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.     

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.     

Effect of a wavy interface on the natural convection of a nanofluid in a cavity with a partially layered porous medium using the ISPH method

The effect of a wavy nanofluid/porous-medium interface on the natural convection of a Cu–water nanofluid in a differentially heated non-Darcy porous cavity was investigated using the ISPH method. Wall boundary conditions were applied by improved scheme using the analytical kernel renormalization function and its gradient based on the quintic kernel function. The effect of the Rayleigh number and the Darcy number on the heat transfer of Cu–water nanofluid with a various solid volume fraction were studied. Results showed that higher amplitude, height, and the undulation number of the sinusoidal interface between the nanofluid and porous medium layer lead to a decrease in the average Nusselt number.     

Effect of Darcy,Reynolds, and Prandtl Numbers on the Performance of Two‐Phase Flow Heat Exchanger Filled with Porous Media

Experimental investigation of two‐phase laminar forced convection in a single porous tube heat exchanger is presented. The effect of Darcy, Reynolds, and Prandtl numbers on the performance of this heat exchanger during the condensation process of carbon dioxide at different test conditions were investigated. Gravel sand with different porosities is used as a porous medium. The flow in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. Parametric studies are also conducted to evaluate the effects of porosity and Reynolds and Prandtl numbers on the heat transfer coefficient and the friction factor. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressure (P_in), mass flow rate (), porosity of gravel sand (ε), and Darcy number (Da) which ranged: 34.5 ≤ P_in ≤ 43 bars, 8 * 10^{? 5} ≤ ≤ 16 * 10^{? 5} kg/s, 34.9% ≤ ε ≤ 44.5%, 1.6 * 10^{? 6} ≤ Da ≤ 5 * 10^{? 6}, respectively. The study predicted the combined effect of the Reynolds number, Darcy number, porosity, and Prandtl number on the heat transfer and pressure drop of carbon dioxide during the condensation process in a porous medium. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21117     

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.     

Analysis of temperature-sensitive magnetic fluids in a porous square cavity depending on different porosity and Darcy number

Magnetic fluids are thermo-sensitive and whose flow and energy transport processes can be controlled by temperature and external magnetic field. In the natural convection of porous cavity, magnetic force is not only the driving force, the effective gravity is also a force related to the natural convection, and the effective gravity is closely depending on the porosity and permeability of porous medium. As is known, the porous medium is in solid state with high heat capacity but low heat transfer coefficient, while the magnetic fluid is a kind of fluid with high heat transfer coefficient and easy to be controlled. Combining the complementary characteristic of magnetic fluids and porous medium, we present a study for temperature-sensitive magnetic fluids in a porous square cavity. In the study, a Lattice Boltzmann method is developed to simulate the laminar convection of temperature-sensitive magnetic fluids in a porous square cavity. We present numerical results for the streamlines, isotherms, magnetization for different values of porosity and Darcy number. In addition, Nusselt numbers on heated and cooled wall and the average Nusselt numbers are also investigated.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

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.     

Non-Darcian effects on natural convection in porous media confined between horizontal cylinders

The inertia, boundary and velocity-square terms, normally not included in the flow analysis, are included in the study of natural convection between isothermal, concentric cylinders (inner cylinder heated) filled with saturated, porous media. The results show that all of these effects reduce the heat transfer rate with the boundary term being the most significant. It is shown that since at high Rayleigh numbers the flow adjacent to the confining walls becomes of boundary-layer type, with a very thin sublayer over which the velocity reaches its maximum value, then as long as the contribution of the velocity-square term is small, Darcy's model holds for very large Rayleigh and Prandtl numbers. A flow regime diagram showing the pseudo-conduction, Darcy and non-Darcy regimes, is given.     

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.     

Numerical simulation of natural convection in an open-ended square cavity filled with porous medium by lattice Boltzmann method

In the present work, natural convection in an open-ended square cavity packed with porous medium is simulated. The double-population approach is used to simulate hydrodynamic and thermal fields, and the Taylor series expansion and the least-squares-based lattice Boltzmann method has been implemented to extend the thermal model. The effect of a porous medium is taken into account by introducing the porosity into the equilibrium distribution function and adding a force term to the evolution equation. The Brinkman–Forchheimer equation, which includes the viscous and inertial terms, is applied to predict the heat transfer and fluid dynamics in the non-Darcy regime. The present model is validated with the previous literature. A comprehensive parametric study of natural convective flows is performed for various values of Rayleigh number and porosity. It is found that these two parameters have considerable influence on heat transfer.     

Numerical investigation of heat transfer enhancement on a porous vortex-generator applied to a block-heated channel

The numerical simulation is used to obtain the unsteady laminar flow and convective heat transfer in the block-heated channel with the porous vortex-generator. The general Darcy–Brinkman–Forchheimer model is adopted for the porous vortex-generator. The parameters studies including porosity, Darcy number, width-to-height ratio of porous vortex-generator and Reynolds number have been explored on heat transfer enhancement and vortex-induced vibration in detail. The results indicate that heat transfer enhancement and vortex-induced vibration increase with increasing Reynolds number and width-to-height ratio. However, the porosity has slight influence on heat transfer enhancement and vortex-induced vibration. When Darcy number is 10^?3 or 10^?4, installing a porous vortex-generator with B/h = 1.0 improves overall heat transfer the best along heated blocks, and has a strong reduction of vortex-induced vibration.     

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.     

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.     

Density maximum effect on buoyancy-driven convection of water in a porous cavity with variable side wall temperatures

The buoyancy-driven convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from θ_a to θ_o and θ_o to θ_b, respectively with height and θ_o is the mean of θ_a and θ_b,  the top and bottom walls of the cavity are thermally insulated. The Brinkman–Forchheimer extended Darcy model is considered to study the effects of density maximum, Grashof numbers, porosity and Darcy numbers on the buoyancy-induced flow and heat transfer. The finite volume method is used to discretize the governing equations, which are solved by Gauss–Seidel and successive over relaxation methods. The temperature distribution and flow fields are presented in the form of streamlines, isotherms and mid-height velocity profiles. It is found that the effect of density maximum is to slow down the natural convection and reduce the average heat transfer. The strength of convection and heat transfer rate become weak due to more flow restriction in the porous medium for small porosity.     

Unsteady Mixed Convection of a Confined Jet in a Fluid-Superposed High Porosity Medium

Numerical study of a confined jet impingement cooling of a fluid-superposed porous medium heated from below is conducted to investigate the oscillatory mixed convection. The effects of the Rayleigh number (2 × 10⁵ ≤ Ra ≤ 1 × 10⁶) and the Darcy number (1 × 10^?5 ≤ Da ≤ 5 × 10^?4) on the heat transfer are investigated for different Péclet numbers. It is found that, the average Nusselt number increases with the increase in Darcy number or Rayleigh number. The values of average Nusselt number are found to oscillate with time for some combination of Rayleigh numbers (Ra ≥ 4 × 10⁵) and Péclet numbers (200 ≤ Pe ≤ 1000), at which the oscillatory convection occurs. The oscillation of average Nusselt number is investigated for different porous medium height and porous medium-to-fluid heat capacity ratio.     

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.     

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.     

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.