Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Effects of interaction between Rayleigh and Marangoni convection in superposed fluid and porous layers

This paper is aimed at investigating the effects of combined Marangoni and Rayleigh convections in a liquid layer, underlain by a porous layer. The two-dimensional numerical model consists of a dual rectangular cavity system in which the porous cavity is located below the fluid cavity. Both cavities are saturated with the same liquid. The interaction between the Marangoni and the Rayleigh convection is investigated in detail. The porous cavity is heated at the bottom while the top liquid cavity has a free surface and heat is lost to the environment by natural convection. The role of the ratio of the liquid layer over the porous layer in determining the convection pattern was studied. Results indicate that the Marangoni convection enhances the flow in the liquid layer, which results in a reduction of the buoyancy convection in the porous layer. A large heat transfer across the liquid layer was noticeable by displaying the variation of the Nusselt number with the liquid Rayleigh number.     

A Thermal Nonequilibrium Approach to Natural Convection in a Square Enclosure Due to the Partially Cooled Sidewalls of the Enclosure

This article presents a numerical investigation of steady non-Darcy natural convection heat transfer in a square cavity filled with a heat-generating porous medium with partial cooling using a local thermal nonequilibrium (LTNE) model. Five different partial cooling boundary conditions and the fully cooled boundary condition are investigated under LTNE and local thermal equilibrium (LTE). The cooling portions of the left and the right sidewalls of the cavity are maintained at temperature T ₀ while the enclosure's top and bottom walls, as well as the inactive parts of its sidewalls, are kept insulated. The simulation results show that the placement order of wall cooling has a significant effect on the flow pattern and heat transfer rate. Compared with the fully cooled wall, the partially cooled wall of the cavity yielded a higher local Nusselt number for both fluid and solid phases. Under the same boundary conditions, the LTNE and LTE models can demonstrate significant differences in flow patterns and temperature fields. The total heat transfer rate increases with both Darcy number and Rayleigh number. Enhancement of interphase heat transfer coefficient (H) reduces the impact of Darcy number on the heat transfer rate of a porous cavity. Also, the total heat transfer rate of the porous medium decreases steadily with thermal conductivity ratio γ and interphase heat transfer coefficient H.     

Heat and Moisture Transfer in a Rectangular Cavity Partially Filled with Hygroscopic Porous Media

Abstract

This work deals with turbulent natural convection heat and moisture transfer with thermal radiation in a rectangular cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous media and moisture content transfer in hygroscopic porous medium were solved by the finite element method. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation, Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and hygroscopic porous medium. With the increase in Rayleigh number, the temperature of porous medium at the interface increased slightly, and the magnitude of moisture change becomes smaller.     

Nonsimilar solutions for mixed convection of water at 4°C over a vertical surface with a convection boundary condition in a porous medium

A boundary layer analysis has been presented for the mixed convection of water at 4°C over a vertical plate embedded in a porous medium. The Robin or convective boundary condition at the surface has been considered where the heat lost from the surface is the product of a heat transfer coefficient and the temperature difference between the surface and the free stream. The governing non‐similar boundary layer equations for both the forced and free convection dominated regimes were solved numerically by means of an implicit finite difference method. The friction factor and dimensionless heat transfer rate (Nusselt number) are presented for several values of the dimensionless heat transfer coefficient and buoyancy parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21022     

Numerical study of natural convection in a vertical porous annulus with discrete heating

In this paper natural convection flows in a vertical annulus filled with a fluid-saturated porous medium has been investigated when the inner wall is subject to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkman-extended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Further, we find that the size and location of the heater effects the flow intensity and heat transfer rate in the annular cavity.     

Natural convection in a shallow porous cavity—the Brinkman model

The natural convection in a shallow porous rectangular cavity with differentially heated sidewalls is examined using the Brinkman model. The heat transfer rate through the cavity is determined in terms of a Nusselt number, in the limit of vanishingly small aspect ratio. Two types of boundary conditions are considered. Case I deals with a cavity with all rigid boundaries so that the no-slip boundary conditions can be imposed. In case II, the cavity has a free upper surface. The present analysis shows that the Brinkman model and Darcy's law give virtually the same result for the heat transfer rate when the Darcy number, based on the depth of the cavity, is less than the order of 10⁻⁴. We also find that the presence of a free surface can significantly increase the heat transfer rate through the cavity, especially when the permeability of the medium is high.     

Buoyancy-induced inclined boundary layer flow in a porous medium resulting from combined heat and mass buoyancy effects

An implicit finite difference method is used to analyze the natural convection boundary layer flow in a saturated porous medium resulting from combined heat and mass buoyancy effects adjacent to an inclined surface. Both the streamwise and normal components of the buoyancy force are retained in the momentum equations. The present formulation permits the angles of from the horizontal. Numerical results indicate that, as the buoyancy ratio or inclination parameter increase, the surface heat and mass transfer rates increase. These results are compared with the approximate similarity solutions that are obtained by neglecting the normal component of the buoyancy force in the momentum equations. It is shown that the approximate similarity solutions may significantly underpredict the heat and mass transfer rates for small values of inclination parameter.     

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

Combined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m². To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.     

Natural convection in an enclosure with localized heating and salting from below

Two-dimensional, double diffusion, natural convection in a rectangular enclosure filled with binary fluid saturating porous media is investigated numerically. Multiple motions are driven by the external temperature and concentration differences imposed across horizontal walls with the simultaneous presence of discrete heat and contaminant sources. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the cavity. The fluid, heat and moisture transport through the isotropic porous layer are analyzed using the streamlines, heatlines and masslines, and the heat and mass transfer potentials are also explained by the variations of overall Nusselt and Sherwood numbers. The numerical simulations presented here span a wide range of the main parameters (thermal Rayleigh numbers, strip pitches and Darcy number) in the domain of destabilizing solutal buoyancy forces. It is shown that the heat and mass transfer potential can be promoted or inhibited, depending strongly on the permeability of porous medium, the strip pitch, the thermal and solutal Rayleigh numbers.     

