Search results for: Brinkman's law

Authors: M. S. Al-Qurashi

Abstract:

This work examines thermal convection in two porous layers. Flow in the upper layer is governed by Brinkman-s equations model and in the lower layer is governed by Darcy-s model. Legendre polynomials are used to obtain numerical solution when the lower layer is heated from below.

Keywords: Brinkman's law, Darcy's law, porous layers, Legendre polynomials, the Oberbeck-Boussineq approximation.

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Authors: Hari Mohan Kushwaha, Santosh K. Sahu

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In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen Number, Modified Brinkman Number, Slip Flow, Velocity Slip.

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Authors: D Bhargavi, J. Sharath Kumar Reddy

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The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γ_p on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: Porous material, channel partially filled with a porous material, axial conduction, viscous dissipation.

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Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

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A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: Rayleigh-Bénard convection, heat transport, porous media, generalized Lorenz model, coupled Ginzburg-Landau model.

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Authors: Hadi Niknami Esfahani , Hossein Shokouhmand, Fahim Faraji

Abstract:

The forced convection heat transfer in high porosity metal-foam filled tube heat exchangers are studied in this paper. The Brinkman Darcy momentum model and two energy equations for both solid and fluid phases in porous media are employed .The study shows that using metal-foams can significantly improve the heat transfer in heat exchangers.

Keywords: Metal foam, Nusselt number, heat exchanger, heat flux.

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Authors: Asghar Shirazpour, Seyed Moein Rassoulinejad Mousavi, Hamid Reza Seyf

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In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

Keywords: Lorentz Force, Porous Media, Homotopy Perturbation method

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Authors: Z. Neffah, H. Kahalerras

Abstract:

A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.

Keywords: Chemical reaction, heat transfer, mass transfer, oscillating flow, porous channel.

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Authors: M. Meenasaranya, S. Saravanan

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Conditions corresponding to the unconditional stability of convection in a mechanically anisotropic fluid saturated porous medium of infinite horizontal extent are determined. The medium is heated from below and its bounding surfaces are subjected to temperature modulation which consists of a steady part and a time periodic oscillating part. The Brinkman model is employed in the momentum equation with the Bousinessq approximation. The stability region is found for arbitrary values of modulational frequency and amplitude using the energy method. Higher order numerical computations are carried out to find critical boundaries and subcritical instability regions more accurately.

Keywords: Convection, porous medium, anisotropy, temperature modulation, nonlinear stability.

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Authors: B. Fersadou, H. Kahalerras

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This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers respectively, as well as the Joule heating represented by Eckert number on the velocity and temperature fields, are examined. The main results show an augmentation of heat transfer rate with the decrease of Darcy number and the increase of Ri and Ha when Joule heating is neglected.

Keywords: Heat sources, magnetic field, mixed convection, porous channel.

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Authors: Ali Mchirgui, Nejib Hidouri, Mourad Magherbi, Ammar Ben Brahim

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The paper provides a numerical investigation of the entropy generation analysis due to natural convection in an inclined square porous cavity. The coupled equations of mass, momentum, energy and species conservation are solved using the Control Volume Finite-Element Method. Effect of medium permeability and inclination angle on entropy generation is analysed. It was found that according to the Darcy number and the porous thermal Raleigh number values, the entropy generation could be mainly due to heat transfer or to fluid friction irreversibility and that entropy generation reaches extremum values for specific inclination angles.

Keywords: Porous media, entropy generation, convection, numerical method.

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Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

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Authors: N. Targui, H. Kahalerras

Abstract:

The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy- Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: Double pipe heat exchanger, Nanofluids, Nanoparticles, Porous baffles.

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Authors: Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, MohamedSuleiman

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The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.

Keywords: Deformable, Marangoni, Porous, Stability.

