,A,(T _{2}-T _{1})}{x} $ On comparing it with given equation we get $ f=\frac{1}{3} $
BETA
