Transient thermal analysis

Hi,



I have developed a 2D transient thermal analysis FE code which doesn't
seem to be correct. I am sure there is a conceptual problem in the
formulation itself which I have not been able to understand and could
not find concrete information in books.



I am putting up the question in a very simplified form so as to address the correctness of the formulation.



Let's say we have a square of unit length with 4 nodes at each corner
(Q4 element). Initial temperatures are specified as 100 for all nodes