Darcy Brinkman Forchheimer Model Research Articles

Local thermal non-equilibrium (LTNE) effects on thermal-free convection in a nanofluid-saturated horizontal elliptical non-Darcian porous annulus

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are out of local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy–Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach

The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement.

A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

AbstractThis article displays a numerical investigation on natural convection within non‐Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10–4 ≤ Fs/Pr* ≤ 10–2), thermal conductivity ratio (0.1 ≤ K r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K r.

Magnetohydrodynamic bioconvection of oxytactic microorganisms in porous media saturated with Cu–water nanofluid

Purpose The purpose of this study is to address magnetohydrodynamic (MHD) bioconvection caused by the swimming of oxytactic microorganisms in a linearly heated square cavity filled with porous media and Cu–water nanofluid. The effects of different multiphysical aspects are demonstrated using local distributions as well as global quantities for fluid flow, temperature, oxygen concentration and microorganisms population. Design/methodology/approach The coupled transport equations are converted into the nondimensional partial differential equations, which are solved numerically using a finite volume-based computing code. The flow of Cu–water nanofluid through the pores of porous media is formulated following the Brinkman–Forchheimer–Darcy model. The swimming of oxytactic microorganisms is handled following a continuum model. Findings The analysis of transport phenomena of bioconvection is performed in a linearly heated porous enclosure containing Cu–water nanofluid and oxytactic microorganisms under the influence of magnetic fields. The application of such a system could have potential impacts in diverse fields of engineering and science. The results show that the flow and temperature distribution along with the isoconcentrations of oxygen and microorganisms is markedly affected by the involved governing parameters. Research limitations/implications Similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity and light. Practical implications The outcomes of this investigation could be used in diverse fields of multiphysical applications, such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery. Originality/value The insight of the linear heating profile reveals a special attribute of simultaneous heating and cooling zones along the heated side. With such an interesting feature, the MHD bioconvection of oxytactic microorganisms in nanofluid-filled porous substance is not reported so far.

Numerical analysis of activation energy on MHD nanofluid flow with exponential temperature-dependent viscosity past a porous plate

The current investigation scrutinized the incompressible steady flow with temperature-dependent viscosity of magnetohydrodynamics nanofluid through a vertically stretched porous sheet. The Reynolds exponential model is employed to formulate the mathematical modeling. The momentum equation is further devised utilizing the Darcy–Brinkman–Forchheimer model. Electrically conducting nanofluids encompass uniformly suspended nanoparticles in the viscous base fluid. The Buongiorno model is adopted that aspects the behavior of thermophoretic forces and Brownian motion. The momentum, mass conservative, energy, and nanoparticle concentration equations are defined with magnetic body force. The looming nonlinear coupled differential equations are resolved numerically by employing the spectral local linearization method (SLLM). The SLLM algorithm is straightforward to develop and apply, as it is based on a smooth univariant linearization of nonlinear functions. The numerical performance of SLLM is more impressive as it grows a set of equations; those are successively solved by operating the results from the one equation into the subsequent equation. To accelerate and improve the convergence for the SLLM scheme, the successive over relaxation scheme has been utilized. The accuracy of the SLLM will be confirmed through the known methods, and convergence analysis is also presented. Graphical conduct for all the emerging parameters across temperature, velocity, and concentration distributions, as well as the Nusselt number, skin friction, and Sherwood number, is presented and discussed in detail. A comparative study of the novel proposed technique along with the preceding explored literature is also granted. It is costly to affirm that the spectral local linearization scheme is uncovered to be much stable and adaptable to solve the nonlinear problems.

