Sorry for the long post but I could use some help. I am having a problem with a professor in my heat transfer class and I was wondering if anyone could help. Before I go on, I am not looking to get points back on my test, I only lost 2 so I dont care, I just want to know whether I am right or not. We recently had a test where there was a question in which we had to use the finite difference method to solve for the unknown temperatures in a rectangular 2D block. The professor took the question from the text book and modified it for the test. In the test the 2D block was insulated on two sides and the other two sides were held at 300 C. The known temperatures at various nodes inside the block were HOTTER than 300 C and there was NO heat being added to the system. The prompt told us the block was in a STEADY STATE condition and that we should us the finite difference method to solve for the temperatures at the various unknown nodes. Now, my problem is that this situation cannot possibly be in a steady state condition. Two sides insulated, two sides held at 300 C and temperatures within being hotter than 300 C with NO heat addition. The heat from inside must be conducting too the the boundaries held at 300C until the entire block is at a uniform temperature of 300 C. Now the issue here is that during this test nobody (including the professor) realized that this situation could not be at steady state and we all solved the problem using the steady state form of the heat diffusion equation with no heat generation. When we received our tests back nearly the entire class had gotten the problem wrong. The professor then showed us his method in which he was also used the steady state heat diffusion equation without heat generation and he arrived at a different solution than the rest of the class. He used the equation differently than the rest of us and arrived at a different answer however when I showed him my solution he was unable to explain why it was wrong and just assumed that I typed the numbers into my calculator wrong, which is ridiculous because the majority of a 30+ student class arrived at the same answer as me. So I have told my professor that this question was flawed because it told us to assume steady state but it is clearly a transient problem. However he still believes that if you just assume steady state (even though it is clearly not) you will arrive at his answer. So finally why I need your help. It is obvious to me that applying the steady state diffusion equation with no heat generation to this problem can lead to different (incorrect) solutions depending on the particular way you apply it. Is there a way to prove this to the professor other than just applying it in different ways and arriving at different solutions? Because if I just work out the problem in different ways and arrive at different answers he always assumes I made an error and he wont try it for himself.