Numerical analysis of one dimensional heat transfer on varying metal

Abstract

Heat is an energy that we often encounter in our daily lives. Heat can be transferred from one medium to another, such as a solid medium. Heat transfer in a solid is called heat conduction or diffusion. Numerical analysis is one approach used to solve differential diffusion in many cases. In this paper, the concern is the proposed finite difference method to simulate one-dimensional heat transfer on varying metals. This numerical method utilizes the Neumann boundary conditions as well as the Taylor series in finding differential diffusion solutions. The solution obtained was applied and simulated in the case of heat transfer by conduction on various metals. From this simulation, we can obtain data in the form of temperature distribution across various metals by adjusting to boundary conditions. Then, the distribution is used to predict when various metals reach their equilibrium temperature. The final equilibrium temperature on varying metal must satisfy Thermodynamics Law. In order to illustrate the accuracy, the varying boundary conditions are presented. The results obtained in the form of temperature distribution will be simulated with the help of the MATLAB program to obtain conclusions from the objects of this paper. The conclusion indicates that using finite difference is accurate in some boundary conditions.

Simulations and Results for the Heat Transfer Problem

“…Other operations like finding the square root of a number, solving a system of linear equations, solving a differential equation are made possible only through the use of numerical algorithms (Harbrecht & Multerer, 2022) that can be studied in mathematics, studing elements of finite method (Yang, 2018), an efficent solving method for nonlinear convection diffusion equation (Cui et al, 2018) and numerical analysis of one dimensional heat transfer (Mahardika & Haryani, 2020).…”

An approach to solving real-life problems using normal distribution. Approximation of results using the Lagrange-Euler method

“…Comparison of Numerical Methods are applied. Distributed energy resource [1], distributed energy of heat transfer problem are connected with with associated Electric power systems interfaces [3].…”

“…In the end, we will provide our conclusions on the performance of the numerical methods One of the approaches that has gained much attention in recent times is the use of aproximations. [1][2][3][4]. Nonlinearities in the problem make solving and analyzing initial boundary value problems.…”

Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation

“…It is easy to solve PDEs using this method [18]. Taylor series approach is used to find the solutions of a partial differential equation in this method [19]. The technique of this method is that all the derivatives in a partial differential equation are replaced by their finite difference approximations, and the PDEs are converted to a set of linear algebraic equations.…”