Energy-saving method of heat transfer enhancement during magneto-thermal convection in typical thermal cavities adopting aspiration

In the area of energy-efficient system development, the paper presents a novel approach aiming to enhance heat transfer during magnetohydrodynamic convection in thermal cavities by implementing a technique of free aspiration. Through two small openings, the proposed free aspiration naturally allows a partial admission of fresh fluid into the cavity (from its immediate surroundings) and eventually vents the admitted fluid out the cavity without any pumping device. The efficacy of aspiration technique, whether viable under different problem conditions, is worked out for various classical configurations like differential heating, corner heating, and split heating. The mathematical formulations are derived by applying the Maxwell model (for magnetic fields) and the Brinkman–Forchheimer–Darcy model (for porous media). The evolved complex and coupled mathematical equations (involving the laws of continuity, momentum, and energy) are solved by an indigenously developed computing code. The study is conducted exhaustively addressing both a porous domain and a clear domain in terms of pertinent design parameters—Hartmann number (Ha = 0–100), porosity (ε = 0.1–1), Darcy number (Da = 10−7–10−3), Darcy–Rayleigh number (Ram = 0.1–103), and Rayleigh number (Ra = 103–106). The obtained results conclusively bring out an improved trend of heat transfer for all three thermal cavities due to the aspiration (without any pumping means). Even with the existence of flow-hindering porous substance and magnetic force, the augmentation in heat transfer could be as high as seven times more compared to their respective non-aspiration cases.

Investigation of Forced Convection Enhancement and Entropy Generation of Nanofluid Flow through a Corrugated Minichannel Filled with a Porous Media.

Corrugating channel wall is considered to be an efficient procedure for achieving improved heat transfer. Further enhancement can be obtained through the utilization of nanofluids and porous media with high thermal conductivity. This paper presents the effect of geometrical parameters for the determination of an appropriate configuration. Furthermore, the optimization of forced convective heat transfer and fluid/nanofluid flow through a sinusoidal wavy-channel inside a porous medium is performed through the optimization of entropy generation. The fluid flow in porous media is considered to be laminar and Darcy–Brinkman–Forchheimer model has been utilized. The obtained results were compared with the corresponding numerical data in order to ensure the accuracy and reliability of the numerical procedure. As a result, increasing the Darcy number leads to the increased portion of thermal entropy generation as well as the decreased portion of frictional entropy generation in all configurations. Moreover, configuration with wavelength of 10 mm, amplitude of 0.5 mm and phase shift of 60° was selected as an optimum geometry for further investigations on the addition of nanoparticles. Additionally, increasing trend of average Nusselt number and friction factor, besides the decreasing trend of performance evaluation criteria (PEC) index, were inferred by increasing the volume fraction of the nanofluid (Al2O3 and CuO).

Magneto-hydrodynamic thermal convection of Cu–Al2O3/water hybrid nanofluid saturated with porous media subjected to half-sinusoidal nonuniform heating

The present work aims to examine the thermal efficacy of half-sinusoidal nonuniform heating at different spatial frequencies for a porous natural convection system using Cu–Al2O3/water hybrid nanofluid and magnetic field. The system is presented utilizing a classical square enclosure heated nonuniformly at the bottom wall, and the sidewalls are allowed to exchange heat with the surroundings. The Brinkman–Forchheimer–Darcy model is adopted catering other additional terms for buoyant force and magnetic field. The governing equations are transformed into nondimensional forms and then solved numerically using a finite volume-based computing code. The importance and fundamental flow physics are explored in terms of the pertinent parameters such as the amplitude (I) and spatial frequency (f) of half-sinusoidal heating, Darcy–Rayleigh number (Ram), volume fraction of hybrid nanoparticles ( $$ \phi $$ ), and Hartmann number (Ha). The flow structure and heat transfer characteristics are analyzed and presented utilizing heatlines, streamlines and isotherms and average Nusselt number. The results show that the use of half-sinusoidal nonuniform heating along with hybrid nanofluid can be a viable method for enhancement and control of the overall thermal performance. The study indicates that half-sinusoidal heating could be a promising technique for better heat transfer even in the presence of flow dampening effects like porous media and magnetic fields.

