Porous Enclosure Research Articles

Numerical investigation on the effect of magnetic field on natural convection heat transfer from a pair of embedded cylinders within a porous enclosure

The present work examines the influence of magnetohydrodynamic field on natural convection phenomena inside a porous square enclosure with a pair of embedded hot circular cylinders. Numerical investigations are performed to understand the effects of interspacing distance between the embedded cylinders, Hartmann number, Rayleigh number and Darcy number on the thermal transport process and the total irreversibility generation. It is observed that the isotherm distribution is strongly affected by the presence of magnetic field although the distribution of streamlines remains independent of the strength of magnetic field. This underlines the fact that magnetic field strongly influences the heat transfer process and entropy generation characteristics. It reveals that the natural convection is suppressed in the presence of a higher magnetic field as evident from the reduction in Nusselt number. It is observed that an increase in the spacing between the cylinders increases the heat transfer rate, and moreover, the effect of the magnetic field on heat transfer is more pronounced at higher interspacing distance between the embedded cylinders. The heat transfer rate increases significantly with the increase in the permeability of the medium. The entropy generation rate is independent of the strength of applied magnetic field. Further, the contribution of the entropy generation owing to friction is found to be negligible in total irreversibility obtained at lower values of Rayleigh number irrespective of Darcy number. However, the contribution of irreversibility owing to heat transfer is found to be minimal at higher values of Rayleigh number.

Second law analysis of magneto-natural convection in a nanofluid filled wavy-hexagonal porous enclosure

Purpose Natural convection heat transfer analysis can be completed using entropy generation analysis. This study aims to accomplish both the natural convection heat transfer and entropy generation analyses for a hexagonal cavity loaded with Cu-H2O nanoliquid subjected to an oriented magnetic field. Design/methodology/approach Control volume-based finite element method is applied to solve the non-dimensional forms of governing equations and then, the entropy generation number is computed. Findings The results portray that both the average Nusselt and entropy generation numbers boost with increasing aspect ratio for each value of the undulation number, while both of them decrease with increasing the undulation number for each amplitude parameter. There is a maximum value for the entropy generation number at a specified value of Hartmann number. Also, there is a minimum value for the entropy generation number at a specified value of angle of the magnetic field. When the volume fraction of nanoparticles grows, the average Nusselt number increases and the entropy generation number declines. The entropy generation number attains to a maximum value at Ha = 14 for each value of aspect ratio. The average Nusselt number ascends 2.9 per cent and entropy generation number decreases 1.3 per cent for Ha = 0 when ϕ increases from 0 to 4 per cent. Originality/value A hexagonal enclosure (complex geometry), which has many industrial applications, is chosen in this study. Not only the characteristics of heat transfer are investigated but also entropy generation analysis is performed in this study. The ecological coefficient of performance for enclosures is calculated, too.

Numerical Modelling for Nanoparticle Thermal Migration with Effects of Shape of Particles and Magnetic Field Inside a Porous Enclosure

Computational modelling for nanoparticle migration inside a permeable space has been reported. Impacts of shape factor and radiation were included in the mathematical model. CVFEM was employed to analyse magnetic force impact. Impacts of magnetic radiative parameters, buoyancy forces and nanoparticle shape on nanomaterial behaviour were demonstrated. Utilizing the Darcy model helps us to predict the behaviour of porous media. Outputs revealed higher convective mode can be achieved with augmenting buoyancy force while opposite outcome appears when magnetic field is imposed. Thermal plume vanishes with the rise of conductive mode which is gained as Hartmann increases.

