Heat and mass transfer in unsaturated porous media with solid–liquid change

 A model on heat and mass transfer in unsaturated porous media with solid/liquid phase change was developed with extending the three-variable model previously proposed. The movement of air phase and its effect on the motion of water is considered. The model has been checked with comparison of the experimental results of the temperature distribution for two dimensional freezing process. The evolution of air pressure, water and ice saturation were predicted by solving the governing equations. The ice segregation and moisture movement toward the front of freezing were numerically simulated. Received on 8 December 1999     

Heat conduction in a rock mass with an annular hot water store

Vast subterranean caverns may be used for hot water storage in distinct heating schemes; such caverns can be annular, with a central pillar. This paper considers the quasi-steady solution of the heat conduction equation for this geometry with periodic temperature variations     

Heat and mass transfer with phase change in a rectangular enclosure packed with unsaturated porous material

The paper has presented a seven-field mathematical model with ten variables to describe the simultaneous heat and mass transfer with phase change in the unsaturated porous medium that is enclosed in a rectangular enclosure. Both liquid and vapor migration in the porous matrix are evaluated at the same time, and gaseous bulk motion is simulated numerically. The numerical results are discussed with emphasis on the effect of evaporation and condensation of R113 in the vertical enclosure, which may have an application in the room passive heating for the buildings in winter. As solar energy or low-grade waste heat could be used if the enclosure is adequately designed to transfer heat from the outside to the room of the building, the present method may be propitious to the energy conservation. Aimed to this purpose, the heat transfer character of the enclosure is analyzed for the change of Nu number with different Ra number and Da number.     

Heat and mass transfer analysis in unsteady boundary layer flow through porous media with variable viscosity and thermal diffusivity

In this paper, a comprehensive mathematical analysis is carried out on an unsteady boundary-layer flow with heat and mass transfer characteristics of a viscous fluid through porous media. Fluid suction or blowing is assumed to take place at the surface. The governing coupled nonlinear partial differential equations are transformed into coupled nonlinear ordinary differential equations by using a similarity transformation and are solved analytically and numerically by using the homotopy analysis method and the Runge-Kutta and shooting technique, respectively. A comparison between analytical and numerical results is conducted, which shows excellent agreement.     

Heat and brine transport in porous media: the Oberbeck-Boussinesq approximation revisited

This paper discusses the Oberbeck-Boussinesq approximation for heat and solute transport in porous media. In this commonly used approximation all density variations are neglected except for the gravity term in Darcy’s law. However, in the limit of vanishing density differences this gravity term disappears as well. The main purpose of this paper is to give the correct limits in which the gravity term is retained, while other density effects can be neglected. We show that for isothermal brine transport, fluid volume changes can be neglected when a condition is fulfilled for a dimensionless number, which is independent of the density difference and specific discharge. For heat transfer an additional condition is required. One-dimensional examples of simultaneous heat and brine transport are given for which similarity solutions are constructed. These examples are included to elucidate the volume effects and the corresponding induced specific discharge variations. Finally, a two-dimensional example illustrates the relative effects of volume changes and gravity.     

A general mathematical modelling for heat and mass transfer in unsaturated porous media: an application to free evaporative cooling

The present paper develops a general mathematical model with some improvements in mass, momentum and energy equations, which introduce more transport mechanisms to simulate simultaneous transfer of heat and mass in the porous media unsaturated with liquid. Numerical calculation results in two-dimension are obtained for the vertical packed bed with its right opening surface exposing to atmospherical environment. The calculating data can demonstrate the cooling effect of the water evaporation for the bed if it is used as a cooling wall of building for room air-conditioning in the hot and dry climate.     

Heat transfer in a vertically-layered porous medium heated from below

Some studies already made have investigated the criterion for onset of convection and heat and mass flow distributions in a porous slab composed of horizontal layers of different materials. This paper reports a study of such criteria for the case where the slab is composed of vertically-aligned strata with different permeabilities and thermal conductivities. This has particular relevance to where blocks of different materials abut in a vertical plane, as well as the case of very narrow highly permeable vertical layers which represent vertical faults in a geological structure. Results indicate that permeability and/or thermal conductivity contrasts between layers can significantly affect the flow pattern and the spatial distribution of the surface heat flux. The concentration of flow in highly permeable faults produces marked irregularities in the heat flow through the surface above them.     

Continuous time random walks and heat transfer in porous media

An approach to describe heat transfer in porous media is presented on the basis of the continuous time random walk (CTRW) framework. CTRW is capable of quantifying both local equilibrium and non-equilibrium heat transfer in heterogeneous domains, and is shown here to match published experimental data of non-equilibrium thermal breakthrough. It is argued that CTRW will be particularly applicable to the quantification of heat transfer in naturally heterogeneous geological systems, such as soils and geothermal reservoirs.     

