Darcy Boussinesq Approximation Research Articles

Numerical Study of Natural Convection Flow in a Square Porous Enclosure Filled with Casson Viscoelastic Fluid

The present simulation, a numerical investigation of natural convection of Casson viscoelastic fluid in a porous square enclosure has been reported. Darcy-Boussinesq approximation mathematical model has been considered. The enclosure has been uniformly heated from the left wall and uniformly cooled from right side wall. The developed partial differential equations of the present computational domain are employed by using stream function approach along with finite difference scheme. The house-computational numerical algorithm has been validated against with the previous work and the computational results have been registered a good correlation. All the important results as shown by streamlines, isotherms, and local Nusselt numbers, the impact of Casson fluid parameter (β), Rayleigh number (Ra) is examined. It has been observed that with the increase in Casson fluid parameter (β), the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Casson fluid parameter (β), for which the heat transfer inside the enclosure takes place solely by conduction mode. It has been also observed that at high Casson viscoelastic fluid the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Casson viscoelastic fluid.

Возникновение концентрационной конвекции в длинной прямоугольной области пористой среды

We solve a problem of the convective flow stability in an elongated rectangular region of a porous medium. The transport of a mixture is described using the MIM (mobile-immobile media) approach. This approach consists in dividing the concentration of the solute into mobile and immobile compo-nents. The effect of density inhomogeneity on the flow of a solution in a porous medium is taken in-to account by the filtration equation within the Darcy-Boussinesq approximation. The problem is solved numerically with the use of the finite difference method. The fields of pressure and concen-tration are obtained. The influence of the parameters of the problem on the disturbance profiles is analyzed. A modified problem of stability is solved. The modification is necessary for finding the oscillatory convective mode. To obtain the solution, the spectrum of Lyapunov exponents is calcu-lated with Gram-Schmidt orthogonalization. Neutral curves are found that make it possible to detect the threshold for the onset of convection. The ranges of parameters in which oscillatory perturba-tions are realized are obtained. The effect of sorption parameters on the occurrence of oscillations is analyzed.

Синхронизация конвективных течений двухкомпонентной жидкости в смежных ячейках пористой среды

In this work, we study the Soret-driven convection of a two-component fluid in adjacent rectangu-lar cells of a porous medium heated from below in the presence of a gravitational field. In each cell, a long-wavelength oscillatory instability is possible; it can be described by means of phase reduction, which makes it possible to study the synchronization of currents. The horizontal bounda-ries of the cells are assumed to be impenetrable (including for impurities), the heat flux is assumed to be fixed. The vertical boundaries have low thermal conductivity. Fluid motions are described by the Darcy-Boussinesq approximation. Additionally, in this system there is a distributed heat source term describing the heat exchange between the cells. In this way, the equations become coupled via the temperature field. The equations within the long-wavelength approximation are derived using the standard method of multiple scales. An analytical description of the system within the frame-work of a weakly nonlinear analysis can only be constructed near the threshold of the convective instability of the system, and the issue of collective effects is relevant for oscillatory modes; there-fore, we restrict our study to the case of an oscillatory instability. On the basis of equations for the amplitudes of the coupled oscillatory modes, we derived equations for the oscillation phases, which are the key equations of the phase description. For these equations, we found the values of the pa-rameters at which the system has the regime of synchronization of currents; the solution for a stable synchronous regime is also reported.

Nanofluid Bioconvection in Porous Enclosure with Viscous Dissipation

In this paper, the bioconvective nanofluid flow in porous square enclosure containing oxytactic microorganism associated with viscous dissipation, is discussed. The bioconvection flow in porous medium is framed by Darcy-Boussinesq approximation. Galerkin finite elements method is employed to solve the governed equations. The computational numerical results are exhibited by the surface plots of stream function, temperature, concentration of oxygen and microorganisms, average Nusselt number, average Sherwood numbers of oxygen and microorganism concentrations. The effects of key parameters such as Peclet number (Pe), Rayleigh number of bioconvection (Rb), viscous dissipation (Ec), thermophoretic parameter (Nt), parameter of Brownian movement (Nb), Lewis number (Le) and Rayleigh number (Ra) are presented and analyzed.

