Ok, lets apply that same idea to this configuration pictured above. Where the larger cube is "the right edge" and the fin is the "left edge" that should deflect. Lets assume the accerating force is a point force at the center of the back face of the larger cube. Im guessing I didn't set up my equations properly..

I understand what you are saying. If i grab my notebook by the right edge and accelerate it forward with my arm, the left edge deflects backwards. Does this happen ONLY because of air drag? If we repeat this experiment in a vacuum, and I accelerate my notebook forward while gripping the right edge, will the left edge still deflect due to internal inertial forces? In my mind, I think it would - am i wrong? Those are the stresses I want to measure. We can ignore Air drag for now. Will it still deflect/create internal stress at the base of the due to accelerating the larger cube?

Strange answers as in unrealistically small d values. The air resistance force may be negligible, but i figured The acceleration would result in some sort of inertial stresses. So in a vacuum are you saying the body would not experience higher internal stresses at the base of the fin, even if the accelerating force is a point force at the center of the larger cube volume? I may have the wrong approach here, but id expect for there to be higher stresses at the base of the fin because when I picture this body accelerating I imagine the fin deflecting backwards

what do you mean by closed form expression?

Interesting. This is what I was looking for

nothing. I think what I am going to do is consider a single (trapezoidal) face, and where the area that heat passes through increases as you go further towards the outer surface. Integrate like that, then multiply by 4 (for each edge). Either that or find an "effective" radius of the square and use the above formula