Convective heat transfer porous media

In chemical micro process technology with porous catalyst layers attached to the channel walls, convection through the porous medium can often be neglected. When the reactor geometry allows the flow to bypass the porous medium it will follow the path of smaller hydrodynamic resistance and will not penetrate the pore space. Thus, in micro reactors with channels coated with a catalyst medium, the flow velocity inside the medium is usually zero and heat and mass transfer occur by diffusion alone. 

Many geological flows such as flow in an oil reservoir or in a geothermal power system involve convective heat transfer in a porous medium. 

The present chapter gives no more than a brief introduction to convective heat transfer in a porous medium. It is an area of considerable practical importance and there is a large body of literature on the topic to which the reader is referred for more detail, for example see [1] to [12]. 

Using the procedure outlined in this chapter for using the boundars laser equations to find the-forced convective heat transfer rate from a circular cylinder buried in a saturated porous medium, investigate the heat transfer rate from cylinders with an elliptical cross-section with their major axes aligned with the forced flow. The surface velocity distribution should be obtained from a suitable book on fluid mechanics. 

Oosthuizen, P.H. and Paul, J.T., Forced Convective Heat Transfer from a Flat Plate Embedded Near an Impermeable Surface in a Porous Medium , Symp. on Fundamentals of Forced Convection Heat Transfer, ASME HTD-Vol. 101. Am. Soc. Mech. Eng., New York, 1988, pp. 105-111. 

KwendakwemS, N.J. and Boehm, R.F., Parametric Study of Mixed Convection in a Porous Medium Between Vertical Concentric Cylinders , J. Heat Transfer, Vol. 113, pp. 128-134, 1991. 

Oosthuizen, P.H., Mixed Convective Heat Transfer from a Heated Horizontal Plate in a Porous Medium Near an Impermeable Surface", ASME J. Heat Transfer, Vol. 110, No. 2. pp. 390-394, 1988. 

Oosthuizen. PH. and Naylor. D.. Natural Convective Heat Transfer from a Cylinder in an Enclosure Partly Filled w ith a Porous Medium, Ini. J. Sumer. L riiods Heat and Fluid Flow. Vol. 6, No. 6. pp. 51-63. 1996. 

Bejan, A. and Poulikakos. D.. The NonDarcy Regime for Vertical Boundary Layer Natural Convection in a Porous Medium , Int. J. Heat Mass Transfer, Vol. 27, pp. 717-722, 1984. 

M. R. Fand, T. E. Steinberger, and P. Cheng, Natural Convection Heat Transfer From a Horizontal Cylinder in a Porous Medium, Int. J. Heat Transfer (29/1) 119-133,1986. 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

Chen, G.M., Tso, C.P., 2012. Field synergy principle analysis on convective heat transfer in porous medium with uniform heat generation for thermally developing flow. Int. J. Heat Mass Transf. 55, 4139-4147. 

Havstad, M.A., Burns, P.J., 1982. Convective heat transfer in vertical cylindrical annuli filled with a porous medium. Int. J. Heat Mass Transf. 25, 1755-1766. 

In the last section, convection in a two-dimensional porous medium is presented as a physical problem. Porous media is important in environmental heat transfer studies, transpiration cooling, and fuel cells, as some examples. Using the slug flow assumption, the energy equation is solved using an alternating implicit method to show its effectiveness. 

An example of heat transfer through a porous medium is heat transfer through a layer of granular insulating material. This material will be saturated with air, i.e., the space between the granules of insulating material is entirely filled with air, and this air will flow through the insulation material as a result of the temperature difference imposed on the material, i.e., there will be a free convective flow in the porous material. Even when a fibrous insulation is used, the flow in the insulation can be... 

If the Darcy assumptions are used then with forced convective flow over a surface in a porous medium, because the velocity is not assumed to be 0 at the surface, there is no velocity change induced by viscosity near the surface and there is therefore no velocity boundary layer in the flow over the surface. There will, however, be a region adjacent to the surface in which heat transfer is important and in which there are significant temperature changes in the direction normal to the surface. Under many circumstances, the normal distance over which such significant temperature changes occur is relatively small, i.e., a thermal boundary layer can be assumed to exist around the surface as shown in Fig. 10.9, the ratio of the boundary layer thickness, 67, to the size of the body as measured by some dimension, L, being small [15],[16]. 

