Now we apply the simplification of fixing the temperature so that the temperature at x@0 and x@2L are equal. This can be achieved with two heat sources.
Start with the general equation as always.
Set the equations for the endpoints, and equate them to solve for the M and N.
This is our general equation with the constants solved for.
The temperature at the midpoint.
The temperature minimum (@L) can be reduced to a simple equation.
Heat Conduction in the Steady State