Main Article Content
This paper presents an analysis of heat conduction in one-dimensional Cartesian coordinate system under steady state condition for homogeneous material by using the dual mesh finite domain method. This method used element for interpolation of functions and the calculation of heat fluxes at both ends of control domain. In this paper, the detail of discrete equation formulation was presented for the nodes of domain. The accuracy of numerical solutions was evaluated by comparison with the exact solutions of three problems including 1) heat conduction in a rod without heat generation, 2) heat conduction in a plane wall with heat generation and 3) heat conduction through a fin with uniform cross section. The percentage of error of the dual mesh finite domain method with four elements for problem 1, 2 and 3 were 0, 0 and 0.01, respectively.
Reddy JN. An Introduction to the Finite Element Method. 3th edition, New York, McGraw Hill, 1993.
Versteeg HK, Malalasekera W. Computational Fluid Dynamics, the Finite Volume. 2nd edition, Harlow, England, UK, Pearson Education (Prentice-Hall), 2007.
Ferziger JH, Peric M. Computational methods for fluid dynamics, 3rd edition, New York, Springer-Verlag, 2002.
Mazumder S. Numerical methods for partial differential equations. Finite Difference and Finite Volume methods, New York, Elsevier, 2016.
Baliga BR, Patankar SV. A new finite-element formulation for convection-diffusion problems. Numerical Heat Transfer; 3(4):393-409, 1980.
Patankar SV. Numerical heat transfer and fluid flow. Boca Raton, FL. CRC Press, 1980.
Reddy JN. A dual mesh finite domain method for the numerical solution of differential equations, International Journal of Computational Methods in Engineering Science and Mechanics; 20(3):212-28, 2019.
Reddy JN. A dual mesh finite domain method for steady-state convection-diffusion problems, Computers and Fluids;214(104760), 2021.
Reddy JN, Nampally P. A dual mesh finite domain method for the analysis of functionally graded beams, Composite Structure; 251(112648), 2020.
Nampally P., Reddy JN. Bending analysis of functionally graded axisymmetric circular plates using the dual mesh finite domain method, Latin American Journal of Solids and Structures;17(7), e302, 2020.