Porous Enclosure Research Articles

Natural convection in an inclined porous triangular enclosure with various thermal boundary conditions

The aim of the study is to analyse the effect of two different thermal boundary conditions on natural convection in a porous triangular enclosure. Sinusoidal and linearly varying temperature profiles on the left wall are considered. The top wall of the enclosure is kept to be adiabatic. The Darcy model is adopted in this study and the governing equations are solved using the finite difference method for various values of inclination angle and Darcy-Rayleigh number. The results are presented in the form of streamlines, isotherms, and Nusselt numbers. The heat transfer rates are calculated and compared between two thermal boundary conditions. The heat transfer is more enhanced in the case of sinusoidal wall temperature than linearly varying wall temperature.

Transient free convection in an inclined square porous cavity filled with a nanofluid using LTNE and Buongiorno’s models

The combined effect of Brownian diffusion, thermophoresis and cavity inclination angle on natural convective heat transfer in an inclined porous enclosure has been studied numerically. Fluid containing nanoparticles of low concentration circulates inside the cavity under the effect of the buoyancy force. Governing equations with corresponding boundary conditions formulated using the non-dimensional stream function and vorticity variables have been solved by the finite difference method. An influence of the cavity inclination angle, Darcy and Nield numbers on nanofluid flow and heat transfer has been investigated. It has been found that high Nield numbers illustrate more equilibrium temperature distribution inside the porous cavity.

VISUALIZATION ANALYSIS OF NATURAL CONVECTION IN A POROUS ENCLOSURE USING THE CHEBYSHEV SPECTRAL COLLOCATION METHOD WITH TEMPERATURE-DEPENDENT THERMAL DIFFUSIVITY

We studied the effects of temperature-dependent thermal diffusivity and aspect ratio on natural convection in a rectangular porous cavity. Thermal diffusivity is assumed to vary as a linear function of temperature.We used the Chebyshev spectral collocation method to solve coupled nonlinear partial differential equations. The domain of the problem is discretized by Chebyshev–Gauss–Lobatto collocation points, and time derivatives are discretized by a semi-implicit scheme with finite-difference approximation. We executed the treatment of variable thermal diffusivity using array multiplication in the computation and used the matrix diagonalization method to solve discretized equations. Results from the current study are compared with those available in the literature. Numerical solutions are visualized using the isotherm, streamline, and heatline for different values of Rayleigh number, thermal diffusivity coefficient, and aspect ratio. For the first time, the visualization tool of heatline is applied to a porous enclosure with temperature-dependent thermal diffusivity. On the basis of these results, the heat-transfer process across the enclosure was analyzed. We found that variable thermal diffusivity has a considerable influence on flow pattern and corresponding heat transfer in the enclosure.

Numerical investigation of boiling and forced convection heat transfer in inclined porous enclosure using modified enthalpy formulation

Two-Phase flow in an inclined rectangular porous media, under unsteady-state condition, has been numerically investigated in this article, based on the modifiedh-formulation of Two-Phase Mixture Model (TPMM). The governing equations have been discretised using Finite Volume Method (FVM) and solved iteratively in a SIMPLE-like manner. Effects of various parameters on the flow and temperature fields have been investigated, which clearly demonstrated that the inclination angle strongly affect the boiling initiation. Recirculating flow has been observed when the inclination angle θ>0˚. The results clearly indicated that the operating conditions and the porous medium properties have significant effects on the initiation and termination of phase change process. A closer inspection of the results reveals that the presence of a critical inclination angle depending on the value of K*and, Re1which correspond to a maximum values of vapour volume. The modified h-formulation requires significantly less computational time as compared with the existingH-formulation of TPMM.

Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: Effects of a heat sink and source size and location

The effects of a heat sink and the source size and location on the entropy generation, MHD natural convection flow and heat transfer in an inclined porous enclosure filled with a Cu-water nanofluid are investigated numerically. A uniform heat source is located in a part of the bottom wall, and a part of the upper wall of the enclosure is maintained at a cooled temperature, while the remaining parts of these two walls are thermally insulated. Both the left and right walls of the enclosure are considered to be adiabatic. The thermal conductivity and the dynamic viscosity of the nanofluid are represented by different verified experimental correlations that are suitable for each type of nanoparticle. The finite difference methodology is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published works is performed, and the results show a very good agreement. The results indicate that the Nusselt number decreases via increasing the nanofluid volume fraction as well as the Hartmann number. The best location and size of the heat sink and the heat source considering the thermal performance criteria and magnetic effects are found to be D = 0.7 and B = 0.2. The entropy generation, thermal performance criteria and the natural heat transfer of the nanofluid for different sizes and locations of the heat sink and source and for various volume fractions of nanoparticles are also investigated and discussed.

Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu–water nanofluid

In this work, the influences of heat generation/absorption and nanofluid volume fraction on the entropy generation and MHD combined convection heat transfer in a porous enclosure filled with a Cu–water nanofluid are studied numerically with of partial slip effect. The finite volume technique is utilized to solve the dimensionless equations governing the problem. A comparison with already published studies is conducted, and the data are found to be in an excellent agreement. The minimization of entropy generation and the local heat transfer according to various values of the controlling parameters are reported in detail. The outcome indicates that an augmentation in the heat generation/absorption parameter decreases the Nusselt number. Also, when the volume fraction is raised, the Nusselt number and entropy generation are reduced. The impact of Hartmann number on heat transfer and the Richardson number on the entropy generation and the thermal rendering criteria are also presented and discussed.

Coupled Free and Forced Convection Heat Transfer in a Porous Enclosure Saturated by Nanofluid with Irregular Temperature Distributions on Sidewalls

Abstract A two dimensional steady and laminar mixed convection flow in lid-driven porous cavity filled with Cu-water nanofluid is presented in this numerical investigation. The vertical side walls are considered with two spatially varying sinusoidal temperature distributions of different amplitude ratios and phase deviations while the horizontal walls are thermally insulated. The transport equations are solved using finite volume method on a uniformly staggered grid system. The variations of fluid flow, heat transfer, mid-plane velocity, and Nusselt number were discussed over a wide range of Richardson number $(Ri)$ , Darcy number $(Da)$ , porosity $(\epsilon)$ , amplitude ratio $(\epsilon_a)$ , phase deviation $(\phi)$ , and solid volume fraction $(\chi)$ . The results show that the total heat transfer rate increases on increasing Darcy number, amplitude ratio, and solid volume fraction with fixed $Ri$ . For $\phi=\frac{3\pi}{4}$ , the average Nusselt number gets its maximum value when the natural convection dominates. It is found that for $Ri =0.01$ and $1$ , the total heat transfer rate decreases on increasing porosity whereas for $Ri=100$ it is contradictory. It is also observed that the heat transfer is affected mainly on the right side wall where the phase deviation varies from $0$ to $\pi$ . But the effect of $\phi$ is not significant on the left side wall. The sinusoidal temperature distribution along the sidewalls gives better heat transfer rate than the uniform temperature.

Influence of electric field on Fe3O4- water nanofluid radiative and convective heat transfer in a permeable enclosure

In this article, Fe3O4- water nanofluid EHD forced convection is investigated. Different shapes of nanoparticles are considered. The porous enclosure has one moving wall which is considered as positive electrode. Control Volume based Finite Element Method is employed to simulate this problem. Outputs show the roles of Reynolds number (Re), Fe3O4- H2O nanofluid volume fraction (ϕ), Darcy number (Da), radiation parameter (Rd) and supplied voltage (Δφ). Results demonstrate that temperature gradient is an enhancing function of Coulomb force and permeability. Maximum values for temperature gradient is obtained for platelet shape nanoparticles.

Onset of fractional-order thermal convection in porous media.

