Heat and mass transfer between an evaporative interface in a porous medium and an external gas stream

Abstract

Steady state heat and mass transfer between a submerged evaporative interface in a porous medium and an external gas stream were analyzed theoretically. Local and average evaporation rates for laminar and turbulent flow over a flat plate as well os for fully developed laminar or turbulent flow near the thermal entry region of a duct were obtained as a function of the position of the evaporative interface. Calculated local evaporation rates are significantly lower than values computed by Luikov, who did not take into account the variation of evaporative surface temperature with recession, indicated both by the present analysis and by observations related to the drying of thick porous materials. Application to the analysis of the drying process is discussed.This investigation is concerned with heat and mass transfer between an evaporating liquid in a porous medium and an external gas stream, an area of research which is of particular relevance to the field of drying. An analysis is presented of steady state heat and mass transfer at low mass transfer rates between a submerged evaporative interface parallel to the surface of a porous medium and an external gas stream. The results of the analysis permit calculation of both local and average evaporation rates for different geometries and flow regimes, provided that the location of the evaporative interface is known.The use of a receding plane of evaporation to analyze drying processes was suggested by Cilliland in 1938 (8). Nissan, George, and Bolles (19) used the concept of a submerging plane of evaporation in order to develop a complete description of drying but their analysis neglects to take into account the influence of the fluid boundary layer. The direct precursor to this paper is a 1962 study by Luikov (15, la), who applied boundary-layer theory to the problem of evaporation of liquid from a porous body into a flowing air stream, Based on earlier experimental results ( 1 7 ) , Luikov as well as Nissan had concluded that most of the evaporation during the drying process takes place in a very narrow layer at the junction between wet and dry regions. Accordingly, Luikov's analysis was based upon the hypothesis that all evaporation takes place from a submerged surface which is parallel to the surface of the porous medium. In contrast to Nissan's analysis (19), the effects of the fluid boundary layer as well as those of the porous medium on the evaporation process were taken into account.There are two main distinctions between Luikov's previous analysis and the analysis reported in this paper. Whereas Luikov's solution depends upon the assumption that the velocity is constant across the fluid boundary layer, our analysis employs an integral representation that can be used for the more general flow situation in which the heat and mass transfer coefficients past a single step in wall temperature and concentration at x = 5 are of the form Robert P. Morgan is with the University of Missouri, Columbia, Missouri.

Evaporation and Humidification

“…In this manner, Morgan and Yerazunis (14) were able to obtain a linear equation in q s (x) which can be expanded in a MacLaurin series in the parameter Θ/Bi, where Θ is related to the rise in the evaporative-interface temperature at the leading edge, Θ = ^^ (6.30) to -tw and Bi is the Biot number, the ratio of the thermal resistance of the porous solid to that of the air boundary layer.…”

“…6.4, has been described analytically in the following way. (14) The temperature at the exposed surface t s is related to the heat flux there q s {x\ and thus the [-(C/x) 4 ]*-1…”

“…Morgan and Yerazunis (14) also evaluate normalized rates of evaporation of water from 12-7-mm-thick beds of densely packed, uniform spheres with Θ-functions ranging from 0-137 (polystyrene) to 0-508 (steel). The normalized rates f(0/Bi) are plotted against relative depth ξ/b in Fig.…”

“…The spread of the curves is not very wide and thus approximately we can write Table 6.5. (14) The evaporation rate, then, is primarily a function of the Biot number, that is the thickness of the material being dried and the thermal conductance of the solid and of the air. Since the relative depth ξ/b is a function of the mean moisture content, equation (6.34) suggests that the relative drying rate of a given porous body depends only on its thickness and moisture content.…”

“…This conclusion forms the basis of the justification for drawing up characteristic drying curves for materials. The experimentally determined relationship (15) between relative depth of evaporation and moisture content is shown in Fig. 6.7 for a 12-7-mm-thick bed of closely graded, glass spherules (88 < d p < 105 μπι).…”