Simulation Examination for Nanoparticle Flow in a Permeable Enclosure via CVFEM Involving MHD Effect

In the present investigation, innovative complex porous enclosure is chosen to simulate the MHD (magnetohydrodynamic) natural convection. One side of porous cavity packed with radiative nanofluid (CuO–water) has curve-shaped triangular wave pattern. To gain insight into outputs, CVFEM (control volume-based finite element method) has been used. Nanofluid behavior is inspected by employing two-temperature model for solid matrix and nanoliquid and KKL model for effective properties of nanofluid with an extensive range of key parameters acting as Hartmann number, radiation parameter, buoyancy impact, phase interacting heat transfer factor. Not only imposing magnetic field but also wavy surface and dispersion of nanomaterial have been considered in the current paper. New numerical approach has been utilized to demonstrate the behavior of nanomaterial through the porous tank. Interrelation of average Nusselt number with involved parameters is also proposed. Outcomes reveal that radiation term has straightforward association with Nusselt number. Greater vortex generates with the rise in shape factor.

Entropy analysis for a nanofluid within a porous media with magnetic force impact using non-Darcy model

Abstract In this study, the entropy treatment of a nanomaterial flow in the existence of Lorenz forces within a porous domain is carried out via the non-Darcy model. Fe3O4-water is the ferrofluid flowing through the porous enclosure under the magnetic force impact. Simulations for different Darcy, Rayleigh and Hartmann numbers have been reported by applying the novel numerical simulation approach of the control-volume FEM. The outputs of the simulations showed that increasing permeability makes Be to decline, boundary layer thickness enhances with a rise of Lorentz force. In the end, based on the obtained outcomes and employing curve-fitting on the plots, two precise formulas were suggested for the estimation of the Bejan number and average Nusselt number.

Natural convection of Nanoliquid from a Cylinder in Square Porous Enclosure using Buongiorno\u2019s Two-phase Model

Natural convection of nanoliquid in a square porous enclosure has been studied using non homogeneous two-phase Buongiorno’s model. The outer of enclosure has cold temperature and a circular cylinder is put at the center. A finite heated segment is located on the top cylinder surface which is otherwise insulated. The momentum in the porous layer is modeled applying the Brinkman-Forchheimer equations. The analysis are conducted in the following interval of the associated groups: the portion of heated surface (5% ≤ H ≤ 100%), the concentration (0.0 ≤ ϕ ≤ 0.04), the Darcy number, 10−5 ≤ Da ≤ 10−2 and the cylinder size, (0.15 ≤ R ≤ 0.25). The minimum heat transfer rate of the active surface were obtained at location ξ = 90°. In general, the ratio of the heat transfer per unit area of the heat source decreases as the length of the heated surface increases. The heat transfer rate is intensified for the half thermally active surface and high value of Darcy number at higher nanoparticles concentration.

Optimization of heating-cooling generators with porous components/cryogenic conductors on natural convection in a porous enclosure: Using different two-phase models and single-phase model and using different designs

Abstract In the present study, the effect of the use of heating and cooling generators along with cryogenic conductors on flow and heat transfer characteristics in a porous chamber are investigated. The finite volume method (FVM) is used to simulate the phenomena. Single-phase and two-phase models (Mixture model and Eulerian-Eulerian model) have been used to predict heat transfer. Water-Copper oxide nanofluid is assumed to be Newtonian, incompressible, and steady. Several cases have been investigated in order to evaluate the heat transfer rate and streamlines visualization accurately. Investigations include a change in the number of heating and cooling generators, a change in the size of the cryogenic conductors, and the use of porous components as an alternative to cryogenic conductors. The volume fraction is assumed to be constant in the whole simulation and is 3%. The Rayleigh and Darcy numbers ranges are 104 ≤ Ra ≤ 107 and 10−2 ≤ Da ≤ 10−4, respectively. The Darcy-Forchheimer model is used for fluid flow and heat transfer in a porous medium. The results of this study are compared with the results of a regular enclosure that has been studied by many previous researchers. The findings show that the effect of using heating-cooling generators is favorable and that cryogenic conductors can also help to improve heat transfer. However, in some conditions using a regular porous enclosure yields better results. In addition, the difference in the results of single-phase and two-phase models depending on the operating conditions can be low or high. The goal is to achieve the highest heat transfer rate using the available tools. It is hoped that using the results of this research can be a useful guide to better understanding the phenomena and optimum and better designs.

Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method

In this work, numerical simulation of nature convection of Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid in an inclined square porous enclosure is investigated to analyze the influence of different physical parameters on fluid flow and heat transfer via the lattice Boltzmann method. Due to stable chemical properties and low price in the dispersion system, Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid is widely used in the field of industrial heat transfer enhancement, which is the focus of present work. When the nanofluid is transport in a porous media, the Darcy-Brinkman-Forchheimer model is usually used to describe the porous media effects on nanofluid flow. Compared with uniform thermal boundary condition, the natural convection of nanofluids with non-uniform thermal boundary condition has not received much attention. In this paper, the sinusoidal boundary condition is applied to the left side wall to analyze the heat transfer mechanism of Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid in the inclined square porous enclosure. The effect of porosity (0.3 ≤ <inline-formula><tex-math id="Z-20200813202835">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202835.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202835.png"/></alternatives></inline-formula> ≤ 0.9), Rayleigh number (10<sup>3</sup> ≤ <i>Ra</i> ≤ 10<sup>6</sup>), volume fraction of nanoparticle (0 ≤ <i>ϕ</i> ≤ 0.04), tilt angle (0° ≤ <i>γ</i> ≤ 120°) on the heat transfer performance are systematically investigated. Numerical results show that the non-uniform boundary condition can affect the heat transfer performance on Al<sub>2</sub>O<sub>3</sub>-H<sub>2</sub>O nanofluid with different physical quantities, which is different from the uniform boundary condition. When <i>γ</i> = 0° and <i>Ra</i> is fixed, the <i>Nu</i><sub>ave</sub> number (average Nusselt number) at the heated wall increases with porosity. When <i>γ</i> = 40°, 80° or 120°, the <i>Nu</i><sub>ave</sub> reaches its maximum value at <inline-formula><tex-math id="Z-20200813202844">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202844.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202844.png"/></alternatives></inline-formula> = 0.7. In addition, if <inline-formula><tex-math id="Z-20200813202907">\begin{document}$\epsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202907.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20200308_Z-20200813202907.png"/></alternatives></inline-formula> and <i>Ra</i> are fixed, the results show that the heat transfer performance is most efficient at <i>γ</i> = 40° whereas it is weakened at <i>γ</i> = 80°. Moreover, when different inclination angles are applied to the square cavity, the <i>Nu</i><sub>ave</sub> increases slightly with an augmentation of <i>ϕ</i>. In all, compared with the uniform temperature boundary condition, the effect of volume fraction of nanoparticles on the enhanced heat transfer is not significant, therefore, to improve the heat transfer performance of nanofluids with given <i>ϕ</i> and <i>Ra</i>, it is necessary to take advantage of the improvement of effective thermal conductivity for the nanofluids in porous media and the perturbation influence of inclination angles on the system together with using appropriate porosity and square cavity tilt angle to intervene the flow.

Natural Convection in Inclined Porous Square Enclosure

Steady, laminar, natural convection flow in porous square enclosure with inclination angle is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Darcy- Brinkman-Forchheimer model is considered. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on five parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), Darcy number (Da=0.01), inclination angle φ=(0°-227°), porosity of the medium (ε=0.7) and the aspect ratio of the enclosure (A=1). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rates. The effect of inclination angle is also considered. The results including streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra and φ. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also φ affects the fluid motion and heat transfer in the enclosure. Velocity and heat transfer are more important when φ takes the value (30°).

