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A numerical study is conducted to analyze the effects of a flexible fin on unsteady convective flow in a square enclosure composed of a vertical fluid layer and a porous layer. The fin is attached to the heated left wall of the enclosure. The Brinkman-Forchheimer-extended Darcy flow model is assumed in the porous layer. The governing equations are written in the Arbitrary Lagrangian–Eulerian (ALE) formulation in the fluid and structure domains and then solved using the FEM. The result shows that the fin oscillation impacts the area below the fin rather than the area above the fin or the area in the center. The overall rate of heat transfer is improved as the Darcy number, the fluid layer thickness, and the fin elasticity increase. The overall rate of heat transfer increases exponentially with the rise of the oscillation amplitude. An oscillation amplitude of 0.1 could result in 3.4 percent improvement in the heat transfer rate. [ABSTRACT FROM AUTHOR]

The problem of transient flow of incompressible third grade fluid on the two-dimensional magnetohydrodynamic (MHD) flow in a porous space is analyzed. The flow is generated due to the motion of the plate in its plane with a periodic velocity. Under the flow assumptions, the governing nonlinear partial differential equation is transformed into steady-state and transient nonlinear equations. The reduced equation for the transient flow is solved analytically using symmetry approach while the nonlinear steady-state equation is solved using a modified version of He’s homotopy perturbation method. The effect of several operating parameters on the flow hydromagnetic is discussed. The results indicated that for the considered case, t = 1:5 is the moment after which the time-dependent transient motion of the fluid can be approximated with the steady-state motion, described by the steady-state solution. It is clear that, after this value of time t the time-dependent transient solution can be neglected. [ABSTRACT FROM AUTHOR]

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width $$(0.02 \le D \le 0.3)$$ , the wall to porous thermal conductivity ratio $$(0.1 \le k_\mathrm{r} \le 10.0)$$ , the internal heating $$(0 \le \gamma \le 5)$$ , and the local heating exponent parameters $$(1 \le \lambda \le 20)$$ . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls. [ABSTRACT FROM AUTHOR]

Effect of rotation on linear and nonlinear instability of cross-diffusive convection in an anisotropic porous medium saturated with Newtonian fluid has been investigated. Normal mode technique has been used for linear stability analysis, however nonlinear analysis is done using spectral method, involving only two terms. The Darcy model with Coriolis terms, has been employed in the momentum equation. Nonlinear analysis is used to find the thermal and concentration Nusselt numbers. The effects of various parameters, including Soret and Dufour parameters, on stationary and oscillatory convection, have been obtained, and shown graphically. [ABSTRACT FROM AUTHOR]

In this article we study the combined effect of internal heating and time-periodic gravity modulation on thermal instability in a closely packed anisotropic porous medium, heated from below and cooled from above. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the porous medium. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. The effects of various parameters such as; internal Rayleigh number, amplitude and frequency of gravity modulation, thermo-mechanical anisotropies, and Vadász number on heat transport has been analyzed. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further it is found that the heat transport can also be controlled by suitably adjusting the external parameters of the system. [ABSTRACT FROM AUTHOR]

The natural convection in an inclined porous square cavity is investigated numerically. The left wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, while the right wall is cooled. The horizontal walls are considered adiabatic. A finite difference method is used to solve numerically the nondimensional governing equations. The effects of the inclination angle of the cavity, the amplitude and wave numbers of the heated sidewall temperature variation on the natural convection in the cavity are studied. The maximum average Nusselt number occurs at different wave number. It also found that the inclination could influence the Nusselt number. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the flow of nanofluid and heat transfer characteristics between two horizontal plates in a rotating system. The lower plate is a stretching sheet and the upper one is a solid porous plate. Copper (Cu0 as nanoparticle and water as its base fluid have been considered. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved analytically using the homotopy analysis method (HAM). Comparison between HAM and numerical solutions results showed an excellent agreement. The results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction, suction/injection parameter, rotation parameter, and Reynolds number. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable of causing change in the flow pattern. It is found that for both suction and injection, the heat transfer rate at the surface increaseswith increasing the nanoparticle volume fraction, Reynolds number, and injection/suction parameter and it decreases with power of rotation parameter. [ABSTRACT FROM AUTHOR]

Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure. [ABSTRACT FROM AUTHOR]

Abstract: Feedback control on thermal convection in a fluid-saturated porous medium is investigated based on the approach of dynamical systems. A low dimensional Lorenz-like model was obtained using the Galerkin truncated approximation. The possible suppression or enhancement of chaotic convection is demonstrated. [Copyright &y& Elsevier]

The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency. [ABSTRACT FROM AUTHOR]

Feedback control on thermal convection in a fluid-saturated porous medium is investigated based on the dynamical systems approach. A low dimensional Lorenz-like model was obtained using the Galerkin-truncated approximation. The possible suppression or enhancement of chaotic convection is demonstrated when the fluid layer is subjected to feedback control in a low-dimensional framework. [ABSTRACT FROM AUTHOR]

Abstract: Using the theory of dynamical systems, this study investigated the effects of a uniform internal heat generation on chaotic behaviour in thermal convection in a fluid-saturated porous layer subject to gravity and heated from below for low Prandtl number. A low-dimensional, Lorenz-like model was obtained using Galerkin truncated approximation. The fourth-order Runge–Kutta method was employed to solve the nonlinear system. We found that there is an inverse proportional relation between the level of internal heat G and the scaled Rayleigh number R, and consequently the porous media gravity-related Rayleigh number Ra. [Copyright &y& Elsevier]

