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.     

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.     

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.     

Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations

This work examines the effects of the vortex viscosity parameter and the buoyancy ratio on the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The closed-form analytic solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived. Increasing the vortex viscosity parameter tends to increase the magnitude of microrotation and thus decreases the fluid velocity in the vertical channel. Moreover, the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid for micropolar fluids are lower than those of Newtonian fluids.     

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.     

Modelling of Non-Darcy Flows through Porous Media Using Extended Incompressible Smoothed Particle Hydrodynamics

In this article, a novel numerical method is presented for the simulation of non-Darcy flows through porous media by the incompressible smooth particle hydrodynamics (ISPH) method with a predictor-corrector scheme. In the ISPH algorithm, a semi-implicit velocity-correction procedure is used and the pressure is obtained by solving the pressure Poisson equation. The key point for the application to non-Darcy flows is to include porosity and drag forces of the medium (the Darcy term and the Forcheimer term) in the ISPH method. Unsteady lid-driven flow, natural convection in non-Darcy porous cavities, and natural convection at a porous medium–fluid interface are examined separately by our extended ISPH method. The results are presented with flow configurations, isotherms, and average Nusselt numbers for different Darcy numbers from 10^?4 to 10^?2, porosity values from 0.4 to 0.9, and Reynolds/Rayleigh numbers. The flow pattern and rate of heat transfer inside the cavity are affected by these parameters. The results demonstrate the important effect of the Darcy number on both the heat transfer rate and the flow regime. The results from this investigation are well validated and compare favorably with previously published results.     

Non-Darcy natural convection of a non-Newtonian fluid in a porous cavity

A numerical study of non-Darcy natural convection in a porous enclosure saturated with a power-law fluid is presented. Hydrodynamic and heat transfer results are reported for the configuration in which the enclosure is heated from a side-wall while the horizontal walls are insulated. The flow in the porous medium is modeled using the modified Brinkman–Forchheimer-extended Darcy model for power-law fluids, which accounts for both inertia and boundary effects. The results indicate that when the power law index is decreased, the circulation within the enclosure increases leading to a higher Nusselt number and these effects are enhanced as the Darcy number is increased. Consequently as the power law index decreases, the onset of the transitions from Darcy regime to Darcy–Forchheimer–Brinkman regime to asymptotic convection (boundary layer) regime shift to higher corresponding values of the Darcy number. An increase in Rayleigh number produces similar effects as a decrease in power law index.     

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.     

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.     

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.     

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.     

Double diffusive natural convection in an enclosure filled with a step type porous layer: Non-Darcy flow

The double diffusive natural convection between a saturated porous layer and an overlying fluid layer in an enclosure has been investigated using the non-Darcy flow model. The problem has been investigated for two cases; namely case I where the interface between fluid and porous layer is horizontal, and case II where the interface contains a step that has a height a. The fluid flow and heat and mass transfer has been investigated for different values of the step height and the Rayleigh and Darcy numbers. The results show that the height of the step at the interface has a significant effect on the flow field and heat and mass transfer from the left-hand to the right-hand walls in the composite enclosure. This is very important for insulation problems and for heat and mass blockage in enclosure systems.     

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.     

Accurate numerical simulation for non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity using SEM

The non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity with two thermosolutal sources is numerically investigated in this article, depicting the effects of different physical parameters on heat and mass transfer in the drying chamber. The flow is generated due to the motion of the horizontal moving lids and the buoyancy produced by the temperature and concentration gradients. The governing equations are discretized by the Legendre spectral element method (SEM) with high accuracy, and an improved time-splitting method is developed to deal with the coupled pressure and velocity in the Brinkman-Forchheimer extended Darcy model. The effects of Darcy number (Da?=?10^?5～10^?1), Richardson number (Ri?=?10^?2～10¹), and buoyancy ratio (Br = ?5?～?5) are investigated, and numerical results are analyzed by contours of streamline, isotherm, heatline, isoconcentration, and massline in detail. Results reveal the pattern of heat and mass transfer with the variation on significant parameters by the average Nusselt and Sherwood numbers on the moving lids of the cavity.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

Buoyancy-induced flow,heat, and mass transfer in a porous annulus

This paper reports on double-diffusive natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. A pressure-based segregated finite volume method is used to solve the problem numerically. The diffusion fluxes are discretized using the MIND fully implicit scheme. Furthermore, a modified pressure correction equation is derived that implicitly accounts for the nonorthogonal diffusion terms, which are usually neglected in the standard SIMPLE algorithm. Results indicate that convection effects increase with an increase in Rayleigh number, Darcy number, porosity, and enclosure aspect ratio. Further, at low Darcy values, porosity has no effect on the flow, temperature, and concentration fields.     

Non-darcy mixed convection in a vertical porous channel with discrete heat sources at the walls

A numerical study of mixed convection in a parallel-plate vertical channel filled with a fluid-saturated porous medium and containing discrete heat sources at the walls is performed using the Brinkman-Forchheimer-extended Darcy model. The evolution of buoyancy-assisted mixed convection is examined for both the Darcy and the non-Darcy regimes. The results indicate that as the Darcy number is decreased, the location of flow separation from the cold wall did not change while reattachment moved further downstream. The Nusselt number increased with decreasing Darcy number and the effect of Darcy number is more pronounced over the first heat source and in the non-Darcy regime.     

Stability of Natural Convection of Power—law Fluid and non—Darcy Flow in Forous Media

IutnductionThe convection in porous media has been stUdied fora half centUryl"']. In recent years the nonlinear Propanesof the convection are emphatically sindiedp-7]. They areimPOrtant parts of nonlinear conhnuous media meChhocs,and this stUdy is of oportant theoretical sense as well aswide-ranging aPPlication Prospect such as thedevelopment of geothermal technique and heaVy Oilindustry. But up tO date the effect of the non-Newtonianfluid and the non-Darcy flow on the nonlinear behavior…     

NON-DARCIAN FORCED CONVECTION ANALYSIS IN AN ANNULUS PARTIALLY FILLED WITH A POROUS MATERIAL

Numerical solutions are presented for fully developed forced convection in concentric annuli partially filled with a porous medium. The porous medium is attached at the inner cylinder, which is maintained at uniform heat flux or at uniform wall temperature while the outer cylinder is adiabatic. The Brinkman-Forchheimer-extended Darcy model was used to model the flow inside the porous medium. The dependence of the fluid flow and heat transfer on several parameters of the problem is thoroughly documented. The inertia coefficient at which the inertial effects reduce the flow rate by 5% is determined as a function of the Darcy number for various thicknesses of the porous substrate. It is also shown that a critical thickness at which the value of the Nusselt number reaches a minimum does not exist if the effective thermal conductivity of the fluid-saturated porous medium is much higher than the fluid conductivity.     

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.