Thermo: Heat Transfer

  • Zhen (Leo) Liu


Heat transfer is a great example to show how a fundamental monolithic physical phenomenon can be mathematically formulated. In this chapter, the fundamentals of heat transfer for continua and mixtures including porous materials will be described consecutively. We will start with the concept of the representative elementary volume (REV) and conservation laws. Based on that, the general governing equation of conservation problems will be derived. Following that, we will derive the governing equation of the heat transfer in continuous materials. The validity of the REV assumption and conservation laws will help us extend the basics of continuum mechanics to the theories in porous materials. Emphasis will be placed on the heat transfer in porous materials which represents a much more complicated and general framework for heat transfer. Boundary conditions for heat transfer will be discussed from both a mathematical and a physical perspective. Finally, a practice problem will be solved using the MATLAB PDE Toolbox and compared against the analytical solution.


Thermal field Heat transfer Representative elementary volume Continuum mechanics Conservation law Porous materials Thermal conductivity Heat capacity 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Zhen (Leo) Liu
    • 1
  1. 1.Michigan Technological UniversityHoughtonUSA

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