Thermal and flow investigation of MHD natural convection in a nanofluid-saturated porous enclosure: an asymptotic analysis

In the present investigation, asymptotic solutions are obtained regarding the laminar natural convection of a nanofluid in a porous enclosure subject to internal heating and magnetic field, which appears in a plethora of industrial and bioengineering applications. The complicated nature of the nanofluids along with the computational time needed for the magnetohydrodynamic numerical simulations makes this problem too difficult to face with. Hence, the innovation of this study relies on providing a first-principles approach that includes three kinds of widely utilized nanoparticles (Cu, Al2O3 and TiO2) dispersed in aqueous suspension by incorporating a unified way for describing the nanofluid thermal conductivity and viscosity. In addition, the effect of the magnetic field, internal heating, porous medium permeability as well as nanoparticle size and volume fraction is examined via the derived analytical relationships. In brief, the current study suggests that the increase in the magnetic field intensity and the decrease in the medium permeability tend to suppress the nanofluid flow, thus resulting in deterioration of the heat transfer. This deterioration also occurs when the nanofluid becomes denser and the nanoparticles enlarge. Conversely, increasing the internal heating reinforces the convective currents in favor of cooling process. Finally, the present asymptotic solutions are expected to be very useful in various scientific fields given the rapidly growing interest in nanofluids.

P.790 Adjunctive pregabalin in patients with major depressive disorder and enduring anxiety

The present article is an analysis of heat and mass transfer phenomena for a two-dimensional magnetohydrodynamic (MHD) free convection process in a thermal and mass stratified fluid containing Darcy porous enclosure under the influence of Soret and Dufour effects. The non-dimensional form of coupled non-linear partial differential equations governing the problem is solved numerically by using finite element method. Following the energy analogy concept of Kimura and Bejan (1983) the equation governing the heat function (H) and mass function (M) are derived to facilitate the better visualization of energy and mass distribution. Obtained results are compared with those from literature and found to be in good agreement. In order to evince the characteristics and inherent structures of heat and mass transfer process in fluid flow, the obtained numerical results demonstrated graphically by cumulative heat/mass flux, streamlines, isotherms, iso-concentration plots including heatline and massline (trajectories of heat/mass flux) plots for various values of parameters involved in the problem like: Magnetic parameter (Mg), Thermal (ST) and Mass (SC) stratification, Buoyancy ratio (B), Rayleigh number (Ra), Lewis number (Le), Soret (Sr) and Dufour (Df) numbers.

Natural convection of a non-Newtonian ferrofluid in a porous elliptical enclosure in the presence of a non-uniform magnetic field

In the present study, laminar natural convection of a non-Newtonian ferrofluid inside an elliptical porous cavity was numerically simulated in the presence of a non-uniform external magnetic field. This natural convection problem was relevant to the cooling of micro-sized electronic devices. The well-known finite volume method was employed to discretize the governing equations for ferrofluid flow under the effect of an external magnetic field. The effects of pertinent non-dimensional numbers including the Rayleigh number, the magnetic number, the power-law index, and the Darcy number were studied on the flow pattern and the heat transfer rate of the non-Newtonian ferrofluid. The results showed that by applying the magnetic field by a wire, the overall heat transfer rate increased significantly. Moreover, to achieve the maximum heat transfer enhancement, the wire should have been placed at the center of the elliptical walls of the enclosure. It was also shown that the impact of the power-law index on the heat transfer rate was considerable, and using a shear-thinning liquid increased the average Nusselt number in the porous elliptical enclosure.

Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls

In this article, a comprehensive numerical investigation of the natural convection in a hydro-dynamically as well as thermally anisotropic porous enclosure with insulated side walls is presented. The two different cases, (I) same heat flux on the top as well as bottom walls and (II) heat flux on the top wall being negative of the heat flux on the bottom wall, are considered. A non-Darcy model that includes Darcy and Brinkman terms have been adopted and the coupled governing equations are solved numerically by SIMPLER algorithm. The influence of periodicity parameter and anisotropy parameters on the flow dynamics as well as heat transfer rate has been addressed. It has been found from our rigorous numerical experiments that the structure of streamlines and isotherms for Case I is multicellular and depends on the value of periodicity parameter (N) as well as media permeability, whereas the same for Case II is unicellular. In general, the profile of local heat transfer rate under Case I possesses points of singularity inducing hyperbolic temperature contour. In contrast to Case I, the profile of local heat transfer rate under Case II is found to be free from points of singularity.

