Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation

Abstract

In this paper, we examine the problem of two-dimensional heat equations with certain initial and boundary conditions being considered. In a two-dimensional heat transport problem, the boundary integral equation technique was applied. The problem is expressed by an integral equation using the fundamental solution in Green’s identity. In this study, we transform the boundary value problem for the steady-state heat transfer problem into a boundary integral equation and drive the solution of the two-dimensional heat transfer problem using the boundary integral equation for the mixed boundary value problem by using Green’s identity and fundamental solution.

Variational Approach to 2D and 3D Heat Conduction Modeling

“…Equation (5) with the given initial (6) and boundary conditions (7) will be solved by the Fourier method of separation of variables, i.e. the analytical solution will be sought in the form:…”