In thermodynamics, is it possible to fin a quantitative and correlative relationship between amount of heat on a disapative structure, to shape of the geometric figures formed?

do you mean: is it possible to work out how heat will distribute itself throughout an object so that you can design the object so this distribution of heat has favourable properties?

 

if so, yes. its simple heat transfer. a lot of equations (they aren't really complex but you'd need to break the structure into lots of little parts to deal with it) so its better left to computer modelling rather than a calculation by hand(unless you want to spenda few years working it out)

Well I am mostly asking the question of can you form a quantatative relationship between the structures formed in the non equilibrium, and the heat being enforced on the system?

I'm not sure I'm following you. If you are talking about an engineering application then do you mean you want to relate the rate of heat transfer through a structure (a fin, for example) while the heat transfer itself is significant enough to cause changes to the structure itself? If so, I can think of basic examples, such as the arms of a heat dissipative device shortening as it cools and therefore losing surface area. A problem like this is pretty straightforward, but this is never an issue since fins are not designed to chock heat flow and therefore the structural changes would have a negligible effect. A better example might be found in some grad texts on hot rolling and other common metalworking.

 

I may be misunderstanding you. If you are talking about how products formed in, let's say combustion, affect the heat transfer based on their chemical structure, or some other micro level question, please disregard.