An introduction to the derivation of surface balance equations without the excruciating pain

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11 Scopus citations


Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the interface and boundary conditions between various domains. This paper provides an elegant, straightforward and universal method that considers the nature of those shared boundaries and derives the appropriate conditions at the interface, irrespective of the governing equations being solved. As a first example, a well-known interface condition is derived using this method. For a second example, the set of boundary conditions necessary to solve a baseline aerothermodynamics coupled plain/porous flow problem is derived. Finally, the method is applied to two more flow configurations, one consisting of an impermeable adiabatic wall and the other an ablating surface.

Original languageEnglish
Pages (from-to)992-999
Number of pages8
JournalInternational Journal of Heat and Mass Transfer
StatePublished - 2017

Bibliographical note

Funding Information:
Financial support for this work was provided by NASA Award NNX15AD73G and NNX13AN04A. ?The authors are also grateful to G.V. Candler and S.C.C. Bailey for insightful discussions and comments.

Publisher Copyright:
© 2017 Elsevier Ltd


  • Boundary conditions
  • Coupled flow
  • Porous flow
  • Surface balance equations

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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