Heat Transfer During Re-entry

Hey, just a quick question. I am trying to figure out the max temperature that will be reached inside a case on a rocket tumbling back to earth. The rocket will go to about 100km and fall back down. What I am curious about is how could one determine the temperature inside an aluminum housing since the only information I have available is the size of the box, the properties of the material and a rough idea of the speed, which should be about 1400 m/s roughly speaking. Are there any formulas that allow for determination of heat flux without knowing the change in temperature since I am trying to solve for the change in temperature? Or is there a rough formula that can be used to figure this out, the simpler the better, since this is for rough calculation. I have attempted to utilized lump capacitance after finding the biot number and such but the calculation of all the necessary values for that have errors due to using yet more equations and the end results are rather jacked up. I also used the supposed "heat shield engineer's" rule of thumb, as said by wikipedia (might get some flak for that), to determine that the temp is roughly 1 degree kelvin for every m/s.....


TL;dr; What are some formulas to roughly estimate how hot it will be inside an aluminum housing inside of a rocket if I know the area of the housing and the speed of the rocket?

There are a lot of variables, and a lot of calculation = formulas that may help. The hot spots on the Concord supersonic passenger plane, that flew about that fast at 40,000 feet were about 250 degrees c, but that was likely because thermal insulation prevented air convection on the inner surface of the sheet aluminum. Also your heating time will be less than for the Concord. The contents, if any, inside your aluminum housing will be a heat sink that heats slowly, so the maximum temperature of the contents will likely occur about the moment your tumbling rocket hits the ground. Neil