Question

Two material of thermal conductivities 5 and 10 W/k K having a thickness of 0.2 m each are used to construct a composite wall. The overall thermal conductivity of the wall is

• A. 0.15 W/m K
• B. 6.67 W/m K
• C. 3.33 W/m K
• D. 7.5 W/m K

Answer 1

The correct option is B 6.67 W/m K

$\begin{array}{cc}\text{for the same heat transfer rate}& \\ Q& =\frac{T_1-T_2}{\left(\frac{L_1}{k_{1}A}\right)+\left(\frac{L_2}{k_{2}A}\right)}=\frac{T_1-T_2}{\left(\frac{L_{eq}}{k_{eq}A}\right)}\\ \frac{L_1}{k_{1}A}+\frac{L_2}{k_{2}A}& =\frac{L_{eq}}{k_{e}q.A}\\ \frac{0.2}{5}+\frac{0.2}{10}& =\frac{0.4}{k_{eq}}\\ k_{e}q& =6.67W/m-K\end{array}$