Bioconvection in oxytactic microorganism-saturated porous square enclosure with thermal radiation impact

This investigation addresses bioconvection of oxytactic microorganisms in a porous square enclosure by thermal radiation impact. The bioconvection flow and heat transfer in porous media are formulated based on Darcy model of Boussinesq approximation. Appropriate transformations lead to the non-dimensionalized governing partial differential equations. Galerkin finite element method for the resulting equations is computed. The role of relevant parameters on the streamlines, isotherms, isoconcentrations of oxygen and microorganisms and average Nusselt number is analysed in the outputs. It is revealed that the flow intensity of bioconvection is pronounced with larger Rayleigh number and reduced with radiation parameter. Furthermore, the temperature distribution is affected significantly with Rayleigh number. Radiation parameter serves to fasten the heat transfer in the enclosure. Oxygen density is enhanced with Rayleigh number and radiation parameter. The profile of motile isoconcentrations is boosted with Rayleigh number. The stability of microorganisms is improved with the radiation parameter.

Study of the Effect of Thermal Dispersion on Internal Natural Convection in Porous Media Using Fourier Series

Natural convection in a porous enclosure in the presence of thermal dispersion is investigated. The Fourier–Galerkin (FG) spectral element method is adapted to solve the coupled equations of Darcy’s flow and heat transfer with a full velocity-dependent dispersion tensor, employing the stream function formulation. A sound implementation of the FG method is developed to obtain accurate solutions within affordable computational costs. In the spectral space, the stream function is expressed analytically in terms of temperature, and the spectral system is solved using temperature as the primary unknown. The FG method is compared to finite element solutions obtained using an in-house code (TRACES), OpenGeoSys and COMSOL Multiphysics®. These comparisons show the high accuracy of the FG solution which avoids numerical artifacts related to time and spatial discretization. Several examples having different dispersion coefficients and Rayleigh numbers are tested to analyze the solution behavior and to gain physical insight into the thermal dispersion processes. The effect of thermal dispersion coefficients on heat transfer and convective flow in a porous square cavity has not been investigated previously. Here, taking advantage of the developed FG solution, a detailed parameter sensitivity analysis is carried out to address this gap. In the presence of thermal dispersion, the Rayleigh number mainly affects the convective velocity and the heat flux to the domain. At high Rayleigh numbers, the temperature distribution is mainly controlled by the longitudinal dispersion coefficient. Longitudinal dispersion flux is important along the adiabatic walls while transverse dispersion dominates the heat flux toward the isothermal walls. Correlations between the average Nusselt number and dispersion coefficients are derived for three Rayleigh number regimes.

Magnetoconvection and Entropy Analysis in T-Shaped Porous Enclosure Using Finite Element Method

In this paper, a computational work has been investigated on mixed convection and entropy generation in a T-shaped porous cavity filled with a copper–water nanofluid in the presence of a sinusoidal heated wall. The dimensionless system of equations is tackled with the help of Galerkin finite element method, and the obtained nonlinear discretized system of equations is solved via Newton’s method. The computed results have an excellent agreement with the already-published literature in a related area for special cases of governing parameters. The results are investigated for various parameters, including particular ranges as given: Richardson number (), Darcy number (), orientation of magnetic field (), aspect ratio (), and Hartmann number (). It was inferred that heat transfer, entropy generation and Bejan number are decreased by increasing the Hartmann number. At and as the Darcy number increases from to , the average Nusselt number has a growth of 30% or more. The effects of the aforementioned parameters on heat transfer and entropy generation are studied and analyzed in detail.