A boundary layer analysis of combined heat and mass transfer by natural convection from a concentrated source in a saturated porous medium

A boundary layer analysis was carried out to investigate the coupled phenomena of heat and mass transfer by natural convection from concentrated heat and mass sources embedded in saturated porous media. Both line and point source problems were treated. The boundary layer equations based on Darcy's law and Boussinesq approximation were solved by means of similarity transformation to obtain the details of velocity, temperature and concentration distributions above a concentrated heat source. Two important parameters, namely the Lewis number Le and the buoyancy ratioN were identified to conduct a series of numerical integrations. For the case of small Le, a substance diffuses further away from the plume centerline, such that the mass transfer influences both velocity and temperature profiles over a wide range. For large Le, on the other hand, the substance diffuses within a narrow range along the centerline. Naturally, the influence of mass transfer is limited to the level of the centerline velocity, so that a peaky velocity profile appears for positiveN whereas a velocity defect emerges along the centerline for negativeN. For such cases of large Le, the temperature profiles are found to be fairly insensitive to Le.     

Heat/mass transfer and pressure drop in a triangular-rib-roughened rectangular channel

In this paper, the heat/mass transfer analogy was used to investigate the heat transfer and pressure drop in a square channel with triangular ribs on its two opposite walls. Reynolds number varied from 1 × 10⁴ to 7 × 10⁴; the dimensionless heights of the triangular ribs H/W were 0.04, 0.07, and 0.1; and their dimensionless pitches S/W were 0.45, 0.63, 1.0, 1.37, 1.55, and 2.1. Experimental results showed that the heat transfer coefficients of the wall with triangular rib were about 1 to 2.3 times larger than those of a smooth-channel wall, and the pressure drops along this roughened channel were about 1 to 10 times larger than those for a smooth channel. Correlations of heat transfer and pressure drop were obtained, which are useful for practical designs.     

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374 °C for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. In the vicinity of the critical point the density and internal energy of fluids show very strong variations for small temperature and pressure changes. This suggests that convective heat transfer from thermal buoyancy flow would be strongly enhanced at near-critical conditions. This has been confirmed in laboratory experiments. We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme nonlinearities in water properties near the critical point. Our numerical simulations show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the simulations are considerably smaller than data reported from laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.     

INSTABILITY AND DISPERSIVITY OF WAVE PROPAGATION ININELASTIC SATURATED/UNSATURATED POROUS MEDIA

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Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects

Dufour and Soret effects on flow at a stagnation point in a fluid-saturated porous medium are studied in this paper. A two dimensional stagnation-point flow with suction/injection of a Darcian fluid is considered. By using an appropriate similarity transformation, the boundary layer equations of momentum, energy and concentration are reduced to a set of ordinary differential equations, which are solved numerically using the Keller-box method, which is a very efficient finite differences technique. Nusselt and Sherwood numbers are obtained, together with the velocity, temperature and concentration profiles in the boundary layer. For the large suction case, asymptotic analytical solutions of the problem are obtained, which compare favourably with the numerical solutions. A critical view of the problem is presented finally.     

Mathematical model of heat and mass transfer in a bidisperse porous material

A model of heat and mass processes in a body with two types of pores is considered. This model describes the initial stage of substance penetration into the porous system (or the inverse process, namely, substance extraction from the system) and takes into account convective transport in large channels. A kinetic function of impregnation (extraction) of the porous medium and the substance flux density are found for a problem with additional conditions.     

Conjugate model for heat and mass transfer of porous wall in the high temperature gas flow

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency. The project supported by the National Natural Science Foundation of China (19889209) and Russian Foundation for Basic Research (97-02-16943)     

Fluid-solid coupling mathematical model of contaminant transport in unsaturated zone and its asymptotical solution

IntroductionThetransportofcontaminantsinunsaturatedzonehascausedmuchattention .Inearly1960s,contaminationproblemsofsoilandgroundwaterhadbeenstudiedathomeandabroad[1].Andinrecentyears ,thetransformationandtransportationofcontaminantshavebeendeeplystudiedinthefieldsofhydrogeology ,petroleumengineering ,environmentalengineeringandsoon[2 ,3].Somecontaminanttransportmodelshavebeenpresentedsofar.Forexample ,Paker[4 ]etal.presentedaconstitutivemodelgoverningparametersofwater,gasandcontaminantswhenth…     

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.     

Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media

Environmental studies are commonly carried out through numerical simulations, which have to be accurate, reliable and efficient. When transient problems are considered, the validity of the solutions requires the calculation and management of the temporal discretization errors. This article describes an adaptive time stepping strategy based on the estimation of the local truncation error via the Richardson extrapolation technique. The time-marching scheme is mathematically based on this a posteriori error estimation that has to be gauged. General optimizations are also suggested making the control of both the temporal error and the evolution of the time step size very efficient. Furthermore, the algorithm connecting these methods is all the more interesting as it could be implemented in many computational codes using different numerical schemes. In the hydrogeochemical domain, this algorithm represents an interesting alternative to a fixed time step as shown by the various numerical tests involving reactive transport and unsaturated flow.     

Heat and mass transfer with natural convection at a vertical porous surface,with blowing of carbon dioxide into air

This paper gives the results of a numerical calculation of a laminar boundary layer with the free convection of a binary mixture of carbon dioxide and air at a vertical heated surface. It compares the numerical solution with an approximate analytical solution and with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 122–125, November–December, 1971.