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Authors: Bouchmel Mliki, Chaouki Ali, Mohamed Ammar Abbassi

Abstract:

In this numerical study, natural convection of Cu–water nanofluid in a cavity submitted to different heating modes on its vertical walls is analyzed. Maxwell-Garnetts (MG) and Brinkman models have been utilized for calculating the effective thermal conductivity and dynamic viscosity of nanofluid, respectively. Influences of Rayleigh number (Ra = 10³−10⁶), nanoparticle volume concentration (f = 0-0.04) and Hartmann number (Ha = 0-90) on the flow and heat transfer characteristics have been examined. The results indicate that the Hartmann number influences the heat transfer at Ra = 10⁶ more than other Raleigh numbers, as the least effect is observed at Ra = 10³. Moreover, the results show that the solid volume fraction has a significant influence on heat transfer, depending on the value of Hartmann, heat generation or absorption coefficient and Rayleigh numbers.

Keywords: Heat transfer, linearly/sinusoidally heated, Lattice Boltzmann Method, natural convection, nanofluid.

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Authors: A. Hasanpour, M. Farhadi, K.Sedighi, H.R.Ashorynejad

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A numerical study of flow in a horizontally channel partially filled with a porous screen with non-uniform inlet has been performed by lattice Boltzmann method (LBM). The flow in porous layer has been simulated by the Brinkman-Forchheimer model. Numerical solutions have been obtained for variable porosity models and the effects of Darcy number and porosity have been studied in detail. It is found that the flow stabilization is reliant on the Darcy number. Also the results show that the stabilization of flow field and heat transfer is depended to Darcy number. Distribution of stream field becomes more stable by decreasing Darcy number. Results illustrate that the effect of variable porosity is significant just in the region of the solid boundary. In addition, difference between constant and variable porosity models is decreased by decreasing the Darcy number.

Keywords: Lattice Boltzmann Method, Porous Media, Variable Porosity, Flow Stabilization

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Authors: Hamid Maidat, Khedidja Bouhadef, Djamel Eddine Ameziani, Azzedine Abdedou

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This work consists of a numerical simulation of convective heat transfer in a vertical plane channel filled with a heat generating porous medium, in the absence of local thermal equilibrium. The walls are maintained to a constant temperature and the inlet velocity is uniform. The dynamic range is described by the Darcy-Brinkman model and the thermal field by two energy equations model. A dimensionless formulation is developed for performing a parametric study based on certain dimensionless groups such as, the Biot interstitial number, the thermal conductivity ratio and the volumetric heat generation, q '''. The governing equations are solved using the finite volume method, gave rise to a multitude of results concerning in particular the thermal field in the porous channel and the existence or not of the local thermal equilibrium.

Keywords: Mixed convection, porous medium, power generation, local thermal non equilibrium model.

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Authors: Partha Sarathi Majee, S. Bhattacharyya

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Migration of a core-shell soft particle under the influence of an external electric field in an electrolyte solution is studied numerically. The soft particle is coated with a positively charged polyelectrolyte layer (PEL) and the rigid core is having a uniform surface charge density. The Darcy-Brinkman extended Navier-Stokes equations are solved for the motion of the ionized fluid, the non-linear Nernst-Planck equations for the ion transport and the Poisson equation for the electric potential. A pressure correction based iterative algorithm is adopted for numerical computations. The effects of convection on double layer polarization (DLP) and diffusion dominated counter ions penetration are investigated for a wide range of Debye layer thickness, PEL fixed surface charge density, and permeability of the PEL. Our results show that when the Debye layer is in order of the particle size, the DLP effect is significant and produces a reduction in electrophoretic mobility. However, the double layer polarization effect is negligible for a thin Debye layer or low permeable cases. The point of zero mobility and the existence of mobility reversal depending on the electrolyte concentration are also presented.

Keywords: Debye length, double layer polarization, electrophoresis, mobility reversal, soft particle.

