1. The problem statement, all variables and given/known data I am curious about the situation of heat transfer between parallel horizontal plates in an enclosed space (particularly with the lower plate being higher temperature and subjected to a steady heat flux) with the enclosure itself being composed of a fictional "perfect insulator". The self-teaching heat transfer text I have mentions how to calculate Grb and the Nusselt number based on Grb, but it only covers situations when the dimensions of the two plates are identical. How should I handle situations where the lengths and widths of the plates are not identical? For example, what if the top plate is 1 meter x 1 meter, but the bottom plate is only .5 meters x .5 meters? Consider the bottom plate to be centered inside a perfect insulator whose surface area, when added to that of the bottom plate itself, is 1 m2. Also, should I use the Nusselt number (and, by logical extension, h) calculated from the standard horizontal plate/bottom plate hotter equation if one or both of the plates are equipped with, say, fins to improve surface area? Or should I calculate h locally for the fins according to equations that pertain to them individually? 2. Relevant equations Grb = (gβ-1(T1 - T2)b3)/v2 For Grb > 4x105, Nub = .068(Grb)(1/3) (note that the situation I'm currently working with appears to have a Grb > 4x105, so I have omitted the other two equations for Nub) 3. The attempt at a solution Lacking any other guidance, I decided to solve the problem of the bottom hot plate being smaller by adjusting the value of b. I used an average of the distance between the midpoint of the bottom plate and the midpoint of a "virtual" plate of identical dimensions embedded within the top plate and moved to the furthest extremes the virtual plate could be moved without encroaching on the perfectly insulated sides of the enclosure. This resulted in a much higher value of b. I am still a bit unsettled as to how to calculate q in this circumstance - by using the surface area of the top plate or the bottom plate. With the adjusted value of b, I would think I'd use the surface area value of the top plate, but . . . I also attempted a different tack involving a double integral, but I do not think my approach was correct. It resulted in an integral I was not skilled enough to solve on my own, which is another matter altogether. I could dig up that work if it is deemed at all relevant to this discussion. When adding fins to the situation, I simply used Nub to calculate h, though I am not sure if doing so is appropriate. I am also still unsettled as to which array of plates I should use to calculate q (the ones on the top plate, or the bottom) when using an adjusted value for b; obviously, this situation is further confused by the question of whether or not an adjusted value of b is even appropriate.