An analytical solution for heat transfer at a boiling front moving through a porous medium

A problem of current interest in geothermal energy extraction is the injection of cold water into a porous medium containing superheated vapor. Such injection will cause a boiling front to move away from the injection point. When flow is approximated as being one-dimensional radial, it can be shown from similarity variable concepts that temperature, pressure, and boiling rate at the front are constant, independent of time. From heat and mass balance considerations an analytical solution is obtained for front temperature and evaporation rate. Comparison with detailed numerical simulations of the injection process shows excellent agreement.     

Natural convective boiling in vertical annular tubes filled with porous medium

Experimental and theoretical studies were carried out on the natural convective boiling heat transfer and critical heat flux (CHF) in uniformly heated vertical annular tubes filled with a porous medium and submerged in saturated water and R11 liquid. The heat transfer experimental results were compared with the case without a porous medium. It was shown that heat transfer is greatly enhanced by the porous medium in the region of low heat flux. By adopting a simple mixing flow model, a generalized approximate relationship was derived for predicting the CHF. The prediction agrees relatively well with the CHF experimental data. © 2000 Scripta Technica, Heat Trans Asian Res, 29(6): 447–458, 2000     

Subcooled flow boiling and microbubble emission boiling phenomena in a partially heated microchannel

A simultaneous visualization and measurement study has been carried out to investigate subcooled flow boiling and microbubble emission boiling (MEB) phenomena of deionized water in a partially heated Pyrex glass microchannel, having a hydraulic diameter of 155 μm, which was integrated with a Platinum microheater. Effects of mass flux, inlet water subcooling and surface condition of the microheater on subcooled flow boiling in microchannels are investigated. It is found that MEB occurred at high inlet subcoolings and at high heat fluxes, where vapor bubbles collapsed into microbubbles after contacting with the surrounding highly subcooled liquid. In the fully-developed MEB regime where the entire microheater was covered by MEB, the mass flux, the inlet water subcooling and the heater surface condition have only small effects on the boiling curves. The occurrence of MEB in microchannel can remove a large amount of heat flux, as high as 14.41 MW/m² at a mass flux of 883.8 kg/m² s, with only a moderate rise in wall temperature. Therefore, MEB is a very promising method for cooling of microelectronic chips. Heat transfer in the fully-developed MEB in the microchannel is presented, which is compared with existing subcooled flow boiling heat transfer correlations for macrochannels.     

Analytical determination of permeability of porous fibrous media with consideration of electrokinetic phenomena

Flow behavior in porous fibrous media with consideration of electrokinetic phenomena is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of effective permeability of porous fibrous media as functions of porosity, dimensionless local averaging net charge density and dimensionless electric resistance number is derived in this paper. The influences of the electrokinetic phenomena can be measured by the dimensionless electric resistance number, which is proportional to the square of the liquid dielectric constant, the solid surface Zeta potential and inversely proportional to the liquid dynamic viscosity, electric conductivity and the square of the maximum pore radius. The analytical results show that when the dimensionless electric resistance number is small and the porosity is large, the dimensionless total flow rate shows a nearly uniform distribution. When the dimensionless electric resistance number is large, the resistant effects of the electrical double layer (EDL) become so significant that the superficial velocity decreases. The effective permeability of the porous fibrous media decreases correspondingly. Furthermore, the theoretical predicted effective permeability values are compared with experimental data, and good agreement is observed between the two. It shows that the mathematical model for the effective permeability of porous fibrous media with consideration of electrokinetic phenomena is satisfactory.     

An estimation of effective thermal conductivity of a fibrous dual-scale porous medium during unsaturated flow

The effective thermal conductivity in the volume-averaged temperature equation for the dual-scale porous media is estimated numerically. A finite-element simulation of a steady Newtonian flow in the unit cell of an idealized dual-scale porous medium is carried out and the relevant component of the effective thermal conductivity tensor is estimated from the resultant temperature and velocity fields. It is discovered that the conductivity is a strong function of Péclet number as well as inter-tow spacing, but is insensitive to the rate of tow wetting or the heat-flux from tows. We also conclude that the conductivity remains unchanged in the saturated as well as unsaturated flow regimes in dual-scale porous media.     

Thermally induced hygroscopic mass transfer in a fibrous medium

A fiberglass sample was used to study the hygroscopic mass transfer produced by a temperature difference across a moist, fibrous medium. Humidity probes and thermocouples were implanted in the sample and used to continuously monitor changes in the relative humidity and temperature as a result of the moisture migration. The effects of average temperature, thermal gradient magnitude and average moisture content were some of the parameters studied. The data was analyzed using a mechanistic analogy to the irreversible thermodynamic model. Vapor and liquid fluxes were evaluated along with vapor and liquid conductivities. The phenomenological coefficients associated with the liquid and vapor fluxes were calculated, and the flux contributions due to the thermal and concentration gradients were determined for steady-state conditions. Transient data for the humidity, temperature and moisture content were also either measured or calculated.     

