Natural convection in fluid–superposed porous layers heated locally from below

A numerical study of two-dimensional natural convection in fluid–superposed porous layers heated locally from below is reported based on the one-domain formulation of the conservation equations. The effects of five dimensionless parameters on overall Nusselt number are investigated: Rayleigh number based on overall layer height, heater-to-cavity length ratio, porous layer-to-cavity height ratio, domain aspect ratio, and Darcy number. Streamline and isotherm patterns indicate that convective motion is restricted to the overlying fluid layer with some penetration into the porous layer. Nusselt numbers increase with a decrease in the heater length and height ratio, and increase with the Darcy number. The size of the heat source does not affect the dependence of the heat transfer coefficient on height ratio and Darcy number. For domains with large aspect ratios, complex flow restructuring is observed with an increase in Rayleigh number. The present results represent an extension of the well studied problem of buoyant convection in fluid–superposed porous layers with a fully heated lower surface.     

Mixed Convection in an Obstructed Open-Ended Cavity

Mixed convection in an obstructed cavity with heated horizontal walls is investigated in this work. Brinkman-Forchheimer-extended Darcy model is utilized to describe the flow characteristics within a porous medium for different angles of attack with respect to the forced convection. Numerical results are obtained for a wide range of Grashof numbers (10²–10⁹), Reynolds numbers (10²–10⁵), Darcy numbers (10^?6–10^?1), and aspect ratios (0.25–2). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the Darcy number plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. For an inclined flow, the vertical velocity component is substantially diminished within a narrow entrance section near the inlet boundary. It is shown that as the aspect ratio increases the thickness of the thermal boundary layer increases, resulting in a decrease in the heat transfer rate though the horizontal walls.     

Convective heat transfer over a heated square porous cylinder in a channel

A numerical study is made of the unsteady flow and convection heat transfer for a heated square porous cylinder in a channel. The general Darcy–Brinkman–Forchheimer model is adopted for the porous region. The parameters studies including porosity, Darcy number, and Reynolds number on heat transfer performance have been explored in detail. The results indicate that the average local Nusselt number is augmented as the Darcy number increases. The average local Nusselt number increases as Reynolds number increases; in particular, the increase is more obvious at a higher Darcy number. In contrast, the porosity has slight influence on heat transfer.     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

Conjugate Mixed Convection Heat Transfer in Plane Laminar Wall Jet Flow

A numerical investigation of heat transfer from a uniformly heated slab of finite thickness by plane laminar wall jet flow under combined forced and natural convection, i.e., mixed convection, is presented. The problem has been solved for two classical cases such as Pr ? 1 and Pr ? 1. The effects of the Grashof number (Gr), Reynolds number (Re), Prandtl number (Pr), and thermal conductivity ratio (R_k) between the slab and fluid medium are investigated on the heat transfer characteristics, i.e., local Nusselt number, interface temperature, and average Nusselt number.     

Numerical investigation of unsteady natural convection heat transfer and entropy generation from a pair of cylinders in a porous enclosure

Abstract

The present study analyses numerically the unsteady heat transfer and entropy generation characteristics in a two-dimensional porous enclosure embedded with two heated circular cylinders at different positions at the vertical mid-plane. The heat transfer is primarily due to conduction for lower values of Darcy number (10^?4), while heat transfer by convection becomes significant for higher values of Darcy number (10^?3, 10^?2). Contrasting features are observed in the variation of time-average Nusselt number with interspacing distance. The major contributor of irreversibility is the entropy generation due to heat transfer for lower values of Darcy number, while for larger values of Darcy number, it varies with Rayleigh number.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Non—Darcian and Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic,is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideratioin to the viscous effect.The results show that:(1)a larger permeability ratio(K^*) causes a lower flow intensity in the enclosure and a smaller Nusselt number,all Nusselt numbers approach unity in the limit of K^*→∞;a larger thermal conductivity ratio(λ^*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls,all the Nusselt numbers approach unity in the limit of λ^*-→0,the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number.(2) an increasing Darcy number decreases the flow intensity and heat tansfer rates,which is more significant at a lower permeability ratio.In particular,with K^*≤0.25,the Nusselt number for Da=10^-3 would differ from that of Darcy flow up to an amount of 30%,an analysis neglecting the non-Darican effect will inevitably be of considerable error.     

Natural Convection in a Non-Darcy Porous Cavity Filled with Cu–Water Nanofluid Using the Characteristic-Based Split Procedure in Finite-Element Method

Natural convection of Cu–water nanofluid in a differentially heated non-Darcy porous cavity was numerically investigated by using the characteristic-based split algorithm in finite element method. Effects of the various thermophysical parameters and the solid volume fraction of nanoparticle on heat transfer and fluid flow in different flow regimes were demonstrated. Although the addition of nanoparticles in the porous medium generally resulted in the higher average Nusselt number in most flow regimes, the average Nusselt number appears to decrease or stay nearly the same with increased solid volume fraction in Darcy flow regime at a high Rayleigh number and low Darcy number.     

Numerical simulation and optimization of turbulent nanofluids in a three-dimensional wavy channel

ABSTRACT

In this study, numerical calculations by single- and two-phase models of nanofluid turbulent forced convection in a three-dimensional wavy channel with uniform wall temperature are investigated. The numerical results for the Nusselt number ratio (Nu/Nu₀) show that the heat transfer performance of a symmetric wavy channel performs better than that of an in-line wavy channel. The multi-parameter constrained optimization procedure integrating the design of experiments (DOEs), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid turbulent convection of the three-dimensional wavy channel.     