Effects of half-sinusoidal nonuniform heating during MHD thermal convection in Cu–Al2O3/water hybrid nanofluid saturated with porous media

The intent of this study is to demonstrate an approach for augmenting heat transfer through porous media subjected to nonuniform heating during the magnetohydrodynamic flow of a hybrid nanofluid of Cu–Al2O3/water. The efficacy of such a heating technique is examined utilizing a classical flow geometry consisting of a square cavity. The heating is made at the bottom following a half-sinusoidal function of different frequencies, along with the presence of a uniform magnetic field. The thermal conditions of the cavity, particularly at the bottom wall, drive thermo-hydrodynamics and associated heat transfer. Furthermore, the addition of different types of nanoparticles to the base liquid in order to boost the thermal performance of conventional fluids and mono-nanofluids is a current technique. The coupled nonlinear governing equations are solved numerically in dimensionless forms adapting the finite volume approach, the Brinkman–Forchheimer–Darcy model, local thermal equilibrium and single-phase model. The study is conducted for wide ranges of parametric impacts to analyze global heat transfer performance. The results of this study reveal that the multi-frequency spatial heating during hybrid nanofluid flow can be utilized as a powerful means to improve the thermal performance of a system operating under different ranges of parameters, even with the presence of porous media and magnetic fields. In addition to different heating frequencies, the variations in amplitude (I) and superposed uniform temperature ( $$\theta_{\text{os}}$$ ) to half-sinusoidal heating are also examined thoughtfully in the analysis for different concentrations of Cu–Al2O3 nanoparticles. Compared to the base liquid, the hybrid nanofluid can contribute toward higher heat transfer.

Error analysis for the finite element approximation of the Darcy–Brinkman–Forchheimer model for porous media with mixed boundary conditions

This paper deals with the finite element approximation of the Darcy–Brinkman- Forchheimer equation, involving a porous media with spatially-varying porosity, with mixed boundary condition such as inhomogeneous Dirichlet and traction boundary conditions. We first prove that the considered problem has a unique solution if the source terms are small enough. The convergence of a Taylor–Hood finite element approximation using a finite element interpolation of the porosity is then proved under similar smallness assumptions. Some optimal error estimates are obtained if the solution to the Darcy–Brinkman–Forchheimer model is smooth enough. We end this paper by providing a fixed-point method to solve the discrete non-linear problems and with some numerical experiments to make more precise the smallness assumptions on the source terms and to illustrate the theoretical convergence results.

Thermal analysis of nanofluid saturated in inclined porous cavity cooled by rotating active cylinder subjected to convective condition

Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper.

Analytical Nusselt number for forced convection inside a porous-filled tube with temperature-dependent thermal conductivity arising from high-temperature applications

The convection heat transfer inside a tube filled with a porous material under the constant heat flux thermal boundary condition which is widely used in practical applications is studied in the present article. The Darcy–Brinkman–Forchheimer model is used to cover a wide range of working mediums from clear fluid flow to slug flow (Darcy flow). The case of temperature-dependent thermal conductivity is considered in the present study and the corresponding Nusselt number is analytically obtained using perturbation techniques for the first time. The change in thermal conductivity with respect to temperature occurs at high-temperature applications wherein high-temperature variations exist as well as the radiation heat transfer. A linear model for the thermal conductivity variation with temperature is considered in the present study. The obtained profile for the Nusselt number can be used for quick calculations as well as validation of numerical and experimental studies, especially at high temperatures wherein the experimental studies are accompanied by higher uncertainties. The results show that the Nusselt number increases linearly with the linear increase in the thermal conductivity and as well the heat transfer rate. Furthermore, results show that the Nusselt number (and the heat transfer rate as well) shows more augmentation to the thermal conductivity enhancement due to the temperature-dependent nature of thermal conductivity (especially arising from the radiation heat transfer) in comparison with the clear fluid flow case.

MHD convection in a partially driven cavity with corner heating

The paper presents a pertinent modification to the wall-moving thermal systems (classically represented by lid-driven cavity) by introducing a partial motion of the boundary walls. The effect of partial wall motion is investigated under magnetohydrodynamic (MHD) mixed convection in the cavity filled with porous medium. The corner heating arrangement is chosen for this investigation. The heater is placed at the right-bottom corner of the cavity, whereas the halves of the adjacent sides (which are moving) of the top-left corner are utilized for cooling. The present MHD thermofluid flow in porous cavity under partially driven condition is solved numerically using Brinkman–Forchheimer–Darcy model and analyzed using heatlines, streamlines, isotherms and average Nusselt number. The detailed insights of partially driven cavity are captured for different values of Richardson number (Ri = 0.1–100), Reynolds number (Re = 10–500), Hartmann number (Ha = 0–100), Darcy number (Da = 10−7 to 10−3) and porosity (e = 0.1–1.0). The result reveals that the partial wall motion and its direction have a significant impact on the thermofluid flow structures and heat transfer rate.

