Kambiz Vafai

Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids

Abstract Heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids is investigated for various pertinent parameters. A model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. The transport equations are solved numerically using the finite-volume approach along with the alternating direct implicit procedure. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. The effect of suspended ultrafine metallic nanoparticles on the fluid flow and heat transfer processes within the enclosure is analyzed and effective thermal conductivity enhancement maps are developed for various controlling parameters. In addition, an analysis of variants based on the thermophysical properties of nanofluid is developed and presented. It is shown that the variances within different models have substantial effects on the results. Finally, a heat transfer correlation of the average Nusselt number for various Grashof numbers and volume fractions is presented.

Boundary and inertia effects on flow and heat transfer in porous media

Abstract The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.

Analysis of dispersion effects and non-thermal equilibrium, non- Darcian, variable porosity incompressible flow through porous media

Abstract The present work involves the numerical simulation of forced convective incompressible flow through porous media, and the associated transport processes. A full general model for the momentum equation was employed. The mathematical model for energy transport was based on the two-phase equation model which assumes no local thermal equilibrium between the fluid and the solid phases. The investigation aimed at a comprehensive analysis of the influence of a variety of effects such as the inertial effects, boundary effects, porosity variation effects, thermal dispersion effects, validity of local thermal equilibrium assumption and two dimensionality effects on the transport processes in porous media. The results presented in this work provide detailed yet readily accessible error maps for assessing the importance of various simplifying assumptions which are commonly used by researchers.

The role of porous media in modeling flow and heat transfer in biological tissues

Flow and heat transfer in biological tissues are analyzed in this investigation. Pertinent works are reviewed in order to show how transport theories in porous media advance the progress in biology. The main concepts studied in this review are transport in porous media using mass diffusion and different convective flow models such as Darcy and the Brinkman models. Energy transport in tissues is also analyzed. Progress in development of the bioheat equation (heat transfer equation in biological tissues) and evaluation of the applications associated with the bioheat equation are analyzed. Prominent examples of diffusive applications and momentum transport by convection are discussed in this work. The theory of porous media for heat transfer in biological tissues is found to be most appropriate since it contains fewer assumptions as compared to different bioheat models. A concept that is related to flow instabilities caused by swimming of microorganisms is also discussed. This concept named bioconvection is different from blood convection inside vessels. The works that consider the possibility of reducing these flow instabilities using porous media are reviewed.

Convective flow and heat transfer in variable-porosity media

The present work analyses the effects of variable porosity and inertial forces on convective flow and heat transfer in porous media. Specific attention is given to forced convection in packed beds in the vicinity of an impermeable boundary. After establishing the governing equations, a thorough investigation of the channelling effect and its influence on flow and heat transfer through variable-porosity media is presented. Based on some analytical considerations, a numerical scheme for the solution of the governing equations is proposed to investigate the variable-porosity effects on the velocity and temperature fields inside the porous medium. The method of matched asymptotic expansions is used to show the qualitative aspects of variable porosity in producing the channelling effect. These qualitative features are also confirmed by the numerical solution. The qualitative effects of the controlling parameters on flow and heat transfer in variable-porosity media are discussed at length. The variable-porosity effects are shown to be significant for most cases. For the same conditions as the perturbation solution, the numerical results are in excellent agreement with the perturbation analysis. The numerical results are also in very good agreement with the available experimental data of previous studies.

Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer

DiAerent types of interfacial conditions between a porous medium and a fluid layer are analyzed in detail. Five primary categories of interface conditions were found in the literature for the fluid flow at the interface region. Likewise, four primary categories of interface conditions were found in the literature for the heat transfer at the interface region. These interface conditions can be classified into two main categories, slip and no-slip interface conditions. The eAects of the pertinent parameters such as Darcy number, inertia parameter, Reynolds number, porosity and slip coeAcients, on diAerent types of interface conditions are analyzed while fluid flow and heat transfer in the neighborhood of an interface region are properly characterized. A systematic analysis of the variances among diAerent boundary conditions establishes the convergence or divergence among competing models. It is shown that in general, the variances have a more pronounced eAect on the velocity field and a substantially smaller eAect on the temperature field and even a smaller eAect on the Nusselt number distributions. For heat transfer interface conditions, all four categories generate results, which are quite close to each other for most practical applications. However, small discrepancies could appear for applications dealing with large values of Reynolds number and/or large values of Darcy number. Finally, a set of correlations is given for interchanging the interface velocity and temperature as well as the average Nusselt number among various models. ” 2001 Elsevier Science Ltd. All rights reserved.

Analysis of flow and heat transfer at the interface region of a porous medium

Abstract Fluid flow and heat transfer at the interface region are analyzed in depth for three general and fundamental classes of problems in porous media. These are the interface region between two different porous media, the interface region between a fluid region and a porous medium, and the interface region between an impermeable medium and a porous medium. These three types of interface zones constitute a complete investigation of the interface interactions in a saturated porous medium. Detailed analytical solutions, for both the velocity and temperature distributions are derived for all of these interface conditions. The analytical temperature distributions are found in terms of confluent hypergeometric functions for two different regimes, which are found to cover almost the entire range of real fluids. The numerical and analytical results are found to be in excellent agreement. The numerical and analytical results are also checked against an empirically based hypothesis for one of the interface conditions, namely the interface between a fluid region and a porous medium, and are found to be in excellent agreement with that experimental hypothesis.

Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media

Abstract An analytical characterization of forced convective flow through a channel filled with a porous medium is presented in this work. Based on a two-equation model, including transverse conduction contributions, exact solutions are obtained for both fluid and solid phase temperature fields. The Nusselt number is also obtained in terms of the pertinent physical parameters, namely the Biot number for the internal heat exchange and the ratio of effective conductivities between the fluid and solid phases. It is shown that the heat transfer characteristics can be classified within three regimes, each of which is dominated by one of three distinctive heat transfer mechanisms, i.e., fluid conduction, solid conduction and internal heat exchange between solid and fluid phases. Based on these results, a complete electrical thermal network representative of transport through porous media is established. In addition, an analytical characterization and conceptual assessment of solid and fluid temperature differentials is presented, the validity of the one-equation model is investigated and a practical criterion is suggested for channels with different cross sections.

Analysis of two-layered micro-channel heat sink concept in electronic cooling

Abstract In this work, a new concept for a two-layered micro-channel heat sink with counter current flow arrangement for cooling of the electronic components is proposed. The thermal performance and the temperature distribution for these types of micro channels were analyzed and a procedure for optimizing the geometrical design parameters is presented. While the power supply system of the two-layered design is not significantly more complicated than the one-layered design, the streamwise temperature rise on the base surface was found to be substantially reduced compared to that of the one-layered heat sink. At the same time, the pressure drop required for the two-layered heat sink was found to be substantially smaller than that of the one-layered heat sink. The results demonstrate that the two-layered micro-channel heat sink design is a substantial improvement over the conventional one-layered micro-channel heat sink.

Fluid mechanics of the interface region between a porous medium and a fluid layer—an exact solution

The description of the fluid mechanics at the interface between a fluid layer and a porous medium which was first investigated by Beavers and Joseph is revisited in this work. An exact solution describing the interfacial fluid mechanics is presented. The effects of the Darcy number and inertia parameter are briefly discussed.