Numerical study of heat transfer enhancement for a novel flat-plate solar water collector using metal-foam blocks

This paper reports a numerical study of enhanced forced convection in a channel of solar water collector using multiple metal-foam blocks. Both Darcy–Brinkman–Forchheimer flow model and two-equation energy model based on local thermal non-equilibrium are used to characterize the thermo-flow fields inside the porous regions. Solution of the coupled governing equations for the porous/fluid composite system is obtained using a stream function-vorticity analysis. The results show that the recirculation caused by metal-foam block will significantly augment the heat transfer rate on heated surface. Besides, a useful correlated equation to predict Nu_m is proposed and the validity of the LTE condition is examined.     

Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium

The classical Graetz methodology is applied to investigate the effect of local thermal non-equilibrium on the thermal development of forced convection in a parallel-plate channel filled by a saturated porous medium, with walls held at constant temperature. The Brinkman model is employed. The analysis leads to an expression for the local Nusselt number, as a function of the dimensionless longitudinal coordinate, the Péclet number, the Darcy number, the solid-fluid heat exchange parameter, the solid/fluid thermal conductivity ratio, and the porosity.     

Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions with the limitation of the Darcy model. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 1.0), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The correlation for Nu_avg in the forced convection regime is suggested. It is shown that mixed convection mode can cause minimum average Nusselt number unfavorably due to counteraction of jet flow against buoyancy driven flow. Hence, careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

EFFECT OF HEATED WALL POSITION ON MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY

Mixed convection in an open cavity with a heated wall bounded by a horizontally insulated plate is studied numerically. Three basic heating modes are considered: (a) the heated wall is on the inflow side (assisting flow); (b) the heated wall is on the outflow side (opposing flow); and (c) the heated wall is the horizontal surface of the cavity (heating from below). Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of streamlines, isotherms, wall temperature, and the velocity profiles in the cavity for Ri=0.1 and 100, Re=100 and 1000, and the ratio between the channel and cavity heights (H/D) is in the range 0.1-1.5. The present results show that the maximum temperature values decrease as the Reynolds and the Richardson numbers increase. The effect of the H/D ratio is found to play a significant role on streamline and isotherm patterns for differentheating configurations. The present investigation shows that the opposing forced flow configuration has the highest thermal performance in terms of both maximum temperature and average Nusselt number.     

Forced convection in a channel partly occupied by a bidisperse porous medium: Asymmetric case

This paper presents an analytic investigation of forced convection in parallel-plate channel partly occupied by a bidisperse porous medium and partly by a fluid clear of solid material, the distribution being asymmetrical. The walls of the channel are subject to an uniform heat flux; the flow is assumed to be hydrodynamically and thermally fully developed. The layer of a bidisperse porous medium is attached to one of the channel walls; it is modeled utilizing a two-velocity two-temperature formulation using Darcy’s law. The Beavers–Joseph boundary condition is employed at the bidisperse porous medium/clear fluid interface. The dependences of the Nusselt number on a conductivity ratio, a velocity ratio, a volume fraction, internal heat exchange parameter, and the position of the porous-fluid interface are investigated. Both cases of symmetric and asymmetric heating are investigated, which is specified by the asymmetry heating parameter introduced here. For the case of asymmetric heating, a singular behavior of the Nusselt number is found and explained.     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross‐section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss–Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (10⁴, 10⁵, and 10⁶), and Darcy number (10^?3, 10^?4, and 10^?5). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58° and 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure.     

HEAT TRANSFERPREDICTIONS AROUND THREE HEATED CYLINDERS BETWEEN TWO PARALLEL PLATES

The objective of this article is to investigate the heat transfer of convective flow across three heated cylinders arranged in an isosceles right-angled triangle between two parallel plates. The variations in drag coefficient and time-averaged Nusselt number around the surface of the three cylinders as well as the surface-averaged values of the time-averaged Nusselt number for each cylinder are investigated. This investigation is considered under the conditions where the gap-to-diameter ratio is changed (0.5 to 1.25) with forced convection (Re = 100 to 300) and mixed convection (Gr = 80,000 and 200,000). The maximum value of surface- and time-averaged Nusselt number for both forced convection and mixed convection is obtained at a gap-to-diameter ratio equal to 0.75 among the gap-to-diameter ratios considered in this article.     

Buoyancy-induced flow and heat transfer in a porous annulus between concentric horizontal circular and square cylinders

ABSTRACT

This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature T_h, whereas the cooled outer square duct is held at the uniform cold temperature T_c. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (?), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ?. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.     

Electromagnetic field effects on transport through porous media

The effect of an imposed electromagnetic field on forced convection in porous media is analyzed in this work. The transient Maxwell’s equations are solved to simulate the electromagnetic field inside the waveguide and within a porous medium. The Brinkman–Forchheimer extended Darcy (generalized model) equations are used to represent the flow fluid inside a porous medium. The local thermal non-equilibrium (LTNE) is taken into account by solving the two-energy equation model for fluid and solid phases. Computational domain is represented for a range of Darcy number from 10^?5 to 10^?7 and dimensionless electromagnetic wave power P¹ from 0 to 1600, and dimensionless electromagnetic wave frequency f¹ from 0 to 8. The effect of variations of the pertinent electromagnetic field parameters in affecting the flow and thermal fields and the Nusselt number are analyzed. This investigation provides the essential aspects for a fundamental understanding of forced convection in porous media while experiencing an applied electromagnetic field such as applications in the material-processing field.