Entropy generation analysis for thermomagnetic convection of paramagnetic fluid inside a porous enclosure in the presence of magnetic quadrupole field

The entropy generation characteristics for thermomagnetic convection in a porous cavity filled with paramagnetic air in the presence of a magnetic quadrupole field are investigated numerically using a finite volume method. The vertical walls of the porous cavity are maintained at different temperatures, whereas the horizontal walls are insulated. The Darcy–Brinkman–Forchheimer model is used for mathematical formulation of the fluid flow in porous media. Thermal, frictional and total entropy generation and Bejan number for a selected range of magnetic force number (γ = 1–100), Darcy number (Da = 5 × 10−4–5 × 10−2) and Rayleigh number (Ra = 104–106) are examined for both cases: (1) with gravity and (2) without gravity. The results indicate that the magnetic field had little or no effect on the total entropy generation for the lower values of Darcy number and the process is dominated by the heat transfer irreversibility. In contrast, the magnetic force provokes various irreversibilities to rise as a result of improved convection at higher Darcy numbers, and the irreversibility is dominated by the viscous effects. This work may give an insight into the design-related concept of entropy generation for various thermal systems and clarifying energy loss.

Convective heat transfer enhancement: effect of multi-frequency heating

PurposeThis study aims to enhance natural convection heat transfer for a porous thermal cavity. Multi-frequency sinusoidal heating is applied at the bottom of a porous square cavity, considering top wall adiabatic and cooling through the sidewalls. The different frequencies, amplitudes and phase angles of sinusoidal heating are investigated to understand their major impacts on the heat transfer characteristics.Design/methodology/approachThe finite volume method is used to solve the governing equations in a two-dimensional cavity, considering incompressible laminar flow, Boussinesq approximation and Brinkman–Forchheimer–Darcy model. The mean-temperature constraint is applied for enhancement analysis.FindingsThe multi-frequency heating can markedly enhance natural convection heat transfer even in the presence of porous medium (enhancement up to ∼74 per cent). Only the positive phase angle offers heat transfer enhancement consistently in all frequencies (studied).Research limitations/implicationsThe present research idea can usefully be extended to other multi-physical areas (nanofluids, magneto-hydrodynamics, etc.).Practical implicationsThe findings are useful for devices working on natural convection.Originality/valueThe enhancement using multi-frequency heating is estimated under different parametric conditions. The effect of different frequencies of sinusoidal heating, along with the uniform heating, is collectively discussed from the fundamental point of view using the average and local Nusselt number, thermal and hydrodynamic boundary layers and heatlines.

SEM-based numerical framework for non-Darcy mixed convection in a porous cavity with three adiabatic thin baffles on the hot wall

PurposeThe purpose of this paper is to develop a numerical framework based on the accurate spectral element method (SEM) to simulate the mixed convective heat transfer within a porous enclosure with three adiabatic thin baffles of different lengths in nine cases and analyze the effects of several parameters.Design/methodology/approachThe authors develop an improved time-splitting method to solve the Darcy–Brinkman–Forchheimer model. No extra assumptions are introduced for the intermediate velocity, and the final velocity field satisfies the incompressible constraint strictly compared with the classical method. The governing equations are split into a pure convection problem, a Stokes problem and a thermal diffusion problem. The least-squares variation is adopted for the Stokes problem, and the Galerkin variation is used for the other two problems, such that the pressure and velocity can be discretized with the same interpolation order, which benefits the numerical accuracy and program design.FindingsRegarding the method, the excellent spectral accuracy, the capability of discretizing complex computational regions and the improved time-splitting methods make SEM an effective tool to accurately predict the non-Darcy convective heat transfer; as for the numerical tests, it is observed that weakened convection and heat transfer are induced by the increasing length of the baffles. The flow and heat transfer in channel 1 is only related to the length of baffle 1 because of the downward-driven right sidewall, and it is more difficult for baffle 3 to form the secondary flow on its tip.Originality/valueA novel numerical framework for Darcy–Brinkman–Forchheimer model is developed, expanding the application of SEM for simulating non-Darcy convective heat transfer to improve the numerical accuracy. Numerical results and analysis for flow and heat fields could help designers understand the control of heat transfer using adiabatic baffles better.

