The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer

Abstract

Abstract Heat transfer problems are of critical importance in almost all areas of engineering and technology, especially in mechanical engineering. Over several decades, engineers and scientists have been working on solving these problems by designing and optimizing components and systems needed to transfer, handle, and store thermal energy. Heat can be transmitted via different mechanisms, like conduction and convection. In this article, two nonlinear heat transfer problems are solved by allowing for the changeable specific heat coefficient. The mathematical calculations are permitted out via a Hermite wavelet method (HWM). By using HWM, the nonlinear unnatural governing equations are abridged to an interconnected system of algebraic equations. The current outcomes are compared with the Homotopy perturbation method (HPM), variational iteration method (VIM), differential transformation method (DTM), and the accurate solutions to confirm the exactness of the future method. The HWM method is helpful and practical for solving the nonlinear heat diffusion equations linked through variable thermal conductivity conditions. Moreover, the equation outcomes in boundary points, and scheming the inaccuracy differences with the accurate amount, the advantages and disadvantages of this technique are considered. The results reveal that the HWM can attain more appropriate consequences in predicting the solution of such problems.