The macroscopic description of buoyancy-driven thermal convection in porous media is governed by advection-diffusion processes, which in the presence of thermophysical heterogeneities fail to predict the onset of thermal convection and the average rate of heat transfer. This work extends the classical model of heat transfer in porous media by including a fractional-order advective-dispersive term to account for the role of thermophysical heterogeneities in shifting the thermal instability point. The proposed fractional-order model overcomes limitations of the common closure approaches for the thermal dispersion term by replacing the diffusive assumption with a fractional-order model. Through a linear stability analysis and Galerkin procedure, we derive an analytical formula for the critical Rayleigh number as a function of the fractional model parameters. The resulting critical Rayleigh number reduces to the classical value in the absence of thermophysical heterogeneities when solid and fluid phases have similar thermal conductivities. Numerical simulations of the coupled flow equation with the fractional-order energy model near the primary bifurcation point confirm our analytical results. Moreover, data from pore-scale simulations are used to examine the potential of the proposed fractional-order model in predicting the amount of heat transfer across the porous enclosure. The linear stability and numerical results show that, unlike the classical thermal advection-dispersion models, the fractional-order model captures the advance and delay in the onset of convection in porous media and provides correct scalings for the average heat transfer in a thermophysically heterogeneous medium.

Analysis of conjugate natural convection within a porous square enclosure occupied with micropolar nanofluid using local thermal non-equilibrium model

This work aims to study the conjugate natural convection of micropolar nanofluid within a porous enclosure considering local thermal non-equilibrium model. The Galerkin finite element method is employed to solve the coupled and non-linear equations. The governing parameters are Darcy–Rayleigh number Ra=10–1000, porosity ε=0.1–0.9, interface parameter H=1–1000, Kr=0.1–10, volume fraction of the nanofluid φnf=0–0.08, vortex viscosity parameter Δ=0–3, the width of the solid wall d=0.1–0.4 and ratio of wall thermal conductivity to that of the base fluid Rk=0.1–10. It has been revealed that the power of micro-rotations increases with Darcy–Rayleigh number, vortex viscosity parameter, ratio of wall thermal conduction to that of base fluid, interface parameter (Kr and H) in conditions that declines with thickness of the solid wall and porosity. The Nusselt numbers for both phases in the porous medium significantly decline as thickness of the solid wall rises, with the exception of d=0.35. Also, it can be concluded as the porosity parameter increases for the passing flow, the nanofluid flow is governed by the classic Navier-Stokes equations.

Critical Dimension of a Circular Heat and Solute Source for an Optimum Transfer within Square Porous Enclosures

The present work refers to the investigation of natural convection within a partitioned porous enclosure, driven by cooperating thermal and solutal buoyancy forces. The side walls are maintained at a uniform temperature and concentration, lower than that of a circular heat and solute source, which located at the center of the porous square, the rest of the horizontal walls are kept insulated. The physical model for the momentum conservation equation makes use of the Brinkman extension of the classical Darcy equation, the set of coupled equations is solved using the finite volume approach and the SIMPLER algorithm. To account for the impact of the main parameters such the buoyancy ratio; Lewis and porous thermal Rayleigh numbers; as well as the source dimension, heat and mass transfer characteristics are widely inspected and then new powerful correlations are proposed, which predict within ±1% the numerical results. Noted that the validity of the used code was ascertained by comparing our results with experimental data and numerical ones; already available in the literature.

Numerical investigation of nanofluid free convection under the influence of electric field in a porous enclosure

Electrohydrodynamic Fe3O4-Ethylene glycol nanofluid radiative and free convective heat transfer is reported in a porous media. Influences of nanoparticles, shape and supplied voltage on properties of nanofluid are taken into account. The hot surface is considered as positive electrode. Control Volume based Finite Element Method is employed to show the roles of radiation parameter, Darcy number (Rd)(Da), Rayleigh number (Ra), nanofluid volume fraction (ϕ) and supplied voltage (Δφ). Results indicate that Nusselt number is an enhancing function of Coulomb forces and permeability of porous media. In order to find highest heat transfer rate, Platelet shape nanoparticles should be selected.

Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation

Influence of thermal radiation and external electric field on Fe3O4-Ethylene glycol nanofluid hydrothermal treatment is presented in this article. The lid driven cavity is porous media and the bottom wall is selected as positive electrode. Influence of supplied voltage on viscosity of nanofluid is taken into account. Control Volume based Finite Element Method is utilized to estimate the roles of radiation parameter (Rd), Darcy number (Da), Reynolds number (Re), nanofluid volume fraction (ϕ) and supplied voltage (Δφ). Results indicate that shape of nanoparticles can change the flow style and maximum rate of heat transfer is obtained by selecting platelet shape nanoparticles. The convective heat transfer improves with augment of permeability and Coulomb force.

Fe3O4-Ethylene glycol nanofluid forced convection inside a porous enclosure in existence of Coulomb force

In this article, impact of shape factor on nanofluid forced convection in existence of electric field is simulated via Control Volume based Finite Element Method. Effect of thermal radiation on energy equation is taken into account. The porous enclosure is filled with Fe3O4- Ethylene glycol nanofluid. Viscosity of nanofluid is varied with electric field. The bottom wall is considered as positive electrode. Numerical method is employed to find the roles of Reynolds number (Re), Darcy number (Da), radiation parameter (Rd), nanofluid volume fraction (ϕ) and supplied voltage (Δφ). Results proved that Nusselt number augments with augment of thermal radiation. Thermal boundary layer thickness decreases with increase of Darcy number and Coulomb force.

Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects – A numerical study

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.

Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall

This current study focuses on the simulation of free convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a localized temperature varying sinusoidally with the space while the upper horizontal wall and rest of the bottom walls are insulated. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in FORTRAN 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number, amplitude and length of source heating on the dynamic and thermal fields are investigated. On the other hand, the effects of the amplitude on the horizontal velocity distribution and the mean horizontal temperature distribution(y=0.5) were presented and discussed. It emerges from this study that the increasing of the amplitude and Rayleigh-Darcy number intensify the flow and the global heat transfer in our physical domain.

Natural convection in an inclined parallelogrammic porous enclosure under the effect of magnetic field

A numerical study is conducted to understand the effect of magnetic field on the natural convection in a tilted parallelogrammic porous enclosure. The two opposing side walls are differentially heated with a temperature difference specified, while the upper and lower walls are adiabatic. Using the Darcy model to formulate the problem, a finite difference scheme consisting of the Alternating Direction Implicit and Successive Line over Relaxation methods are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Rayleigh number ranging from 100 to 5 × 103, inclination of the walls of the parallelogram ϕ from -600 to 600, angle of inclination of the enclosure α from -600 to 600, aspect ratio from 0.5 to 2 and Hartmann number from 0 to 20. The flow structure and the corresponding heat transfer characteristics inside the enclosure are presented in detail. The results revealed that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium. The reported results are in good agreement with the available published work in the literature.

Effects of Mid-Moving Heated Wall on Mixed Convection in a Fluid-Saturated Non-Darcy Porous Enclosure with Sinusoidal Heating Walls and Filled with Cu-Water Nanofluid

Effects of Mid-Moving Heated Wall on Mixed Convection in a Fluid-Saturated Non-Darcy Porous Enclosure with Sinusoidal Heating Walls and Filled with Cu-Water Nanofluid

English

English

Lattice Boltzmann method simulation for CuO-water nanofluid flow in a porous enclosure with hot obstacle

In this research, effect of Lorentz force on nanofluid natural convection inside a porous cavity is reported. Simulations have been done via Lattice Boltzmann Method. KKL model is employed to add Brownian motion effect on nanofluid properties. Impacts of Darcy number (Da), Rayleigh number (Ra), nanofluid volume fraction (ϕ) and Hartmann number (Ha) on heat transfer treatment are demonstrated. Outputs demonstrate that temperature gradient reduces with increase of Hartmann number but it enhances with augment of Darcy number.