Symmetry-Breaking in a Porous Cavity with Moving Side Walls

In this paper, a numerical investigation of the steady laminar mixed convection flow in a porous square enclosure has been considered. This structure represents a practical system such as an external through flow of cooled-air an electronic device from its moving sides. The heating was supplied by an internal volumetric source with an uniform distribution at the middle part of its bottom, while the other walls were assumed thermally insulated. Moreover, the momentum transfer in the porous substrate was numerically investigated using the Darcy-Brinkman-Forchheimer law. The governing equations of the posed problem have been solved by applying the finite difference technique on non-uniform grids. For all simulations, the Reynolds number and the porosity have been fixed respectively to Re=100 and φ=0.9. Darcy’s value was varied in the range from 0.001 to 0.1. The results detected the existence of a radical change in the contour patterns for Richardson number equal to 11.76 and 11.77 with fixed Da=0.1. This behavior signified that the fluid is fully convected for higher Darcy number.

Ohmic and viscous dissipation effects on micropolar non-Newtonian nanofluid Al2O3 flow through a non-Darcy porous media

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

Analysis of combined radiation and convection heat transfer inside a porous medium with heat source electronic devices

In this study, a numerical study is performed on the cooling phenomenon of three heat source electronic devices. The electronic devices are cooled in the form of natural heat transfer by the airflow in a porous medium. Electronic devices are installed on the boundary walls of a square environment. Cooling simulations are performed by drawing flow lines and constant temperature lines. Our main goal is to find the highest cooling rate in different Darcy numbers and different Rayleigh numbers in our investigation. The range of Darcy numbers and Rayleigh numbers is between 0.0001 to 0.01 and 1000 to 100,000, respectively. Our investigation showed the maximum cooling is obtained at the Darcy number of about 0.01. And also, by decreasing the value of Darcy number, a higher cooling rate for the hot boundary walls is achieved.

The Coriolis Effect on Thermal Convection in a Rotating Sparsely Packed Porous Layer in Presence of Cross-Diffusion

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number.

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

Effects of the Control Parameters on the Stability of a Laminar Boundary Layer on a Porous Flat Plate

This work is devoted to the analysis of the linear temporal stability of a laminar dynamic boundary layer on a horizontal porous plane plate. The basic flow is assumed to be laminar and two-dimensional. The basic flow velocity profiles are obtained by numerically solving the Blasius equation using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.

Effect of concentric and eccentric porous layer on forced convection heat transfer and fluid flow around a solid cylinder

In this paper, heat transfer and fluid flow around a solid cylinder wrapped with a porous layer in the channel were studied numerically by computational fluid dynamics (CFD). The homogeneous concentric and eccentric porous medium round a rigid, solid cylinder are supposed at local thermal equilibrium. The transport phenomena within the porous layer, volume averaged equations were employed, however the conservation laws of mass, momentum and energy were applied in the channel. This current numerical analysis, the effects of eccentricity ( ), the variable diameter of porous layer (d=0.07,0.08,0.09), permeability, as well as the different Reynolds number and Darcy number on the heat transfer parameters and fluid flow was investigated. The main purpose of this study is analyzed and compared the heat flux of concentric and eccentric porous layer in Reynolds number range of 1 to 40 and Darcy numbers of to . It is found that with the decline of Darcy number, the vortex length is increased behind the solid cylinder surface. In addition, the heat flux rate of the cylinder is raised with the increase of Reynolds number. Finally, The results have demonstrated that with raising Reynolds and Darcy numbers, the increase of the average Nusselt numbers in the eccentric porous layer is higher than the concentric porous layer.

Influence of entropy on Brinkman–Forchheimer model of MHD hybrid nanofluid flowing in enclosure containing rotating cylinder and undulating porous stratum

The current article aims to discuss the natural convection heat transfer of Ag/Al2O3-water hybrid filled in an enclosure subjected to a uniform magnetic field and provided with a rotating cylinder and an inner undulated porous layer. The various thermo-physical parameters are investigated such as Rayleigh number ($$100 \le Ra \le 100000$$ 100 ≤ R a ≤ 100000 ), Hartmann number ($$0 \le Ha \le 100$$ 0 ≤ H a ≤ 100 ), and the nanoparticles concentration ($$0.02 \le \phi \le 0.08$$ 0.02 ≤ ϕ ≤ 0.08 ). Likewise, the rotational speed of the cylinder ($$- 4000 \le \omega \le + 4000$$ - 4000 ≤ ω ≤ + 4000 ), as well as several characteristics related to the porous layer, are examined li its porosity ($$0.2 \le \varepsilon \le 0.8$$ 0.2 ≤ ε ≤ 0.8 ), Darcy number ($$- 100000 \le Da \le - 100$$ - 100000 ≤ D a ≤ - 100 ) which indicates the porous medium permeability and the number of undulations ($$0 \le N \le 4$$ 0 ≤ N ≤ 4 ). The calculations are carried out based on the Galerkin Finite element method (GFEM) to present the streamlines, isotherms, entropy generation, and average Nusselt numbers in details. The main results proved that increment of Rayleigh number and Darcy number enhances heat transfer convection within the enclosure. Whilst, the porosity presents a minimal impact. Also, the rotational speed in a positive direction has a favorable influence on the heat transfer dispersion across the cavity.

MHD darcy-forchheimer nanofluid flow and entropy optimization in an odd-shaped enclosure filled with a (MWCNT-Fe3O4/water) using galerkin finite element analysis

MHD nanoliquid convective flow in an odd-shaped cavity filled with a multi-walled carbon nanotube-iron (II, III) oxide (MWCNT-Fe3O4) hybrid nanofluid is reported. The side walls are adiabatic, and the internal and external borders of the cavity are isothermally kept at high and low temperatures of Th and Tc, respectively. The governing equations obtained with the Boussinesq approximation are solved using Galerkin Finite Element Method (GFEM). Impact of Darcy number (Da), Hartmann number (Ha), Rayleigh number (Ra), solid volume fraction (ϕ), and Heated-wall length effect are presented. Outputs are illustrated in forms of streamlines, isotherms, and Nusselt number. The impact of multiple parameters namely Rayleigh number, Darcy number, on entropy generation rate was analyzed and discussed in post-processing under laminar and turbulent flow regimes.

Local thermal non-equilibrium conjugate forced convection and entropy generation in an aircraft cabin with air channel partially filled porous insulation

Purpose The purpose of this study is to numerically investigate heat transfer and entropy generation between airframe and cabin-cargo departments in an aircraft. The conjugate forced convection and entropy generation in a cylindrical cavity within air channel partly filled with porous insulation material as simplified geometry for airframe and cabin-cargo departments are considered under local thermal non-equilibrium condition. Design/methodology/approach The non-dimensional governing equations for fluid and porous media discretized by finite volume method are solved using the SIMPLE algorithm with pressure and velocity correction. Findings The effects of the following parameters on the problem are investigated; Reynolds number, Darcy number, the size of inlet and exit cross-section, thermal conductivity ratio for solid and fluid phases, angle between the vertical symmetry axis and the end of channel wall exit and the gap between adiabatic channel wall and horizontal adiabatic wall separating cabin and cargo sections. Originality/value This paper can provide a basic perspective and framework for thermal design between the fuselage and cabin-cargo sections. The minimum total entropy generation number is calculated for various Reynolds numbers and thermal conductivity ratios. It is observed that the channel wall temperature increases for high Reynolds number, low Darcy number, narrower exit cross-section and wider the gap between channel wall and horizontal.