The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

The problem of transient natural convection heat transfer in a nanoliquid-saturated porous oblique cavity is studied numerically using the finite difference method. The hot left wall of the cavity is maintained at a constant temperature and so is the cold right wall. The horizontal walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The heat transfer equations are those of a two-phase medium, one for the nanoliquid and another for the porous medium. Water-based nanoliquids with Ag or Cu or Al 2 O 3 or TiO 2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number ( 10 2 ≤ Ra ⩽ 10 4 ) , modified conductivity ratio ( 0.1 ≤ γ ⩽ 1000 ) , inter-phase heat transfer ( 0.1 ≤ H ⩽ 1000 ) , inclination angle of the sloping walls ( − π 3 ≤ ω ≤ π 3 ) , volume fraction of nanoparticles ( 0 ≤ φ ≤ 0.2 ) and dimensionless time ( 0 ≤ τ ⩽ 0.1 ) . The assumption of local thermal non-equilibrium leads to an enhanced heat transfer situation in nanoliquids saturating a porous medium compared to that in a porous medium with local thermal equilibrium. Explanation for the observed influences of various parameters on streamlines, isotherms and weighted average Nusselt number is given in terms of thermophysical properties of four nanoparticles, water and porous medium. It is shown that the strength of the flow circulation increases for the relative concentration of nanoliquid with the increment of the inclination angle to the positive direction. [ABSTRACT FROM AUTHOR]

Abstract: Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper taking into consideration the Forchheimer–Brinkman-extended Darcy model. The enclosure is filled with a fluid-saturated porous medium and executes a steady counterclockwise angular velocity about its longitudinal axis. The staggered grid arrangement together with the Marker and Cell (MAC) method was employed to solve the governing equations. The governing parameters considered are the porosity, 0.4≤ ϵ ≤0.99, the Darcy number, 0.005≤ Da ≤0.01 and the Taylor number, 8.9×104 ≤ Ta ≤3.8×105, and the centrifugal force is assumed weaker than the Coriolis force. It is found that higher porosities have weaker flow circulation when the Coriolis effect is smaller than the buoyancy effect. The global quantity of the heat transfer rate increases by increasing the porosity and the Darcy number and decreases by increasing the Taylor number. [Copyright &y& Elsevier]

Abstract: Double-diffusive convection in an anisotropic porous layer heated and salted from below with an internal heat source and Soret effect is studied analytically using both linear and nonlinear stability analyses. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number and wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effects of the anisotropy parameters, concentration Rayleigh number, internal heat source, Soret parameter, Vadasz number and Lewis number on the stationary, oscillatory, and heat and mass transfer are shown graphically. Heat and mass transfer have been obtained in terms of the Nusselt number and Sherwood number. [Copyright &y& Elsevier]

Abstract: Thermal convective instability in a fluid-saturated porous layer heated from below and cooled from above is investigated theoretically using dynamical systems approach. A feedback control strategy with an array of sensors situated at the top plate of the fluid layer is adopted. The Galerkin truncated approximation is employed to derive a low dimensional Lorenz-like model. It is shown that suppression or enhancement of chaotic convection is possible via feedback control. [ABSTRACT FROM AUTHOR]

An analysis is presented to investigate the effect of thermophoresis particle deposition and variable viscosity on non-Darcy MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non- Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations are carried out for different values of dimensionless parameter in the problem and an analysis of the results obtained show that the flow field is influenced appreciably by the applied magnetic field. The results are compared with those known from the literature and excellent agreement between the results is obtained. [ABSTRACT FROM AUTHOR]

The effects of finite wall thickness and sinusoidal heating on convection in a nanofluid-saturated local thermal non-equilibrium (LTNE) porous cavity are studied numerically using the finite difference method. The finite thickness vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. Water-based nanofluids with Cu nanoparticles are chosen for investigation. The results of this study are obtained for various parameters such as the Rayleigh number, periodicity parameter, nanoparticles volume fraction, thermal conductivity ratio, ratio of wall thickness to its height and the modified conductivity ratio. Explanation for the influence of the various above-mentioned parameters on the streamlines, isotherms, local Nusselt number and the weighted average heat transfer is provided with regards to the thermal conductivities of nanoparticles suspended in the pure fluid and the porous medium. It is shown that the overall heat transfer is significantly increased with the relative non-uniform heating. Further, the convection heat transfer is shown to be inhibited by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

The problem of natural convection in a trapezoidal cavity partly filled with nanofluid porous layer and partly with non-Newtonian fluid layer is visualized by heatline. Water-based nanofluids with silver or copper or alumina or titania nanoparticles are chosen for investigation. The governing equations are solved numerically using the Finite Volume Method (FVM) over a wide range of Rayleigh number ( Ra = 10 5 and 10 6 ), Darcy number ( 10 - 5 ⩽ Da ⩽ 10 - 1 ), nanoparticle volume fraction ( 0 ⩽ ϕ ⩽ 0.2 ), power-law index ( 0.6 ⩽ n ⩽ 1.4 ), porous layer thickness ( 0.3 ⩽ S ⩽ 0.7 ), the side wall inclination angle ( 0 ° ⩽ φ ⩽ 21.8 ° ) and the inclination angle of the cavity ( 0 ° ⩽ ω ⩽ 90 ° ). Explanation for the influence of various above mentioned parameters on streamlines, isotherms and overall heat transfer is provided on the basis of thermal conductivities of nanoparticles, water and porous medium. It is shown that convection increases remarkably by the addition of silver–water nanofluid and the heat transfer rate is affected by the inclination angle of the cavity variation. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems. [ABSTRACT FROM AUTHOR]