Perturbation Solutions of Transient Heat Transfer to a Porous Medium from a Fluid Stream

Abstract

Asymptotic behavior of the two-phase, thermal response of a porous medium, with a fluid throughflow, to a sudden change of the oncoming stream temperature is examined via four cases of perturbation solutions: (1) massive blowing, fast interphase (thermal) link, small conductivity, and small (thermal) interaction at the entrance, (2) moderate blowing, and fast interphase link, (3) massive blowing, moderate interphase link, and small interaction at the entrance, and (4) small conductivity, as well as weak interphase link. Schumann’s classical, two-phase, and non-diffusive model is shown to be just the outer limit of Case (1). The “single-phase model” is derived. Associated boundary layers are displayed. Certain numerical trend reported in the literature is also explained.