Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

D.A. TARZIA

Advanced Topics in Mass Transfer

InTech

Lugar: Rijeka; Año: 2011; p. 439 - 484

The goal of this chapter is firstly to give a survey of some explicit and approximated solutions for heat and mass transfer problems in which a free or moving interface is involved. Secondly, we show simultaneously some new recent problems for heat and mass transfer, in which a free or moving interface is also involved.  We will consider the following problems:                                   I) Phase-change process (Lamé-Clapeyron-Stefan problem) for a semi-infinite material: i)                    The Lamé-Clapeyron solution for the one-phase solidification problem (modeling the solidification of the Earth with a square root law of time); ii)                  The pseudo-steady-state approximation for the one-phase problem; iii)                The heat balance integral method (Goodman method) and the approximate solution for the one-phase problem; iv)                 The Stefan solution for the planar phase-change surface moving with constant speed; v)                   The Solomon-Wilson-Alexiades model for the phase-change process with a mushy region and its similarity solution for the one-phase case; vi)                 The Cho-Sunderland solution for the one-phase problem with temperature-dependent thermal conductivity; vii)               The Neumann solution for the two-phase problem for prescribed surface temperature at the fixed face; viii)             The Neumann-type solution for the two-phase problem for a particular prescribed heat flux at the fixed face, and the necessary and sufficient condition to have an instantaneous phase-change process; ix)                 The Neumann-type solution for the two-phase problem for a particular prescribed convective condition (Newton law) at the fixed face, and the necessary and sufficient condition to have an instantaneous phase-change process; x)                   The similarity solution for the two-phase Lamé-Clapeyron-Stefan problem with a mushy region. xi)                 The similarity solution for the phase-change problem by considering a density jump; xii)               The determination of one or two unknown thermal coefficients through an over-specified condition at the fixed face for one or two-phase cases. xiii)             A similarity solution for the thawing in a saturated porous medium by considering a density jump and the influence of the pressure on the melting temperature.   II) Free boundary problems for the diffusion equation: i)                    The oxygen diffusion-consumption problem and its relationship with the phase-change problem; ii)                  The Rubinstein solution for the binary alloy solidification problem; iii)                The Zel’dovich-Kompaneets-Barenblatt solution for the gas flow through a porous medium; iv)                 Luikov coupled heat and mass transfer for a phase-change process; v)                   A mixed saturated-unsaturated flow problem representing absorption of water by a soil with a constant pond depth at the surface and an explicit solution for a particular diffusivity; vi)                 Estimation of the diffusion coefficient in a gas-solid system; vii)               The coupled heat and mass transfer during the freezing of the high-water content materials with two free boundaries: the freezing and sublimation fronts.