Single- and dual-phase-lagging heat conduction models in moving media

Motivated by the recent work of Christov and Jordan, ("Heat Conduction Paradox Involving Second-Sound Propagation in Moving Media," 2005, Phys. Rev. Lett., 94, p. 154301), we examine the original single- and dual-phase-lagging heat conduction models without Taylor series approximation and their variants in moving media using the Galilean principle of relativity. It is found that the original single- and dual-phaselagging heat conduction models are Galilean invariant and lead to a single governing equation even for the multidimensional media. However their variants violate the Galilean principle of relativity in the moving media. Although this paradox can be eliminated by replacing the partial time derivatives with the material derivatives, the resulting governing equations cannot be reduced to a single transport equation in the multidimensional media. Therefore we believe that the original single- and dual-phase-lagging heat conduction models are more advantageous in modeling the microscale heat conduction problems.