Mathematical formulation and numerical solution

Aniruddha Bagchi, Francis A. Kulacki

Research output: Chapter in Book/Report/Conference proceedingChapter


In this chapter, the mathematical formulation of the convective heat transfer problem is presented. The governing equations for natural convection in two-dimensional fluid and saturated porous layers are described first. Thereafter the boundary conditions for the problem are elucidated. In particular, boundary conditions at the interface of the fluid and porous layers are discussed in detail. The one-domain formulation is then derived, and the governing equations are presented in dimensionless form using the vorticity-stream function formulation.

Original languageEnglish (US)
Title of host publicationSpringerBriefs in Applied Sciences and Technology
PublisherSpringer Verlag
Number of pages12
StatePublished - 2014

Publication series

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

Bibliographical note

Publisher Copyright:
© The Author(s) 2014.


  • Finite-volume method
  • Interfacial conditions
  • Numerical solution
  • One-domain formulation
  • Two-domain formulation
  • Volume averaging


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