Similarity solutions for pressure-driven boiling flows in capillary porous media

A similarity transformation has been proposed to study the two-phase boundary layer equations derived by Wang and Beckermann for capillary porous media. By virtue of the present transformation, the set of governing equations and boundary conditions for the pressure-driven boiling flow over a body of arbitrary shape reduces to the one for the flow over a flat plate. The dryout heat fluxes for pressure-driven boiling flows over a plate, a wedge, a cone, a sphere and a horizontal circular cylinder are correlated with the fluid thermophysical properties and porous medium parameters. The study confirms that the capillary force plays an important role in boiling flows in porous media.     

The rate of heat transfer for boiling on porous surfaces

It is shown that the constant, C_sf, introduced by Rohsenow⁶ for correlating pool boiling heat transfer data, may be used in order to characterize plates which have been made porous.     

Unsteady mixed convection on a wedge in a porous medium

A numerical solution has been presented for the unsteady mixed convection on a wedge which is embedded in a fluid-saturated porous medium. The flow is impulsively sets into motion from rest and the temperature of the wedge is also suddenly changed from that of the ambient fluid. A second-order upwind finite-difference scheme has been used to solve the governing nonsimilar equations. The results are found to be in excellent agreement with some previously published data.     

Mathematical modelling of silica deposition in a porous medium

The problem of silica deposition in packed columns is considered. Various deposition rate models are investigated and the method of characteristics is used to obtain an analytic solution for the special case where the flow rate through the column of porous material is constant. The theoretical results are compared with measured data from published experimental work. It is found that the dual regime model suggested by Fleming (1986) gives the best match of theory and experiment. The techniques developed can be used to investigate deposition near a reinjection well or in an approximately one-dimensional fractured zone connecting production wells and reinjection wells.     

The onset of convection in a tridisperse porous medium

This paper develops a theory of mass, momentum, and heat transfer in a tridisperse porous medium. Coupling between three different scales present in this medium is accounted for by introducing momentum and interphase heat transfer coupling coefficients. The developed theory is then applied to solve the classical Rayleigh–Bénard problem, for the onset of convection in a horizontal layer uniformly heated from below, for this new type of a porous medium. The formulation uses the Darcy law, which now results in three different filtration velocities in three porosity scales present in this medium. The linear stability analysis leads to an expression for the critical Rayleigh number as a function of three volume fractions, two permeability ratios, two thermal capacity ratios, two thermal conductivity ratios, two inter-phase heat transfer parameters and two inter-phase momentum transfer parameters. The dependence of the critical Rayleigh number on these parameters is investigated.     

Unsteady thermocline degradation in a fluid-saturated,porous medium

A numerical model is developed to describe unsteady, three-dimensional, natural convective flows in a fluid-saturated, porous medium having a rectangular volume with impervious walls and finite heat transfer at the boundaries. The model is used to predict the transient decay of a thermocline in a packed bed during a period of stagnation in which there is zero net flow and no energy input into the bed. The computed results compare favorably with experimental data from a packed bed consisting of air and natural stone of mixed sizes and irregular shapes. The results show an upward shift in the position of maximum temperature along the vertical centerline of the bed and confirm the important influence of internal convection on the process. The results also demonstrate that a purely diffusive model would be incapable of a reliable predication. Further, the recognition of finite heat transfer rates at the boundaries is shown to be a significant factor in improving the predictive capability of the model.     

Mathematical modelling of moisture desorption in a porous medium

This paper discusses heat and mass transfer in desorption drying. A basic equation system is derived to describe coupled heat and mass transfer in a porous medium with moisture desorption under temperature gradients and a vacuum environment. The desorption mushy zone model is used to obtain an exact solution for coupled heat and mass transfer with a moving desorption mushy zone in a porous half-space. The results are analysed numerically to demonstrate the effects of various parameters on desorption.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

One-domain approach for heat transfer between a porous medium and a fluid

The purpose of this work is to investigate the extents of the local thermal equilibrium (LTE) assumption at the fluid-porous medium boundary (i.e., in a heterogeneous region). The analysis is performed in terms of the one-domain approach. Therefore, we posed and solved the associated closure problems in order to compute the spatial dependence of the effective coefficients at the fluid-porous medium boundary. Steady-state comparisons with direct numerical simulations evidence that the LTE is, in general, justifiable everywhere in the system, i.e., in both homogeneous and heterogeneous regions.     

Gas Flow in a Stratified Porous Medium with Crossflow

IntroductionMany ..servoirs are stratified in nature due to thevarying energy level of the original depositionaIenvironment. The transporting medium softs the sourcematerial depositing one layer at a time in any givenenvironment. When the depositionaI energy levelschange, the subsequent overiying layers may be differentin composition and texture, fOrming a series of dissindlarunits of strata. Such fOrmations are calIed multilayersystems. In many cases some of the layers have such lowpermeab…