Abstract : This paper proposes a novel double interpolation approach to approximate the heat conduction equation with a source/sink term. The heat conduction equation is a fundamental partial differential equation governing the transfer of thermal energy in various physical systems. In many practical scenarios, source or sink terms are present, representing external heat generation or absorption. Traditional numerical methods may struggle to accurately capture the behavior of such systems. This approach enhances the accuracy of the approximation by effectively capturing the spatial and temporal variations of the temperature distribution. We demonstrate the effectiveness of our approach through numerical experiments and comparisons with exact solution. The results show that the double interpolation method offers significant improvements in accuracy and computational efficiency particularly when dealing with complex heat conduction problems involving source or sink terms. Overall, this study contributes to advancing the numerical approximation techniques for heat conduction equations with practical implications in various fields, including thermal engineering, materials science, and environmental modeling.
Cite : Singh, K. K. (2024). A Double Interpolation Approach To Approximate Heat Conduction Equation With Source/Sink Term (1st ed., pp. 289-302). Noble Science Press. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-30
References :
Ciegis R. (2009): “Numerical solution of hyperbolic heat conduction equation”,Mathematical Modelling and Analysis, 14(1):11-24.
Lekomtstev A.V. (2020): “About one numerical method of solution of a quasilinear heat conduction equation with delay”, AIP Conference Proceedings, 2312,050012.
Makhtoumi M. (2017): “Numerical solutions of heat diffusion equation over one dimensional rod region”,International Journal of Science and Advanced Technology, 7(3): 10-13.
Mansur W.J., Vasconcellos C.A.B. , Zambrozuski N.J.M. ,Rotunno Filho O.C. (2009): “Numerical solution for the linear transient heat conduction equation using an Explicit Green’s Approach”, International Journal of Heat and Mass Transfer, 52(3-4):694-701.
Reddy K T N.B. (2019):“Solution of 1-dimensional steady state heat conduction problem by finite difference method and resistance formula”, International Journal of Research and Scientific Innovation, VI (VII): 149-153.
Skrzypczak E.W. , Skrzypczak T. (2017): “Analytical and numerical solution of the heat conduction problem in the rod”, Journal of Applied Mathematics and Computational Mechanics, 16(4):79-86.
Wang P., Zheng K. (1999): “Determination of the source/sink term in a heat equation”, Electronic Journal of Differential Equations, 119-125.
White J. (2016): “Numerical solution of heat conduction in a heterogeneous multiscale material with temperature-dependent properties”, Journal of Heat and Mass Transfer, 138(6):061301,13 pages
