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Determination of One Dimensional Temperature Distribution in Metallic Bar Using Green’S Function Method
American Journal of Applied Mathematics
Volume 1, Issue 4, October 2013, Pages: 55-70
Received: Sep. 7, 2013; Published: Oct. 30, 2013
Authors
Virginia Mwelu Kitetu, Department of Mathematics and Computer Science, Faculty of Science, the Catholic University of Eastern Africa, Nairobi, Kenya
Thomas Onyango, Department of Mathematics and Computer Science, Faculty of Science, the Catholic University of Eastern Africa, Nairobi, Kenya
Jackson Kioko Kwanza, Department of Pure & Applied Mathematics, Jomo Kenyatta University of Agriculture & Technology, Nairobi, Kenya
Nicholas Muthama Mutua, Department of Mathematics and Informatics, School of Science and Informatics, Taita Taveta University College, Voi, Kenya
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Abstract
The present study focuses on determination of temperature distribution in one dimensional bar using Green’s function method. The Green’s Function is obtained using separation of variables, variation formulation principles and Heaviside functions. The Boundary Integral Equation is obtained using the fundamental solution, Divergence theorem, Green Identities, Dirac delta properties and integration by parts. The solution of heat equation given by the Green’s Function and the boundary integral equation has satisfied the uniqueness, regularity and stability of heat equation. The uniqueness, regularity and stability have been proved using smooth properties of class k function, Lyapunov function and Norm. The BEM implementation is performed using FORTRAN 95 software. Solutions to the test problems are presented and time dependence results are in agreement with computed analytical solutions.
Keywords
Green’s Function, Heaviside Function, Separation of Variables, Integration by Parts, Lyapunov Function
Virginia Mwelu Kitetu, Thomas Onyango, Jackson Kioko Kwanza, Nicholas Muthama Mutua, Determination of One Dimensional Temperature Distribution in Metallic Bar Using Green’S Function Method, American Journal of Applied Mathematics. Vol. 1, No. 4, 2013, pp. 55-70. doi: 10.11648/j.ajam.20130104.14
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