Analysis of 2-D Steady State Heat Conduction In A Slab Subjected With Different Types of Boundary Conditions Using Method of Lines

Abstract

Many disciplines in science and engineering, heat transfer plays a vital role and the problems associated with heat transfer are of great importance. Generally, two-dimensional steady state conduction is governed and transformed into a second order partial differential equation (PDE). Satisfying the differential equation along with four boundary conditions is essential for a solution to be valid. There are analytical solutions available, but only for simple boundary conditions and these are not suitable for complex boundary conditions. A technique for solving partial differential equations is Method of Lines (MOL), in which one dimension is discretized. In this study an analytical approach to a two-dimensional slab with steady state heat conduction under different types of boundary conditions is considered. The complete description of heat flow through slab using MOL is presented and the obtained PDEs are solved. Temperature distribution profiles in the slab by using MOL were plotted and compared with the profiles of analytical solutions by using MATLAB. The steady state analysis of temperature distribution in a slab with specified Dirichlet boundary conditions and Neumann boundary conditions was developed by using Method of Lines. From the profiles it is observed that as the number of lines increases, the error between analytical and MOL (semi analytical) solutions decreases, and the profiles of analytical and MOL converged which indicates the preference of higher number of lines in order to obtain accurate values.