RADIAL BASIS FUNCTION PSEUDO-SPECTRAL SOLUTION OF THE NON-DARCY MODEL IN A POROUS MEDIUM

Geridönmez B.

JOURNAL OF POROUS MEDIA, vol.20, no.6, pp.479-490, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 6
  • Publication Date: 2017
  • Doi Number: 10.1615/jpormedia.v20.i6.10
  • Journal Name: JOURNAL OF POROUS MEDIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.479-490
  • Keywords: radial basis function approximation, natural convection, porous medium, Brinkman-Forchheimer-extended Darcy model, CONVECTIVE HEAT-TRANSFER, DIFFUSIVE NATURAL-CONVECTION, VARIABLE POROSITY, ENCLOSURE, GENERATION, NANOFLUID, FLOW
  • TED University Affiliated: Yes

Abstract

In this study, the radial basis function pseudo-spectral (RBF-PS) method is applied for solving natural convective flow in a square cavity and in a curved pipe filled with a porous medium. RBF-PS constructs differentiation matrices by the coordinate matrix formed by radial distances using multiquadric radial basis function (MQ-RBF) root r(2) + c(2). The direct implementation of the problem and the cheap computational cost using the small number of grid points make the proposed method captivating. The governing dimensionless equations are solved in terms of stream function, vorticity, and temperature. The results are given for several values of Rayleigh (Ra) number, Darcy (Da) number, and porosity. epsilon(p) in terms of average Nusselt number, or streamlines, isotherms, and vorticity contours. Physically the decrease in Darcy number suppresses the heat transfer while the convective heat transfer becomes prominent with the increase in Ra, and in epsilon(p).