*Corresponding Author Email: shajrulla@gmail.com Proceedings of the International Conference on Academic Research in Science, Technology and Engineering, Vol. 1, Issue. 1, 2022, pp. 21-31 DOI: https://doi.org/10.33422/icarste.v1i1.14 Copyright © 2022 Author(s) ISSN: 2783-7742 online 21 Numerical Methods and Approximations for the Heat Transfer Problem Shkelqim Hajrulla 1* , Arban Uka 1 , Loubna Ali 2 , Taylan Demir 3 1 Epoka University, Albania 2 Tartous University, Syria 3 Atilim University, Turkey Abstract In many studies of heat transfer problems, many researchers have studied heat transfer problems by solving partial differential equations without using approximations or finding solutions with experimental data. This paper analyzes the heat transfer problem using a heat source in a closed environment and how it transfers in the neighboring sections. Referring to mathematical concepts, this work makes possible the simplification of the complexity that associates with such thermodynamic problems. In this framework, the research group discusses such a problem as a discrete one, easily computable, rather than treating it as a continuous one. The reduction of this problem to the solution of a simple system of linear equations and differential equations gives us the possibility to obtain the desired results regarding heat distribution. In many cases, differential equations are hard and difficult to solve. So, we deal with numerical methods to approximate the differential equations to algebraic equations and solve them. Comparing the different algorithms used and showing which of them works best in our testing conditions gives us the possibility of testing and comparing the results and the proper performance. The program will simulate the heat transfer of a single heat source in a closed environment. The results of the simulations will be presented in graphs and demonstrated in visual settings. In the end, our research will provide conclusions on the performance of the numerical methods. The purpose of this article is to study and analyze heat generation and heat transport in three-dimensional space with respect to neighboring sides of a closed environment. Keywords: transforms, decomposition method, image rendering, Poison equation, distribution