Cheng, P. and Minkowycz, W.J., Free Convection About a Vertical Rat Plate Embedded in a Porous Medium with Application to Heat Transfer from a Dike . J. Geophs. Res., Vol. 82, pp. 2040-2044, 1977. 

Parang, M. and Keyhani, M., Boundary Effects in Laminar Mixed Convection Flow Through an Annular Porous Medium , J. Heat Transfer, Vol. 109, pp. 1039-1041, 1987. 

Bejan, A. and Tien, C.L., Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference , J. Heat Transfer, Vol. 100. pp. 191-198, 1978. 

Naylor, D. and Oosthuizen, P.H., Free Convection in a Horizontal Enclosure Partly Filled with a Porous Medium . J of Thermophysics and Heat Transfer, Vol. 9, No. 4, pp. 797-800, 1995. 

Oosthuizen, P.H., Natural Convection in an Inclined Suuure F.nclosure Partly Filled with a Porous Medium and with a Partially Heated Will". Heat Transfer in Porous Media and Two-Phase Flow. ASME HTD-Vol. 302. Energy- Sources Technology Conference and Exhibition. Houston. TX. 1995, pp. 29-42. 

Jang, Jiin Yuh and Chen, Jiing Lin. Thermal Dispersion and Inertia Effects on Vortex Instability of a Horizontal Mixed Convection Flow in a Saturated Porous Medium . Int. J. Heat and Mass Transfer. Vol. 36. No. 2, pp. 383-389. 1993. 

Kumati, M. and Nath. G.. "Non-Darcy Mixed Convection Flow over a Nonisother-mal Cylinder and Sphere Embedded in a Saturated Porous Medium". J. Heat Transfer. Vol. 112, pp.318-521, 1990. 

Lai, F.C. and Kulacki, F.A., "Non-Darcy Mixed Convection Along a Vertical Wall in a Saturated Porous Medium , J Heat Transfer, Vol 113. pp. 252-255. 1991. 

A recent example is coupled T-H-M modelling of the Tunnel Sealing Experiment (TSX) in URL (Guo et al. 2002). To provide data for preliminary validation a surface laboratory experiment known as the Thermal Evaluation of Material Test (TEMT) was conducted. A steel vessel, 1.47 m long with an interior diameter of 0.74 m, was filled with a medium-grained sand and heated by circulating hot water. An array of thermistors monitored the evolution of temperature. Comparison between the physical test results and MOTIF simulation results. Figure 6, shows that MOTIF can be used to simulate convection dominated heat transfer in a porous medium. 

Das, S.S., Mohanty, M., Panigrahi, S.K., Padhy, R.K., Sahu, M., 2012. Radiative heat and mass transfer effects on natural convection Couette flow through a porous medium in the slip flow regime. Int. J. Renew. Energy Technol. Res. 1, 1-14. 

Manglesh, A., Gorla, M.G., Chand, K., 2014. Soret and hall effect on heat and mass transfer in MHD free convective flow through a porous medium in a vertical porous channel. Proc. Natl. Acad. Sci. India A Phys. Sci. 84, 63-69. 

Rath, P.V., Dash, G.C., Parida, A.K., 2013. Three-dimensional MHD free convective flow with heat and mass transfer through a porous medium with periodic permeahihty and chemical reaction. Proc. Natl. Acad. 

Singh, K.D., Sharma, R., 2002. Three dimensional free convective flow and heat transfer through a porous medium with periodic permeability. Indian J. Pure Appl. Math. 33, 941-949. 

A further complication arises in forced convection in fabric, which is a porous medium. There may be significant thermal dispersion, i.e., heat transfer due to hydrodynamic mixing of the fluid at the pore scale. In addition to the molecular diffusion of heat, there is mixing due to the nature of the fabric. 

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