Finite Volume Numerical Grid Technique for Solving One and Two Dimensional Heat Flow Problems

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Finite Volume Numerical Grid Technique for Solving One and Two Dimensional Heat Flow Problems

Author Affiliations

¹Department of Mathematics, M. J. College, Jalgaon, 425 001, Maharashtra INDIA
²Department of Mathematics, M. J. College, Jalgaon, 425 001, Maharashtra INDIA

Res. J. Mathematical & Statistical Sci., Volume 2, Issue (8), Pages 4-9, August,12 (2014)

Abstract

In this paper Finite Volume numerical technique has been used to solve one and two dimensional Steady state heat flow problems with Dirichlet boundary conditions and mixed boundary conditions, respectively. We explained step by step numerical solution procedures with the help of Microsoft excel and TDMA line-by-line solver for the algebraic equations. Finally the numerical solutions obtained by Finite Volume techniques are compared with exact solution to check the accuracy of the developed scheme

References

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[ref1] Kreyszig Erwin, Advanced Engineering Mathematics NewYork: John Wiley and Sons, 10th edition, (2011)
Google Scholar

[ref2] Cheniguel A. and Reghioua M., On the NumericalSolution of three- dimensional diffusion equation with anintegral condition, WCECS2013, San Francisco, USA,(2013)
Google Scholar

[ref3] Chuathong Nissaya and Toutip Wattana, An accuracycomparison of solution between boundary element methodand Meshless method for Laplace equation, AMM2011,Khon Kaen University, Khon Kaen, Thailand, 29-42(2011)
Google Scholar

[ref4] Patil Parag V. and Prasad Krishna J.S.V.R., NumericalSolution for Two Dimensional Laplace Equation withDirichlet Boundary Conditions, InternationalOrganization of Scientific Research- Journal ofMathematics, 6(4), 66-75 (2013)
Google Scholar

[ref5] Lau Mark A. and Kuruganty Sastry P., SpreadsheetImplementations for Solving Boundary-Value Problems inElectromagnetic, Spreadsheets in Education (eJSiE), 4(1)(2010)

[ref6] Ozisik M. Necati, Heat Transfer A Basic Approach, McGraw-Hill Book Company first edition, (1985)
Google Scholar

[ref7] Patil Parag V. and Prasad Krishna J.S.V.R., Solution ofLaplace Equation using Finite Element Method, Pratibha:International Journal of Science, Spirituality, Businessand Technology, 2(1), 40-46 (2013)
Google Scholar

[ref8] Patil Parag V. and Prasad Krishna J.S.V.R., A numericalgrid and grid less (Mesh less) techniques for the solutionof 2D Laplace equation, Advances in Applied ScienceResearch, Pelagia Research Library, 5(1), 150-155,(2014)

[ref9] Sadiku M.N.O., Elements of Electromagnetics, NewYork: Oxford University Press, 4th edition, (2006)
Google Scholar

[ref10] Versteeg H.K. and Malalasekera W., An Introduction tocomputational fluid dynamics: The finite volume method,Longman Scientific and Technical, 1th edition, (1995)
Google Scholar