Drying in porous media involves complex processes of heat, mass and momentum transfer as well as phase change. Understanding these phenomena through mathematical models leads to considerable improvement in energy savings and cost reduction in industrial drying. This chapter provides an overview of the transport phenomena in porous media with specific application to drying. It reviews available drying models for porous media ranging from the liquid diffusion model to single phase to complex multiphase models along with the conjugate ambient model. The governing equations and their constitutive relations are discussed along with associated assumptions, approximations and limitations. Detailed discussion of the interphase mass, momentum, energy and species transfer is highlighted along with guidelines for future research direction. This provides an overview for the researcher as well as the drying practitioner to select the most suitable model depending on their need and purpose.
Heat and Mass Transfer in Porous Media
heat pipes (micro-heat, sorption and pulsating heat pipes with longitudinal grooves, micro- and nanoscale porous coatings, long heat pipes, vapourdynamic thermosyphons, etc.); in sorption cooling or heating systems; in mini-channels with porous nanocoating; in catalytic systems based on metals and metal-oxide porous materials, etc.
Recent developments in the optimization of the platelet structure of materials used in various branches of technology for heat and mass transfer processes in porous spaces saturated with liquid or gas (evaporation, condensation, capillary transport, etc.) are of special interest.
Articles and reviews on the study of internal mechanisms of mass and energy transfer in porous media, including predictions and efficiency assessment of porous materials used in various branches of engineering and technology, would be an asset.
In food systems, an enormous range of processes can be viewed as involving transport of heat and mass through porous media. Examples include extraction (Schwartzberg & Chao, 1982), drying, frying, microwave heating, meat roasting, rehydration of breakfast cereals (Machado, Oliviera, Gekas, & Singh, 1998), beans (e.g., Hsu, 1983) and dried vegetables (Sanjuan, Simal, Bon, & Mulet, 1999). Illustration of a range of porous media situations and structures in food can be seen in Fig. 1. Methodologies for creating tailor-made porous structures with a wide range of porosities have also been reported (Rassis, Nussinovitch, & Saguy, 1997). Most solid food materials can be treated as hygroscopic and capillary-porous (explained later). Liquid solutions and gels are non-porous. In these materials, transport of water is considered only due to the relatively simple phenomena of molecular diffusion and is not discussed in this article.
In non-hygroscopic materials, the pore space is filled with liquid if the material is completely saturated, and with air if it is completely dry. The amount of physically bound water is negligible. Such a material does not shrink during heating. In non-hygroscopic materials, vapor pressure is a function of temperature only. Examples of non-hygroscopic capillary-porous materials are sand, polymer particles and some ceramics. Transport of materials in non-hygroscopic materials does not cause any additional complications as in hygroscopic materials noted below.
The approach taken in porous media is still a continuum one, but on a coarser level of averaging as compared to the standard continuum approach that averages at a more microscopic level. All variables and parameters of the continuum approach to porous media are averaged over a representative elementary volume (REV). In this continuum approach, the actual multiphase porous medium is replaced by a fictitious continuum: a structureless substance, to any point of which we assign variables and parameters that are continuous functions of the spatial coordinates of the point and of time (Bear, 1972).
Study of transport in porous media is a very active field. Entire textbooks (Bear, 1972, Kaviany, 1995, Vafai, 2000) and journals (Nassar & Horton, 1997) have been dedicated to this field. However, applications of transport in porous media to food materials have been little, perhaps due to the difficulty in obtaining the many process parameters needed, the complexity of such formulations and the unavailability of software tools to solve the resulting set of equations. Porous media approaches to the study of drying processes have been summarized in Plumb (2000, Chap. 17), where applications to food materials is noted. Although many food researchers are active in studying food structure parameters such as porosity (e.g., Aguilera, 2003, Rahman, 2003) and certainly some of these studies have the intention of relating structure to transport properties, quantitative relationships between structure and transport properties continue to be elusive in the literature.
This formulation covers the vast majority of food processing situations when our interest is transport within a plant or animal tissue or a structured food material. Excellent reviews of heat and moisture transfer in porous media in the context of foods have appeared in the past (Bruin and Luyben, 1980, Fortes and Okos, 1980). For our discussion, a porous medium can be conceptually viewed as shown in Fig. 4, with the various phases and the associated modes of transport. This representation
Relationship between various models used to study simultaneous heat and mass transfer in food processes is clearly shown here, starting from the most elaborate multiphase porous medium model that includes evaporation and going down in complexity to the simplest equation of isothermal diffusion. The fundamental transport modes of molecular diffusion, capillary diffusion and pressure driven Darcy flow are clearly shown in the detailed models. The relationship of a simple model to the detailed
Phase change heat transfer in capillary porous media is of great relevance in diverse industrial applications. Heat pipes, vapor chambers, thermosyphons and cold plates are some of the phase change devices which employ microscopic porous media and are used in the thermal management of high-power electronics. These devices realize high heat transfer rates by exploiting latent heat exchange. The increasing power density of electronic chips requires that the performance of these devices be optimized so that heat can be efficiently removed from the electronic chip while limiting the temperature differential between the chip and ambient. The efficiency of heat spreading in heat pipes and vapor chambers relies on the capillary porous medium (wick structure) used in the device. The wick structure also determines the maximum heat transport capability. The study of phase change heat and mass transfer in wick structures can lead to the optimization of wick design and improved performance of the phase-change cooling devices. In the first part of this thesis, numerical models are developed to study the heat and mass transport in wick structures at the pore scale. The microstructures are characterized on the basis of their wicking and thin-film evaporation performance by modeling the rates of evaporation from the liquid menisci formed in common wick microstructures. Evaporation at the interface is modeled by using appropriate heat and mass transfer rates obtained from kinetic theory. At higher heat inputs, nucleate boiling occurs in the wick structure causing a decrease in the wick thermal resistance and improvement in the device performance. A volume-of-fluid-based model is developed to study the growth of vapor bubbles in wick microstructures. In the second part of this thesis, a transient three-dimensional heat pipe model is developed which is suitable for predicting the hydrodynamic and thermal performance of vapor chambers at high heat flux inputs and small length scales. The influence of the wick microstructure on evaporation and condensation mass fluxes at the liquid-vapor interface is accounted for by integrating a microstructure-level evaporation model (micromodel) with the device-level model (macromodel). The effect of boiling in the wick structure at higher heat inputs on the vapor chamber performance is modeled and the model predictions are validated with experiments performed on custom-fabricated vapor chambers. The model is further utilized to optimize the performance of an ultra-thin vapor chamber. The last part of this work focuses on the design of novel wick micro- and nano-structures for performance improvement of vapor chambers. The thermal and hydrodynamic performance of micro-pillared structures are first modeled and a ten-times improvement in the maximum heat transport capability of vapor chambers is revealed. The viability of utilizing nanostructures such as carbon nanotubes (CNTs) and metallic nanowires as wick structures for heat pipes is also assessed. Using theoretical models, it is concluded that the flow resistance of nanostructures poses a major bottleneck to their use as passive flow-conveying media. An alternative design which combines the micro- and nano-level wicks is proposed which leads to a 14% decrease in the wick thermal resistance.
In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile. 2ff7e9595c
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