Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface
Domingo Alberto · InTech eBooks · 2011
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: 1. 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 overspecified 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.www.intechopen.com