# Force Matrix for Transient Thermal Analysis

1. Oct 21, 2009

### Shriram

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
(at t=0). The temperature of the nodes 1 and 2 are specified as 200
and 300 at the first time step and we investigate the temperature distribution on other 2
nodes with time say 0 to 100 seconds (with the specified temperatures
maintained). No other thermal load is applied.

-- Now, while solving the FE discreet equation, during the first time step would there be any force matrix on the R.H.S?

-- If no, then would the R.H.S be simply (1/dt)*C*tn (using time integration parameter'theta=1'). 'C' being the specific heat matrix, 'tn' is vector of initial dofs and
'dt' is time-step. (Reference: Ansys theory manual, transient thermal
analysis, eq 17-33)

I have tried to keep the problem as simple as possible without much
theory. Hope it is clear. Any suggestion or comment is deeply
appreciated.

Thanks,
Shriram
------------------------
Research Assistant
Structural and Multidisciplinary Optimization Lab.
University of Florida