MHD conjugate natural convection in a porous cavity involving a curved conductive partition and estimations by using Long Short-Term Memory Networks

In this study, MHD conjugate free convection of a porous cavity having a curved shape conductive partition is numerically analyzed by using the Galerkin weighted residual finite element method. The numerical simulation is performed for different values of pertinent parameters: Rayleigh number (between $$10^4$$ and $$10^6$$), Hartmann number (between 0 and 60), Darcy number (between $$5 \times 10^{-4}$$ and 0.05), porosity of the medium (between 0.25 and 0.75), curvature of the partition (minor axis radius of the horizontal ellipse, between 0.01H and 0.3H) and conductivity ratio (between 0.05 and 50). It was observed that the heat transfer rate enhances locally and in average for higher values of Rayleigh number, Darcy number, porosity of the medium and conductivity ratio, whereas the impact is opposite for higher values of Hartmann number. The amount of average Nusselt number reduction is obtained as $$22\%$$ when Hartmann number is changed from 0 to 60 at Rayleigh number of $$10^5$$. Curvature and conductivity of the curved partition affect the variation in fluid flow and heat transfer characteristics. Maximum of $$7\%$$ variation in the average Nusselt number is achieved when the curvature of the conductive partition is varied but the effects of thermal conductivity ratio on heat transfer rate are higher. Long Short-Term Memory Networks are used for estimation of the velocity and temperatures in the computational domain for various values of pertinent input parameters variation in the system which includes conjugate heat transfer mechanism in a porous enclosure with complex-shaped conductive partition under the effects of magnetic field.

Spectral time-dependent solutions for Darcy model of natural convection in a porous enclosure

According to his high accuracy in the simply connected domains, the Galerkin spectral method having Fourier series as trial functions is chosen to develop a space-time dependent solution for the Darcy model coupled with the convection-diffusion heat transfer equation in a square porous cavity. Applying the Fourier-Galerkin (FG) procedure for the stream function formulation of the governing equations, we obtain a system of nonlinear algebraic differential equations that we simplify in ordinary differential equations and integrate in time using the variable order Runge-Kutta method. Two configurations dealing with transient and unsteady regimes are considered where the solution is derived for a wide range of Rayleigh numbers. The developed FG solution shows high accuracy with a reduced computational cost and excellent agreement with a finite element solution. The FG solution is used to provide physical insight into the effect of time variation on the mechanisms of natural convection (NC). The results provide a set of high-accurate data that can be used for testing numerical codes of heat transfer in time-dependent configurations.

Two-phase modeling of the free convection of nanofluid inside the inclined porous semi-annulus enclosure

In the present paper, the modeling of the free convection of two-phase nanofluid inside the inclined porous semi-annulus enclosure is considered. The cavity is filled with Fe3O4-water magnetic nanofluid. Buongiorno and Darcy models are used for modeling two-phase and porous media, respectively. The governing equations are discretized by finite volume method and SIMPLE algorithm. The effect of parameters such as inclination angle of cavity (0 ≤ θ ≤ 90), porous Rayleigh number (10 ≤ Rap ≤ 103), porosity number (ε = 0.4 and 0.7), and volume fraction of nanoparticles (0 ≤ φAve ≤ 0.04) on the flow pattern, temperature field, nanoparticle distribution, and Nusselt number are studied. In low porous Rayleigh numbers, Nusselt number is not the function of porosity number and the inclination angle of the enclosure. Also, Nusselt number increases by adding the volume fraction of nanoparticles. However, in high porous Rayleigh numbers, the heat transfer rate is reduced by increasing the inclination angle of the enclosure. Furthermore, with the increase in the porosity number, Nusselt number is increased.

Natural convection induced by undulated surfaces in a porous enclosure filled with nanoliquid

Effect of surface undulation on convective flow in a porous enclosure is investigated in this present article. The porous enclosure is filled with a water-base nanoliquid containing Cu solid nanoparticles, and the porous layer is modeled using the Darcy law. The governing equations are solved numerically using the built-in finite element method of COMSOL. The investigation was carried out for several parameters: the nanoparticle concentration, [Formula: see text]; the amplitude of undulations, [Formula: see text]; the number of undulations, [Formula: see text]; and the Rayleigh number, [Formula: see text]. It is concluded that the strength of the nanoliquid circulation increases with increasing the amplitude or number undulations. It is found that the heat transfer rates were sensitive to the variation of undulation property, convection intensity, and nanoparticle concentration.