| Nonlinear heat-wave propagation in a rigid thermal conductor |
| Paper ID : 1095-ISCHU |
| Authors |
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Nahla Bahaa El Din * Mathematics department, Faculty of science, Helwan university. |
| Abstract |
| The objective of this article is to present the nonlinear one-dimensional equations of damped heat wave propagation in a rigid thermal conductor slab and predicts the dependence of second sound velocity on temperature and heat flux. The suggested system evolved from a restriction to one spatial dimension and pure thermodynamics of a thermo-electro elasticity model, nonlinear evolution equations for temperature and heat flow. Nonlinear systems of partial differential equations in mathematical physics are widely recognized to be a prominent research subject of ongoing interest. There are very few explicit solutions to such systems in the literature. So, the numerical and approximation methods are very important to study the behavior of the solutions of these systems. An efficient numerical method is presented for solving the proposed model. This method is a kind of fourth order compact finite difference. The matrix form and solving methods for the linear system of equations are discussed. Numerical experiments are given to demonstrate the efficiency and accuracy of the scheme proposed, and these show excellent agreement through test numerical examples. |
| Keywords |
| Nonlinear heat wave propagation equation, Fourth compact finite difference method, Error estimates |
| Status: Abstract Accepted (Poster Presentation) |