Analytical and Numerical Methods for SolvingHeat Conduction problems Transient

The modeling of systems involving heat conduction problems is widely spread among scientists and engineers due to their wide range of applications in science and technology. In this work, we will present some important analytical and numerical results concerning heat conduction problems and their applications. First, we will use the Fourier law of heat conduction to derive the composition equation of heat transfer for different regions. The concept of boundary and initial conditions will also be illustrated. The heat conduction problems subject to some boundary and initial conditions for various domains will be solved analytically using the separation of variables, Laplace transforms, Duhamel's and Green's function methods. Numerical approach based on the finite difference method (FDM) has been analyzed and implemented to solve some heat conduction problems. A comparison between the analytical and numerical results have been drawn. Numerical results have shown to be in a close agreement with the exact ones. In fact, the FDM is one of the most efficient numerical methods for solving heat diffusion problems.