LBM modeling and analysis on microchannel slip flow and heat transfer under different heating conditions

Abstract

This article aims to explore the effects of buoyancy force and thermal boundary condition on the mixed convection heat transfer performance of air in a horizontal microchannel. Three different heat flux models, including bottom wall heated, top wall heated (single wall heating – a novel heating approach compared to recent studies) and both walls heated, are analyzed at four different values of the Grashof number (Gr?=?0, 100, 300, 600) using a lattice Boltzmann method (LBM). The slip velocity boundary condition is also applied to the bottom and top walls. It can be found that the buoyancy force changes the velocity distribution structure near the bottom wall and top wall, particularly at the inlet regions in all models, and a negative slip velocity is generated due to the backflow formed at a relatively large Grashof number and it strictly determines the local wall friction coefficient. Either the bottom wall or the top wall is heated. A vortex is found close to the top wall because the mixing position of the hot and cold fluids is in the vicinity of the top wall. This feature facilitates the heat transfer near the top wall and core flow zone. The thermal performance is most positive for the case when the top wall is heated due to the generation of an induced vortex and no influence of the vortex near the bottom wall.     

Convective heat transfer combined with surface radiation in a rotating square cavity with a local heater

The effect of surface radiation on laminar natural convection in a rotating cavity with a discrete heater has been analyzed numerically. The enclosure is insulated at the bottom and top, heated by a constant temperature from the discrete heater located on the bottom wall, and cooled by a constant temperature from the side walls. Governing equations with corresponding initial and boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The effects of surface emissivity, Rayleigh number, and Taylor number on the fluid flow and heat transfer have been studied. Obtained results have revealed that rotation can be a very good control parameter for heat transfer and fluid flow.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.     

Unsteady conjugate natural convection in a porous cavity boarded by two vertical finite thickness walls

The objective of this study is to investigate unsteady conjugate natural convection in a porous cavity sandwiched by finite conductive walls considering time-periodic boundary conditions and local thermal non-equilibrium. The top and bottom boundaries are assumed to be isolated and the continuity of temperature and heat transfer are considered in interface boundaries. The effect of varying a plethora of parameters such as Rayleigh number, Thermal conductivity ratio, wall thickness, and non-dimensional frequency on the streamlines, isotherms, and Nusselt number has been studied. It is shown that, apart from non-dimensional frequency and wall thickness, the amplitude of periodic fluid Nusselt number is an increasing function of all aforementioned parameters. Furthermore, aside from Rayleigh number and heat transfer coefficient, the behavior of the solid Nusselt number is the same as fluid Nusselt number. Eventually, the time-averaged Nusselt number and heat transfer through the vertical walls for different values of non-dimensional frequencies are calculated.     

Mixed convection plume about a line heat source in micropolar fluid

This paper analyses the flow and heat transfer characteristics of the mixed convection in the boundary layer flow of micropolar fluids about a line heat source embedded on the edge of a plate. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and investigated numerically in order to characterize the behaviors of the mixed convection wall plume. The numerical results have been obtained using the method of cubic spline collocation and the finite difference scheme. The micropolar parameter reduces the velocity but increases the temperature in the boundary layer, whereas the effects of buoyancy parameter trend conversely. Furthermore, the micropolar parameter decreases the skin friction parameter and the wall couple stress but increases the wall temperature, whereas the effects of buoyancy parameter trend conversely. Finally, the higher the value of Prandtl number, the greater the skin friction parameter, the wall couple stress and the wall temperature.     

WALL HEAT CONDUCTION EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM

ABSTRACT

A numerical analysis has been made of the conjugate natural convection in a rectangular enclosure filled with a fluid-saturated porous medium and surrounded with four solid walls. The conductance of the walls is assumed to be much greater than that of the cavity filled with a porous medium. The main objective was to investigate the influences of the ratio of thermal conductivity of the wall to that of the fluid-porous matrix composite, the Darcy-modified Rayleigh number, the Prandtl number, and the aspect ratio. The streamlines and isotherms are presented; also, the local and average Nusselt numbers are presented along the interface between walls and cavity. A non-Darcian model was employed and the numerical method was SIMPLE-C. The numerical results indicate that the wall heat conduction effects decrease the heat transfer rate. When the wall heat conduction is considered, the greater the conductance of the solid walls surrounding the cavity, the greater is the rate of heat transfer.     

Effects of buoyancy assisting and opposing flows on mixed convection boundary layer flow over a permeable vertical surface

The present study deals with new similarity solution of steady mixed convection boundary layer flow over a permeable surface for convective boundary condition. It has been shown that a self similar solution is possible when the mass transfer velocity at the surface of the plate varies like x^−1/2, where x is the distance from the leading edge of the solid surface. Two point boundary value problem governed by non-linear coupled ordinary differential equations have been solved numerically using implicit finite difference scheme in combination with the quasi-linearization technique. It is interesting to note that dual solutions exist for buoyancy assisting flow, besides that usually reported in literature for buoyancy opposing flow. Further, the buoyancy assisting force causes considerable overshoot in the velocity profile and the Prandtl number strongly affects the thermal boundary layer thickness including the surface heat transfer rate.