An approximate solution of transient heat conduction equation by the Galerkin method

This thesis presents a semi-analytical method to solve the transient heat conduction equation for inhomogeneities material using the Galerkin method. Symbolic algebra software is extensively used to perform necessary calculations.; In this thesis, the temperature distribution is expressed in a series of polynomials each of which satisfies the given homogeneous boundary conditions. The coefficients of these polynomials are found out by the Galerkin method. Symbolic algebra software works best while handling necessary algebra to generate admissible polynomials and build required matrices for solving for the coefficients.; Solutions to the problems arising in the electronic packaging field are a major part of this thesis. This thesis demonstrates the calculation of the temperature distribution for different geometries under the homogeneous boundary condition and initial condition. As this analysis involves very complicated computation, it is almost impossible to handle all the calculation without the help of symbolic algebra software.; Numerical examples are presented and the results are compared with the known analytical solutions and numerical solutions from finite element analysis, Ansys. It was shown that a reasonable level of convergence is achieved with the present method.