Сплошносредная модель биоконвекции с центростремительной силой

The paper is devoted to mathematical modeling of the unusual collective behavior of emperor penguins in winter. Recent observations of flocks of penguins of this species in their natural habitat have shown that penguins use various forms of adaptive behavior that help them survive in theconditions of the Antarctic winter. Despite the fact that each penguin is well protected from cold, these sea-birds are periodically forced to gather in dense groups, within which the temperature necessary for survival is maintained. Observations have revealed the effect of a sudden liquefaction of a dense huddle of penguins, accompanied by a macroscopic circulation of birds from the edge of the group to its center and back. This paper is the first to assert that the observed phenomenon is bioconvection, which should be interpreted as a second-order phase transition. Moreover, the circulation of birds in a dense group can be explained by the mechanism of thermal convection, with the desire of penguins to move toward the temperature maximum playing the role of an effective force field. In the continuum approximation, we propose a mathematical model of the phenomenon, which is reduced to the equation of a self-gravitating porous disk saturated with an incompressible fluid that generates heat. We derive the governing equations in the Darcy-Boussinesq approximation and formulate a nonlinear boundary value problem. An exact solution of the linearized problem for infinitesimal perturbations of the base state is obtained, and the critical values of the control parameter for the onset of bioconvection are calculated. For finite-amplitude perturbations, the boundary value problem is solved using a finite-difference method. We show that in the case of axial symmetry, the most dangerous is the four-vortex motion. In the case of wind breaking the symmetry of the problem, the two-vortex circulation of penguins becomes the most dangerous. The numerical results obtained based on our theoretical developments are compared with observations of penguins in the Antarctic.

Analysis of Heat Transfer in a Triangular Enclosure Filled with a Porous Medium Saturated with Magnetized Nanofluid Charged by an Exothermic Chemical Reaction

This paper intends to numerically study the steady-state free convection heat transfer in the presence of an exothermal chemical reaction governed by Arrhenius kinetics within a right-angled enclosure of triangular shape filled by porous media saturated with magnetized nanofluid. An approximation named as Darcy–Boussinesq approximation along with a nanofluid model mathematically propounded by Buongiorno has been implemented to model physical phenomenon representing fluid flow, heat transfer, and nanoparticle concentration. The mathematical equations in a dimensionless form describing the stream function for circulation of the fluid, the energy equation for heat, and nanoparticle volume fraction for concentration are solved using the finite difference method. The validity of the numerical procedure is established by comparing present results with the formerly available works in both statistical and graphical approaches. Streamlines, isotherms, and isoconcentrations are plotted and discussed for the various parametric regimes. The graphical description depicts that the average Nusselt and Sherwood numbers are the decreasing function of the Rayleigh number. The study revealed the accountable influence of model parameters such as thermophoresis and Brownian diffusion on the local Sherwood number, whereas a minimum impact on the local Nusselt number is observed.

Free convection in an inclined cavity filled with a nanofluid and with sinusoidal temperature on the walls

Purpose This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls. Design/methodology/approach Governing equations transformed in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity. Findings The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow. Originality/value The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions.

An application of CVFEM for nanofluid heat transfer intensification in a porous sinusoidal cavity considering thermal non-equilibrium model

In this article, Control volume based finite element method (CVFEM) is employed to simulate magnetohydrodynamic (MHD) nanofluid convective heat transfer through a porous cavity by means of thermal non-equilibrium model. Nanofluid properties are estimated by means of Koo–Kleinstreuer–Li (KKL) model and Darcy–Boussinesq approximation is employed for momentum equation. Numerical simulations are provided to find the effects of Rayleigh number Ra, solid–nanofluid interface heat transfer parameter Nhs, Hartmann numberHaand porosityε. Outputs depict that velocity augments with increase ofNhs while it increases with augment of Rayleigh number. Temperature gradient reduces with augment of porosity.

Magnetic nanofluid flow and convective heat transfer in a porous cavity considering Brownian motion effects

In the present article, the improvement of nanofluid heat transfer inside a porous cavity by means of a non-equilibrium model in the existence of Lorentz forces has been investigated by employing control volume based finite element method. Nanofluid properties are estimated by means of Koo-Kleinstreuer-Li. The Darcy-Boussinesq approximation is utilized for the nanofluid flow. Roles of the solid-nanofluid interface heat transfer parameter Nhs, Hartmann number Ha, porosity ε, and Rayleigh number Ra were presented. Outputs demonstrate that the convective flow decreases with the rise of Nhs, but it enhances with the rise of Ra. Porosity has opposite relationship with the temperature gradient.

