Mathematical formulation and numerical methods

John M. Dixon, Francis A. Kulacki

Research output: Chapter in Book/Report/Conference proceedingChapter


Numerical solution of the mass, momentum, and energy conservation equations governing mixed convection in fluid-superposed porous layers is described. The momentum equation includes the Brinkman and Forchheimer terms and the Boussinesq equation of state accounts for buoyancy. The lower boundary of the system is heated over a finite length with the heat sink on the upper surface of the fluid sublayer. Test cases against prior investigations give very good results for free and mixed convection in saturated porous layers and cavities with full bottom heating.

Original languageEnglish (US)
Title of host publicationSpringerBriefs in Applied Sciences and Technology
PublisherSpringer- Verlag
Number of pages5
StatePublished - Jan 1 2017

Publication series

NameSpringerBriefs in Applied Sciences and Technology
ISSN (Print)2191-530X
ISSN (Electronic)2191-5318


  • Darcy-Brinkman-Forchheimer equation
  • Interfacial conditions
  • One-domain formulation


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