The Volume-Averaged Energy Equations

  • Hitoshi Sakamoto
  • Francis A. Kulacki
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


The chapter presents an exposition of the governing equations for heat transfer between the solid and fluid phases of a saturated porous medium. Volume-averaged equations are developed from first principles based on Wittaker’s formulation for the solid and fluid phases with application to the current case where there is convective motion and dispersion in the fluid phase. A one-equation model is developed. Determining thermal dispersion is a remaining unsolved problem.


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Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hitoshi Sakamoto
    • 1
  • Francis A. Kulacki
    • 2
  1. 1.Japan Research Center, Huawei Technologies JapanYokohamaJapan
  2. 2.Department of Mechanical EngineeringUniversity of MinnesotaMinneapolisUSA

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