Chapter 17, Problem 1P

To determine

State the conditions at which the temperature distributions in the wall will be a straight line.

Explanation of Solution

During the steady and one-dimensional transfer of heat with unchanged wall thermal conductivity, the temperature distributions in the plane wall will be a straight line when the heat is conducted through the wall.

Write Fourier’s law of heat conduction through the wall as follows:

  ${\dot{Q}}_{\text{cond,wall}}=-kA\frac{dT}{dx}$

Here, ${\dot{Q}}_{\text{cond,wall}}$ is the rate of heat conduction through the wall, $k$ is the thermal conductivity of the wall, $A$ is the area of the wall, and $\frac{dT}{dx}$ is the temperature gradient.