Free convection in a partially heated wavy porous cavity filled with a nanofluid under the effects of Brownian diffusion and thermophoresis

Numerical analysis of natural convective heat transfer and fluid flow inside a porous wavy cavity filled with a nanofluid has been carried out. The domain of interest is a square cavity with a left isothermal wavy wall, while other walls are flat. A heat source of constant temperature is located on the right vertical wall. Governing equations formulated in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved on the basis of finite difference method of the second order accuracy. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been used for simulation of nanofluid transport inside the cavity. Analysis has been conducted in a wide range of the Rayleigh number, undulation number and heat source size. It has been found that the local heat source has an efficient influence of the nanofluid flow and heat transfer rate.

Heatline visualization of MHD natural convection in an inclined wavy open porous cavity filled with a nanofluid with a local heater

Numerical study of free convection in an inclined wavy open porous cavity filled with a nanofluid under an influence of the uniform magnetic field in the presence of right bottom corner heater of the constant temperature has been carried out. The domain of interest is a tilted tall cavity with aspect ratio 4 having left isothermal wavy wall and open top boundary. A heat source of constant temperature is located at the right bottom corner. Heatline visualization technique is applied to see the heat transport way. Governing equations formulated on the basis of Darcy–Boussinesq approximation with a single-phase nanofluid model have been solved by means of finite difference method. The effects of the Hartmann number, inclination angles of the cavity and magnetic field on the heat transfer and fluid flow at Ra=1000 have been shown in terms of streamlines, heatlines, isotherms, average Nusselt number and fluid flow rate.

Effect of thermal dispersion on transient natural convection in a wavy-walled porous cavity filled with a nanofluid: Tiwari and Das’ nanofluid model

Transient natural convection in a porous wavy-walled cavity filled with a nanofluid has been studied numerically. The domain of interest is bounded by vertical flat and horizontal wavy walls having constant temperatures. The unsteady governing equations formulated in dimensionless stream function and temperature, within the Darcy–Boussinesq approximation and the mathematical nanofluid model proposed by Tiwari and Das in the presence of thermal dispersion with corresponding initial and boundary conditions have been solved numerically using an iterative implicit finite-difference method. The main objective is to investigate the effect of the dimensionless time, thermal dispersion parameter and solid volume fraction parameter of nanoparticles on the fluid flow and heat transfer characteristics. Results are presented in the form of streamlines, isotherms and distributions of the average Nusselt number at the bottom wavy wall.

Natural Convection in a Wavy Porous Cavity With Sinusoidal Temperature Distributions on Both Side Walls Filled With a Nanofluid: Buongiorno's Mathematical Model

A numerical study of the natural convection flow in a porous cavity with wavy bottom and top walls having sinusoidal temperature distributions on vertical walls filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation and the Buongiorno's nanofluid model. The boundary-value problem has been solved numerically on the basis of a second-order accurate finite difference method. Efforts have been focused on the effects of five types of influential factors such as the Rayleigh (Ra = 10–300) and Lewis (Le = 1–1000) numbers, the buoyancy-ratio parameter (Nr = 0.1–0.4), the Brownian motion parameter (Nb = 0.1–0.4), and the thermophoresis parameter (Nt = 0.1–0.4) on the fluid flow and heat transfer characteristics. It has been found that the average Nusselt and Sherwood numbers are increasing functions of the Rayleigh number, buoyancy- ratio parameter, and thermophoresis parameter, and decreasing functions of the Lewis number and Brownian motion parameter.

Free convection in a porous horizontal cylindrical annulus with a nanofluid using Buongiorno’s model

Natural convection flow in a porous concentric horizontal annulus saturated with a water based nanofluid is numerically investigated. The mathematical model used is of single-phase and is formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation and the nanofluid model proposed by Buongiorno. The transformed dimensionless partial differential equations have been solved using a second-order accurate finite-difference technique. The results indicate that inclusion of nanoparticles into pure water changes the flow structure at low values of the Rayleigh number.

Effect of thermal stratification on free convection in a square porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

Natural convection in a square porous cavity filled with a nanofluid in conditions of thermal stratification has been numerically studied. The mathematical model has been formulated in terms of the dimensionless stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das' nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids. Formulated partial differential equations along with the corresponding boundary conditions have been solved by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, thermal stratification parameter, porosity of the porous medium, solid volume fraction parameter of nanoparticles, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It has been observed an essential effect of thermal stratification parameter on heat and fluid flow fields.

