Journal of Mathematical Chemistry

, Volume 53, Issue 3, pp 911–924 | Cite as

DRBEM solution of natural convective heat transfer with a non-Darcy model in a porous medium

  • B. Pekmen
  • M. Tezer-Sezgin
Original Paper


This study presents the dual reciprocity boundary element (DRBEM) solution of Brinkman–Forchheimer-extended Darcy model in a porous medium containing an incompressible, viscous fluid. The governing dimensionless equations are solved in terms of stream function, vorticity and temperature. The problem geometry is a unit square cavity with either partially heated top and bottom walls or hot steps at the middle of these walls. DRBEM provides one to obtain the expected behavior of the flow in considerably small computational cost due to the discretization of only the boundary, and to compute the space derivatives in convective terms as well as unknown vorticity boundary conditions using coordinate matrix constructed by radial basis functions. The Backward-Euler time integration scheme is utilized for the time derivatives. The decrease in Darcy number suppresses heat transfer while heat transfer increases for larger values of porosity, and the natural convection is pronounced with the increase in Rayleigh number.


DRBEM Natural convection Porous medium  Brinkman–Forchheimer-extended Darcy model 

Mathematics Subject Classification

76S99 76R10 76D05 65M38 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsAtilim UniversityAnkaraTurkey
  2. 2.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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