Given the two domains pictured below, calculate the heat transfer rate (Q [W]) for each case.
The domain on the left is insulated on the left, right, and right half of the bottom side, while the domain on the right is only insulated on the left and right sides. The domain on the left has the left half of the bottom side held at constant Tc and the domain on the right has the entire bottom side held at Tc. Both domains have the top surfaces held at Th.
The Attempt at a Solution
I've solved for the temperature distributions numerically; however, I don't know how to calculate the heat transfer rate for the left scenario.
I believe the domain on the right would simply be:
But I am not sure how to treat the domain on the left because of the half-insulated base. Any help/hints would be appreciated. Thanks!