Numerical Study of the Heat Transfer Process in a Flat Wall with Internal Heat Sources under Boundary Conditions of the First Kind

Abstract

Numerical Study of the Heat Transfer Process in a Flat Wall with Internal Heat Sources under Boundary Conditions of the First Kind

Zinina S.A., Popov A.I., Bragin D.M.

Incoming article date: 18.02.2022

In this paper, we study the process of heat conduction in a flat wall with an internal heat source under boundary conditions of the first kind. Various numerical and analytical methods are used to solve heat transfer problems. Each method has a number of advantages and disadvantages. The paper proposes to use the numerical method of finite differences. The original differential equation, as well as the boundary conditions, are approximated using a finite difference scheme. The essence of the method is to apply a spatiotemporal grid to the computational domain. For each grid node, a difference relation is written (the original differential equation with boundary conditions is replaced by the corresponding expressions obtained using the difference scheme). Solving this scheme, we obtain the temperature values ​​in the plate for each step in time and coordinate. On the basis of the solution obtained, graphical dependences of temperature on time and coordinates are constructed, and their analysis is carried out.

Keywords: finite difference method, thermal conductivity, plate, internal heat source, boundary conditions of the first kind