Asymptotic analysis of a Hiemenz flow in a low-porosity medium with phase change

Abstract

In the present work, the features of liquid evaporation inside a low-porosity medium subjected to an impinging stream of hot gas is investigated analytically. The flow is analysed for a non-Darcy model, in which viscous and convective terms are considered in the Darcy pressure equation. A low-volatility liquid is considered, so that a low-vaporization regime is established. The rates of heat transfer between gas and solid and between liquid and solid are assumed to be high. Owing to differences between phase properties, in the system under study, different physical processes occur at different length scales. Using asymptotic expansions, expressions for the three phases that occur in this problem are obtained, in each of their length scales. The results predict that high injection temperatures are needed for phase change to occur, as a result of the low volatility of the liquid. Likewise, the enhancement of the vaporization rate due to heat conduction in the porous medium is quantified. The Hiemenz flow pressure term is modified to incorporate the effect of the porous medium, which is necessary for a solution to be found.