Unstructured Finite Element Method for Transient Heat Conduction of Moving Heat Source

The primary objective of this study is to develop a space-time finite element formulation of heat transfer involving a moving heat source so that small time steps can be used in area of large time rates of change of temperature. The weighted residual process will be used to formulate a finite element method in a space and time domain based upon the continuous Galerkin method. A mesh refinement algorithm which will be on adaptively controlling the time step is developed and implemented for one-dimensional moving heat source simulation. A moving heat source will produce steep gradients of the temperature within and near the region of moving source. The space-time domain is divided into time-slabs and the mesh generator produces a triangular mesh that has small elements close to the front of moving source and relatively large elements away from the front. A series solution to the moving heat source problem derived will be used to compare to the numeric results obtained from the adaptive refinement technique developed in this study.