Treffer: Numerical Study of Two-Dimensional Transient Heat Conduction Using Finite Element Method.

A mathematical formulation applied to a numerically study of two dimensional transient heat conduction in a building slab to determine the temperature distribution as a function of time. The finite element method is a method of choice and it is a numerical procedure for analyzing structures and continua. Usually the problem addressed is too complicated to be solved satisfactorily by classical analytical methods. The Galerkin method is the method of choice in the formulation, which involves transient heat conduction by using the bilinear quadrilateral element discretization; the integration of weighted residual of the differential equation and also the boundary condition was perform using finite element method. A computer program is developed using Matlab to run the analysis. The finite element analysis software MSC Nastran has also been used to analyze the temperature distribution and for the comparison purposes. It was found that temperature declined in the early stage for delta time, Δt =1 second which is more efficient. For comparison with MSC Nastran, different delta time for 32 and 200 elements is taking into consideration. The result of the analysis shows that the error is less than 1% by using Matlab and MSC Nastran, which was deemed satisfactory. There are 3 nodes selected for comparison, which is Node 5-ML, Node 23-ML and Node 41-ML for Matlab simulation tools and Node 5-MSC, Node 23-MSC and Node 41-MSC is from MSC Nastran simulation tools. It can be said that with 32 elements, Δt =0.4 s shown not much difference as most of the point situated at the same exponential curve line for both MSC Nastran and Matlab simulation tools. It achieves saturation at 213°C for Node 5-ML and Node 5-MSC, 175°C for Node 23-ML and Node 23-MSC and 67°C for Node 41-ML and Node 41-MSC. [ABSTRACT FROM AUTHOR]