Finite element method for heat transfer phenomenon on a closed rectangular plate

Abstract

In the diagnosis and control of various thermal systems, the philosophy of heat fluxes, and temperatures are very crucial. Temperature as an integral property of any thermal system is understood and also, has well-developed measurement approaches. Though finite difference (FD) had been used to ascertain the distribution of temperature, however, this current article investigates the impact of finite element method (FEM) on temperature distribution in a square plate geometry to compare with finite difference approach. Most times, in industries, cold and hot fluids run through rectangular channels, even in many technical types of equipment. Hence, the distribution of temperature of the plate with different boundary conditions is studied. In this work, let’s develop a finite element method (code) for the solution of a closed squared aluminum plate in a two-dimensional (2D) mixed boundary heat transfer problem at different boundary conditions. To analyze the heat conduction problems, let’s solve the two smooth mixed boundary heat conduction problems using the finite element method and compare the temperature distribution of the plate obtained using the finite difference to that of the plate obtained using the finite element method. The temperature distribution of heat conduction in the 2D heated plate using a finite element method was used to justify the effectiveness of the heat conduction compared with the analytical and finite difference methods.