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A solution of the convection‐conduction heat‐transfer equation in porous media by the von Rosenberg finite‐difference scheme
Author(s) -
Ginosar Daniel M.,
Green Don W.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100604
Subject(s) - thermal conduction , partial differential equation , convective heat transfer , heat transfer , mathematics , convection , finite difference method , thermodynamics , mechanics , porous medium , mathematical analysis , chemistry , porosity , physics , organic chemistry
von Rosenberg developed an explicit finite‐difference scheme for solution of the linear convection‐conduction partial differential equation in one space dimension. The method is stable and accurate when a dimensionless ratio of dispersion to convection is between zero and one. In this work, the von Rosenberg method was applied to a linear, one space dimensional set of coupled convection‐conduction equations. The system examined involves the change in temperature resulting from a fluid flowing through a stationary porous solid with heat transfer between the fluid and solid phases. The equations, which describe heat transfer in each phase, were solved simultaneously and, thus, the solution method was required to be implicit rather than explicit. It was observed that when the interphase convective heat‐transfer rate was small relative to the fluid velocity, an implicit solution of the von Rosenberg weighted equations provided a good solution, but when the interphase convective heat‐transfer rate was relatively large, a modified weighting on the equations provided a more accurate, stable solution. © 1994 John Wiley & Sons, Inc.