Mixed convective magnetonanofluid flow over a backward facing step and entropy generation using extended Darcy–Brinkman–Forchheimer model

This article focuses on a numerical study for the effect of porosity and internal heat generation/absorption parameters on the mixed convective flow of nanofluid over a backward facing step along with the entropy generation. The channel downstream bottom wall is isothermally heated while the remaining walls of the channel are thermally insulated. The dimensionless governing equations are discretized utilizing the Galerkin-based finite element method. The discrete systems of nonlinear algebraic equations are computed using the Newton method and the corresponding linearized systems are treated using the monolithic geometric multigrid solver. Effect of different physical parameters in the specified ranges such as \((10 \le Re \le 200)\), \((0.01 \le Ri \le 20)\), \((0\le Ha \le 100)\), \((-10 \le q \le 10)\), \((10^{-6} \le Da \le 10^{-3})\), \((0.2 \le \epsilon \le 0.8)\) and \((0^\circ \le \gamma \le 180^\circ )\) on the fluid flow is analyzed with the help of the streamlines, isotherm patterns, and various graphs. It is noticed that the average heat transfer increases with the porosity parameter and reduces with the internal heat generation parameter. Furthermore, the entropy generation produced by the heat transfer and fluid friction is found to amplify with the porosity parameter, whereas a decline is recorded in it due to the magnetic field.

Heat and fluid flow analysis of metal foam embedded in a double-layered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid

The present study aims to enhance the hydrothermal performance of a porous sinusoidal double-layered heat sink using nanofluid. The optimum thickness of metal foam (nickel) for different Reynolds numbers ranging from 10 to 100 for the laminar regime and Darcy numbers ranging from 10−4 to 10−2 is obtained. At the optimum porous thicknesses, nanofluid (silver–water) with three volume fractions of nanoparticles equal to 2, 3, and 4% is employed to enhance the heat sink thermal performance. Darcy–Brinkman–Forchheimer model and the local thermal non-equilibrium model or two equations method are employed to model the momentum equation and energy equations in the porous region, respectively. It was found that in the cases of Darcy numbers 10−4, 10−3, and 10−2 the dimensionless optimum porous thicknesses are 0.8, 0.8, and 0.2, respectively. It was also obtained that the maximum PEC number is 2.12 and it corresponds to the case with Darcy number 10−2, Reynolds number 40, and volume fraction of nanoparticles 0.04. The validity of local thermal equilibrium (LTE) assumption was investigated, and it was found that increasing the Darcy number which results in an enhancement in porous particle diameter leads to some errors in results, under LTE condition.

Lattice Boltzmann method for natural convection of a Bingham fluid in a porous cavity

In this paper, natural convection in a porous cavity filled with Bingham fluids has been simulated numerically. In order to study the problem, an innovative Lattice Boltzmann method for porous media of Bingham fluid is introduced. In this study, the Papanastasiou regularisation of the Bingham constitutive model has been applied for the studied Bingham fluid and moreover the Darcy–Brinkman–Forchheimer model has been employed for the porous media. Fluid flow, heat transfer, and yielded/unyielded parts have been conducted for certain pertinent parameters of Rayleigh number ( Ra=104 – 107), Darcy number (Da=10−2, 10−4, 10−6), and porosity (ϵ = 0.1 – 0.9). Moreover, the Bingham number (Bn) is studied in a wide range of different studied parameters. Results indicate that the heat transfer increases and the unyielded section diminishes as Rayleigh number rises. For specific Rayleigh and Darcy numbers, the increase in the Bingham number decreases the heat transfer. Furthermore, the growth of the Bingham number expands the unyielded sections in the cavity. Finally, for fixed Rayleigh and Bingham numbers, the unyielded region is decreased by the augmentation of the porosity. In addition, heat transfer augments gradually as the porosity increases.