Question

If the sides of a wall having thermal conductivity $K$ are maintained at temperatures of $T_1$ and $T_2$, the temperature as a function of $x$ can be written as $T\left(x\right)=(T_2-T_1)\left(\frac{x}{L}\right)+T_1$
Find the heat flux through the wall.
Take $T_1>T_2$

• A. $\frac{K{T}_1}{L}$
• B. $\frac{K{T}_2}{L}$
• C. $\frac{K(T_1-T_2)}{L}$
• D. $0$

Answer 1

The correct option is C $\frac{K(T_1-T_2)}{L}$

Heat flux is the rate of heat transfer per unit area,
$\Rightarrow \dot{q}=\frac{\dot{Q}}{A}=-K\frac{dT}{dx}$
$\Rightarrow \dot{q}=-K\frac{d}{dx}\left[\right(T_2-T_1)\frac{x}{L}+T_1]$
$\therefore \dot{q}=\frac{K(T_1-T_2)}{L}$