Question

A carpenter builds an outer house wall with a layer of wood $2.0cm$ thick on the outside and a layer of an insulator $3.5cm$ thick as the inside wall surface. The wood has $k=0.03W/m-K$ and the insulation has $k=0.01W/m-K$. The interior surface temperature is ${19}^{\circ }C$ and the exterior surface temperature is $-{10}^{\circ }C$. What is the rate of heat flow per square metre through this wall?

• A. $7.0W/m^2$
• B. $14.4W/m^2$
  
• C. $3.4W/m^2$
  
• D. $21.1W/m^2$
  

Answer 1

The correct option is A $7.0W/m^2$

Thermal resistance for a solid block of thickness $L$ and area $A$ =$\frac{L}{kA}$

Since the same amount of heat flows through wood and insulation layer,

Thermal resistance is in series.

Net thermal resistance $R_{th,net}=\frac{L_1}{k_{1}A}+\frac{L_2}{k_{2}A}=\frac{0.02}{0.03\times A}+\frac{0.035}{0.01\times A}=\frac{25}{6A}$

Using fourier's law of conduction,

$\stackrel{\bullet }{Q}=-kA\frac{dT}{dx}=\frac{\Delta T}{R_{th,net}}\Rightarrow Heatflux\left(\frac{\stackrel{\bullet }{Q}}{A}\right)=-\frac{-10-19}{\frac{25}{6}}=7W/m^2$

Hence, option A is correct.