Free Convection in a Square Cavity Filled with a Porous Medium Saturated by Nanofluid Using Tiwari and Das’ Nanofluid Model

Free convection in a square differentially heated porous cavity filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation. The Tiwari and Das’ nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids has been used for numerical analysis. The governing equations have been solved numerically on the basis of a second-order accurate finite difference method. The developed algorithm has been validated by direct comparisons with previously published papers and the results have been found to be in good agreement. The results have been presented in terms of the streamlines, isotherms, local, and average Nusselt numbers at left vertical wall at a wide range of key parameters.

Direct Numerical Simulations of Reaction Fronts Propagation under Quasi-Periodic Gravitational Modulation

periodic gravitational modulation on convective instability of reaction fronts in porous media. The model contains reaction diffusion equations coupled with the hydrodynamic equations under the Darcy-Boussinesq approximation. The direct numerical simulation of the dimensionless problem is fulfilled using the alternative direction method and the fast Fourier transform method. The convective instability boundary is found depending on the Lewis number and the amplitude of vibration.

NATURAL CONVECTION BOUNDARY LAYER ALONG IMPERMEABLE INCLINED SURFACES EMBEDDED IN POROUS MEDIUM

The natural convection boundary layer flow on an arbitrarily inclined plate in a saturated porous medium is considered, where wall temperature is power function of the distance from the leading edge. Darcy-Boussinesq approximation is adopted to account for buoyancy force. Inclination parameter ξ is used such that all cases of the horizontal, Inclined and vertical plates can be described by a single set of transformed boundary layer equations. The non-linear coupled parabolic equations have been solved numerically by using an implicit finite-difference scheme for both positive and negative inclinations of the plate. Also, the similarity equations for the limiting cases of the horizontal and vertical plates are recovered by setting ξ = 0 and ξ = 1, respectively. Detailed results for skin friction coefficient and Nusselt number as well as for dimensionless velocity and temperature profiles are presented for a wide range of the parameter ξ . The comparison with other validated articles shows excellent agreement. http://dx.doi.org/10.5755/j01.mech.17.1.205

Vibration effect on convection onset in a system consisting of a horizontal pure liquid layer and a layer of liquid-saturated porous medium

The onset of convection in a system of two horizontal layers (a pure liquid and a porous medium saturated with the same liquid) heated from below under the action of vertical vibration is investigated. For describing the free thermal convection, in the liquid layer the Boussinesq approximation and in the porous layer the Darcy-Boussinesq approximation are used. In the limiting case of a thin liquid layer, effective boundary conditions on the upper boundary of the porous layer with account for convection in the liquid layer are obtained and it is shown that vibration has a stabilizing effect, whereas the presence of a liquid layer leads to destabilization. For an arbitrary liquid to porous layer thickness ratio the onset of convection is investigated numerically. In the case of a thin liquid layer there are two (short-and long-wave) unstable modes. In the case of thick layers the neutral curves are unimodal. Vibration has a stabilizing effect on perturbations with any wave number but affects short-wave perturbations much more strongly than long-wave ones.

Development of HAM tool for building envelope analysis

Moisture-related building envelope failures have resulted in costly rehabilitation in various regions of North America. To advance building envelope design towards an engineering approach and reduce the occurrence of future failures, an advanced numerical tool was developed, in conjunction with an extensive full-scale experiment, to investigate hygrothermal performance of various wood-frame wall assemblies. Major features of the tool are multi-dimensional and transient coupling of heat and moisture transport; natural air convection integrated in hygrothermal simulation through Darcy–Boussinesq approximation; heat transfer by conduction and convection of sensible and latent heat; moisture transport by vapor diffusion, capillary suction and convection; material database of common building materials in North America; experimental settings or weather data as boundary conditions; and moisture added in the building envelope to simulate the wetting process. The numerical tool achieves good compliances to the benchmarking cases of the HAMSTAD project, and its predictions have shown good agreement with data from the full-scale wall experiment. The numerical tool employs the commercial finite-element software to solve the governing equations. This approach provides building science researchers the flexibility to modify, maintain and share their modeling work efficiently.