Question

A furnace has a wall of 20 cm thickness with thermal conductivity k = 2 W/mK. An insulation of 3 cm is applied which has thermal conductivity of 0.008 W/mK. On the left side of the wall there is flue gas at a temperature of ${700}^{\circ }C$ with convective heat transfer coefficient 100 $W/m^{2}K$. Outside temperature of the insulation is ${25}^{\circ }C$. Intermediate temperature is

• A. ${670.8}^{\circ }C$
• B. ${680.7}^{\circ }C$
• C. ${870.8}^{\circ }C$
• D. ${780.7}^{\circ }C$

Answer 1

The correct option is B ${680.7}^{\circ }C$


Let the interface temperature in T. So equivalent electric circuit.
Sine there is series convection between the thermal resistane so,
$\frac{T_{\infty }-T}{R_1+R_2}=\frac{T-T_{\text{insulation}}}{R_3}$
$\frac{700-T}{\frac{1}{100}+\frac{0.2}{2}}=\frac{T-25}{\frac{0.03}{0.008}}$
$T={680.76}^{\circ }C$