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Authors: Partha P. Gopmandal, S. Bhattacharyya

Abstract:

We have studied the migration of a charged permeable aggregate in electrolyte under the influence of an axial electric field and pressure gradient. The migration of the positively charged aggregate leads to a deformation of the anionic cloud around it. The hydrodynamics of the aggregate is governed by the interaction of electroosmotic flow in and around the particle, hydrodynamic friction and electric force experienced by the aggregate. We have computed the non-linear Nernest-Planck equations coupled with the Dracy- Brinkman extended Navier-Stokes equations and Poisson equation for electric field through a finite volume method. The permeability of the aggregate enable the counterion penetration. The penetration of counterions depends on the volume charge density of the aggregate and ionic concentration of electrolytes at a fixed field strength. The retardation effect due to the double layer polarization increases the drag force compared to an uncharged aggregate. Increase in migration sped from the electrophretic velocity of the aggregate produces further asymmetry in charge cloud and reduces the electric body force exerted on the particle. The permeability of the particle have relatively little influence on the electric body force when Double layer is relatively thin. The impact of the key parameters of electrokinetics on the hydrodynamics of the aggregate is analyzed.

Keywords: Electrophoresis, Advective flow, Polarization effect, Numerical solution.

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Authors: Mohsen Torabi, Nader Karimi, Kaili Zhang

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This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.

Keywords: Entropy generation, exothermicity, endothermicity, forced convection, local thermal non-equilibrium, analytical modeling.

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Authors: Manish K. Khandelwal, P. Bera, A. Chakrabarti

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This article presents a numerical study of the doublediffusive mixed convection in a vertical channel filled with porous medium by using non-equilibrium model. The flow is assumed fully developed, uni-directional and steady state. The controlling parameters are thermal Rayleigh number (RaT ), Darcy number (Da), Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer coefficient (H), and porosity scaled thermal conductivity ratio (γ). The Brinkman-extended non-Darcy model is considered. The governing equations are solved by spectral collocation method. The main emphasize is given on flow profiles as well as heat and solute transfer rates, when two diffusive components in terms of buoyancy ratio are in favor (against) of each other and solid matrix and fluid are thermally non-equilibrium. The results show that, for aiding flow (RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a certain value of H, beyond that decreases smoothly and converges to a constant, whereas in case of opposing flow (RaT = -1000), the result is same for N = 0 and 1. The variation of Nuf in (N, Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases (aiding and opposing) the flow destabilize on increasing N by inviting point of inflection or flow separation on the velocity profile. Overall, the buoyancy force have significant impact on the non-Darcy mixed convection under LTNE conditions.

Keywords: buoyancy ratio, mixed convection, non-Darcy model, thermal non-equilibrium

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Authors: Amir Reza Ghahremani, Salman SafariMohsenabad, Mohammad Behshad Shafii

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To achieve reliable solutions, today-s numerical and experimental activities need developing more accurate methods and utilizing expensive facilities, respectfully in microchannels. The analytical study can be considered as an alternative approach to alleviate the preceding difficulties. Among the analytical solutions, those with high robustness and low complexities are certainly more attractive. The perturbation theory has been used by many researchers to analyze microflows. In present work, a compressible microflow with constant heat flux boundary condition is analyzed. The flow is assumed to be fully developed and steady. The Mach and Reynolds numbers are also assumed to be very small. For this case, the creeping phenomenon may have some effect on the velocity profile. To achieve robustness solution it is assumed that the flow is quasi-isothermal. In this study, the creeping term which appears in the slip boundary condition is formulated by different mathematical formulas. The difference between this work and the previous ones is that the creeping term is taken into account and presented in non-dimensionalized form. The results obtained from perturbation theory are presented based on four non-dimensionalized parameters including the Reynolds, Mach, Prandtl and Brinkman numbers. The axial velocity, normal velocity and pressure profiles are obtained. Solutions for velocities and pressure for two cases with different Br numbers are compared with each other and the results show that the effect of creeping phenomenon on the velocity profile becomes more important when Br number is less than O(ε).

Keywords: Creeping Effect, Microflow, Slip, Perturbation.

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