Heating unsaturated medium sand

Abstract

A theoretical, experimental and numerical investigation of combined heat and mass transfer in unsaturated sand is described. The theoretical formulation adopted is that of Philip & de Vries but slightly different forms of the vapour transfer dif-fusivities are developed. Experimental work is reported on the determination, for a medium sand, of the full set of material parameters incorporated in the formulation, using both methods developed by the Authors and standard techniques. Explicit equations are given for the capillary potential, unsaturated hydraulic conductivity and thermal conductivity as functions of moisture content and temperature. Laboratory experimental results are presented for the steady temperature distribution within an unsaturated sample of the sand in which a rod is buried and heated. The pattern of moisture content values achieved reveals a two region response, a dry zone surrounding the rod and wet sand elsewhere. The development of a numerical simulation of the heating experiment using a finite difference solution algorithm is described. A self implicit scheme, driven to steady state through a false transient, was employed. Good agreement was found between temperatures in the simulation and the experiment. The work described is unusual in that equal emphasis has been placed on experimentation, especially the determination of the soil's physical properties, and numerical modelling and the two-dimensional coupled partial differential equations describing combined heat and mass transfer have been solved without simplification. L'article présente une étude théorique, expérimen-tale et numérique du transfert combiné de chaleur et de masse dans du sable non-saturé. La formulation th&cuate;orique adoptée est celle de Philip et de Vries, mais on développe des formes légérement différentes des diffusivités du transfert des vapeurs. Des expériences sont décrites concernant la détermination pour un sable moyen d'un jeu complet des paramétres du matériau incorporés dans la formulation a l'aide des méthodes développées par les auteurs et des techniques usuelles. Des équations explicites sont données pour le potentiel capillaire, la conductivité hydraulique non-saturée et la conductivité thermale en fonction de la teneur en eau et la température. Des résultats des expériences effectuées dans le laboratoire sont présentes pour la distribution stationnaire de température au sein d'un échantillon non-saturé de sable dans lequel une tige est enfouie et chauffée. La distribution des valeurs de teneur en eau révéle une réponse à deux zones, c'est-à-dire une zone séche entourant la tige et du sable humide ailleurs. L'article décrit le dé-veloppement d'une simulation numérique de l'expérience de chauffage à l'aide d'un algorithme de solution a différences finies. On a employé une méthode implicite en soi et poussée à l'état stationnaire en passant par une fausse transition. On a trouvé que les températures de la simulation et de l'expérience s'accordaient bien 1'une avec l'autre. Le travail decrit a été orienté également sur l'expérimentation, surtout la détermination des propriétés physiques du sol, et sur la simulation numérique. Les équations différentielles partielles bidimensionnelles associées décrivant le transfert combiné de chaleur et de masse ont été résolues sans aucune simplification.

Combined heat and mass transfer for drying ceramic (shell) body

“…In eqn (6), v, α are the mass flow factor and tortuosity factor as given in [10]. D atm is the molecular diffusivity of water vapour through dry air, and is given in reference [8].…”

“…This equation shows that the equilibrium of water vapour, P v differs from the saturation pressure, P vs , due to the curvature of the interface between capillary or hygroscopic water and the gas phase inside the pores of the medium. Given that the relative humidity within the porous matrix is given by (10) The partial vapour pressure can be calculated as a function of local temperature and relative humidity using the relationship (11) where the saturation vapour pressure, may be estimated using the saturated vapour…”

“…These are linked together leading to a thermodynamic and also porous transport formulation that is coupled. Thus, these equations are now well established and have been applied in drying process simulations that include both hygroscopic [5][6][7][8] and nonhygroscopic material [9][10][11]. The objective of this work is to develop the coupled heat and moisture governing equation (along with the gas transport consideration) for a ceramic shell body, based on the hygrothermal and thermodynamic transport properties.…”

On the mechanisms and kinetics of evaporation of a compacted silt

“…Various empiric or thermodynamics expressions allow to evaluate this dependence. In this work, the correlation from [18] is used: with T the temperature (°C).…”

Discussion: Analysis of coupled heat, moisture and air transfer in a deformable unsaturated soil

“…Equation (8), presented on p. 679, provides a basic de®nition of moisture velocity, which inherently contains the effect of a temperature gradient, should one exist. The method by which equation (8) is developed to accommodate components of¯ow due to a moisture content and temperature gradient (Ewen & Thomas, 1989) or a potential and temperature gradient (Thomas & King, 1991) has been presented in detail previously by the senior author and co-workers. Again, due to limitations of space, it was not considered appropriate to repeat all the details in this paper.…”