Consider heat conduction through a wall of thickness L and area A. Under what conditions will the temperature distributions in the wall be a straight line?
The condition under which the temperature distribution in the wall is a straight line.
Explanation of Solution
The temperature distribution of a wall with thickness L and area A is shown in the figure below:
The one-dimensional steady state heat conduction equation without heat generation for the wall is
Here, T is the temperature and x is the direction of flow of heat.
Integrate equation (1) with respect to x.
Where, c1 is the constant of integration.
Further integrate the equation (2) with respect to x.
Now, calculate the constant of integration.
At x = 0, T =T1
Substitute the value in equation (3);
Substitute the value of c2 in equation (3);
Substitute the value of c1 and c2 in equation (3);
The above equation is in the form of a straight line equation y = mx+c. Thus, the distribution of temperature in the plane wall will be a straight line during steady-state one dimensional heat transfer.
Thus, the following are the conditions during which the temperature distribution in the wall is a straight line.
- Heat conduction in one-dimensional steady state direction.
- Thermal conductivity should be constant.
- There is no any internal heat generation in the wall.
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Chapter 3 Solutions
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