Heat Transfer in Solid by Using Linear Differential Equation

Abstract

Differential equations are fundamental importance in engineering mathematics because any physical law s and relations appear mathematically in the form of such equations. . The rate of heat conduc- tion in a specified direction is proportional to the temperature gradient, which is the rate of change in temperature with distance in that direction. In this paper we discussed about first order linear homogeneous equations, first order linear non homogeneous and the application of first order differential equation to heat transfer analysis particularly in heat conduction in solids.

Introduction

Conclusion

Finding the temperature distribution in the rod is T (x) ? 216.67 ? 94.97x ?C / m by the method of solution of first order ordinary differential equation. This same procedure is often utilized in Heat convection in fluids and Radiation of heat in space. This application is useful for solving several different types of Fluid Mechanics Analysis. Fundamentally, it consists of finding optimal solution of first order ordinary linear homogeneous equations and first order ordinary linear non homogeneous equations.

References

[1] Ahmad, Shair, Ambrosetti ?A textbook on Ordinary Differential Equations?, Antonio 15th edition, 2014. [2] Earl A. Coddington?An Introduction to Ordinary Differential Equations? 1st Edition. [3] Victor Henner, Tatyana Belozerova,?Ordinary and Partial Differential Equations? Mikhail Khenner January 29, 2013 by A K Peters/CRC Press. [4] Yunus A. Cengel, \"Heat Transfer A Practical Approach\", Tata McGraw Hill, 2010. [5] Frank P. Incropera and David P. Dewitt, \"Fundamentals of Heat and Mass Transfer\", John Wiley & Sons, 1998. [6] Venkateshan. S.P., \"Heat Transfer\", Ane Books, New Delhi, 2004. [7] Ghoshdastidar, P.S, \"Heat Transfer\", Oxford, 2004. [8] Nag, P.K., \"Heat Transfer\", Tata McGraw Hill, New Delhi, 2002. [9] Holman, J.P., \"Heat and Mass Transfer\", Tata McGraw Hill, 2000.

Copyright

Copyright © 2023 Sunilkumar Kuwarlal Shende , Jayprakash Laxman Matlam, Dipak Govindrao Lanjewar . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.