Thermal Conductivity Equations via the Improved Adomian Decomposition Methods
Applied and Computational Mathematics
Volume 9, Issue 3, June 2020, Pages: 30-55
Received: Apr. 1, 2020; Accepted: May 11, 2020; Published: May 27, 2020
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Author
Ashenafi Gizaw Jije, Department of Mathematics, Faculty of Natural and Computational Sciences, Gambella University, Gambella, Ethiopia
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Abstract
Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.
Keywords
Fins, Adomian Decomposition, Thermal Conductivity Equation, Nonnlinear
To cite this article
Ashenafi Gizaw Jije, Thermal Conductivity Equations via the Improved Adomian Decomposition Methods, Applied and Computational Mathematics. Vol. 9, No. 3, 2020, pp. 30-55. doi: 10.11648/j.acm.20200903.11
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Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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