International Journal of Research and Scientific Innovation (IJRSI) | Volume VI, Issue VII, July 2019 | ISSN 2321–2705

Solution of 1-Dimensional Steady State Heat Conduction Problem by Finite Difference Method and Resistance Formula

Nagesh Babu Reddy K T

Assistant Professor, Department of Humanities & Sciences (Mathematics), Navodaya Institute of Technology, Raichur, Karnataka, India

Abstract: In mathematics, Finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. Finite differences method is used in soil physics problems. An important application of finite differences is in numerical analysis, especially in numerical differential equations, which aim at the numerical solution of ordinary and partial differential equations respectively. Finite Difference Method is mainly preferred because of we can solve the problems which are difficult to solve from conventional engineering methods. In this paper we are solving the one dimensional steady state heat conduction problems by finite difference method and comparing the results with exact solutions obtained by using Resistance formula. In this paper we are solving the problems by using the Resistance formula because it gives the exact solutions. To solve the problem by Finite Difference Method we are using some mathematical applications they are Taylor series, Fourier series, crammer’s rule. After the solutions are obtained from the both methods we have to draw the graphs to show that both the obtained results are equal.

Keywords: Finite Difference Method, Resistance formula, Fourier series, Taylor series, crammer’s rule.

I. INTRODUCTION

In this paper we are solving the heat transfer problems by using the finite difference method. Same problem also solved by using the resistance formula. Because solving the problems by using resistance formula is simple and it gives the exact solutions. After this we are comparing results obtained by these two methods.
The equation for solution of finite difference method is basically obtained by 3-Dimensional general heat conduction equation, since we are solving only 1-Dimensional heat conduction problem the equation is reduced only x-direction and we are making assumption that heat generation in y and z is negligible.
Once the solution is obtained by this method we are comparing these results with the results obtained by solutions of resistance formula by assuming the area as unity (i.e. 1m²).