Simulation of Temperature Distribution In a Rectangular Cavity using Finite Element Method

TL;DR

This study uses the finite element method to simulate temperature distribution in a fluid-filled rectangular cavity with heated walls, analyzing transient conduction and steady convection effects using MATLAB.

Contribution

It integrates transient conduction and steady convection-diffusion equations with finite element analysis for cavity temperature simulation.

Findings

Temperature distribution contours generated

Finite element method effectively modeled heat transfer

Results show influence of time and velocity on temperature

Abstract

This paper presents the study and implementation of finite element method to find the temperature distribution in a rectangular cavity which contains a fluid substance. The fluid motion is driven by a sudden temperature difference applied to two opposite side walls of the cavity. The remaining walls were considered adiabatic. Fluid properties were assumed incompressible. The problem has been approached by two-dimensional transient conduction which applied on the heated sidewall and one-dimensional steady state convection-diffusion equation which applied inside the cavity. The parameters which investigated are time and velocity. These parameters were computed together with boundary conditions which result in temperature distribution in the cavity. The implementation of finite element method was resulted in algebraic equation which is in vector and matrix form. Therefore, MATLAB programs used to solve this algebraic equation. The final temperature distribution results were presented in contour map within the region.