Numerical Simulation of 1D Unsteady Heat Conduction-Convection in Spherical and Cylindrical Coordinates by Fourth-Order FDM

E. C. Romao, L. H. P. de Assis


This paper aims to apply the Fourth Order Finite Difference Method (FDM) to solve the one-dimensional unsteady conduction-convection equation with energy generation (or sink) in cylindrical and spherical coordinates. Two applications were compared through exact solutions to demonstrate the accuracy of the proposed formulation.


central difference method; cylindrical and spherical coordinates; numerical simulation; numerical efficiency

Full Text:



T. L. Bergman, A. S. Lavine, F. P. Incropera, D. De Witt, Fundamentals of Heat and Mass Transfer, Fifth Edition, John Wiley & Sons, 2003

E. C. Romao, J. C. Z. Aguillar, M. D. Campos, L. F. M. de Moura, “Central difference method of O(∆x6) in solution of the CDR equation with variable coefficients and Robin condition”, International Journal of Applied Mathematics, Vol. 25, No. 1, pp. 139-153, 2012

M. D. Campos, E. C. Romao, L. F. M. de Moura, “A Finite-Difference Method of High-Order Accuracy for the Solution of Transient Nonlinear Diffusive-Convective Problem in Three Dimensions”, Case Studies in Thermal Engineering, Vol. 3, pp. 43-50, 2014

M. M. Cruz, M. D. Campos, J. A. Martins, E. C. Romao, “An Efficient Technique of Linearization towards Fourth Order Finite Differences for Numerical Solution of the 1D Burgers Equation”, Defect and Diffusion Forum, Vol. 348, pp. 285-290, 2014

S. F. Radwan, “Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers’ equation”, Journal of Computational and Applied Mathematics, Vol. 174, No. 2, pp. 383-397, 2005

M. Cui, “Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation”, Numerical Algorithms, Vol. 62, No. 3, pp. 383–409, 2013.

J. R. Welty, C. E. Wilson, G. L. Rorrer, Fundamental of Heat and Mass Transfer, 4th ed., Wiley, 2001

M .D. Campos, E. C. Romao, “A High-Order Finite-Difference Scheme with a Linearization Technique for Solving of Three-Dimensional Burgers Equation”, Computer Modeling in Engineering & Sciences, Vol. 103, pp. 139-154, 2014

T. J. Chung, Computational fluid dynamics, Cambridge University Press, 2002

eISSN: 1792-8036     pISSN: 2241-4487