Thermal Lattice Boltzmann Model for Incompressible Flows through Porous Media

Seta, Takeshi; Takegoshi, Eisyun; Kitano, Kazuyuki; Okui, Kenichi

doi:10.1299/jtst.1.90

Cited by 28 publications

(28 citation statements)

References 21 publications

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“…The Boussinesq approximation is applied. Indeed, the generalized model for non-compressible fluid flow and heat transfer is governed by the following equations [6,17,18]: Continuity equation…”

Section: Mathematical Equations and Lbm Implementationmentioning

confidence: 99%

“…This expression leads to generalized lattice Boltzmann equation. The forcing term is given by [6]. To avoid the problem of the non-linearity we define a temporal velocity by the following relation [5,6,7,16].…”

Section: Mathematical Equations and Lbm Implementationmentioning

confidence: 99%

“…The inlet and the outlet positions are respectively x 1 and x n The Reynolds number of Poiseuille flow Re is given by Re = Hu 0 υ where u 0 refers to the peak velocity of the flow along the centerline of the channel [5][6][7]. The Darcy number is defined by = K H 2 .…”

Section: Code Validation: Poiseuille Flowmentioning

confidence: 99%

“…This correction is valid for high porosity where the effect of Forchheimer term is undefined. Thus, studying non-compressible fluid flow according to the only Brinkman modification does not generate good agreement with the experimental results also ignoring the impact of Brinkman is not adequate for all conditions [6]. It is necessary to combine the two coefficients to obtain equation that contains inertial and viscous effect.…”

Section: Introductionmentioning

confidence: 99%

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Fluid Flow and Heat Transfer in Porous Media and Post Heated Obstacle: Lattice Boltzmann Simulation

Chatti¹,

Ghabi²,

Mhimid³

2016

IJHT

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The purpose of this paper is to study heat transfer and fluid flow in porous media with and without obstacle. The double-population thermal lattice Boltzmann is applied. The validation of the accuracy of our numerical code is done. We resort to a comparison between the present and the numerical results reported in previous studies on benchmark problems (the generalized Poiseuille flow). Then, the problem of a fluid sheared in a porous media is studied using two approaches of LBM: generalized lattice Boltzmann equation (GLBE) and simplified lattice Boltzmann equation (SLBE). The comparison of these models is achieved at a specific node and cross-section. It includes many dynamic parameters and covers all over the medium. It is so important to conclude that the GLBE is more suitable to study heat transfer in porous media. In the second part, the heat transfer is calculated through a porous media with hot obstacle. The effect of the obstacle dimension and position is presented. The dependence of fluid flow and heat transfer to several parameters is studied. We conclude by showing that the model presented here is particularly well-suited to study heat and mass transfer in porous media with many applications. transfer is calculated through a porous media with hot obstacle. The effect of the obstacle dimension and position is presented. The dependence of fluid flow and heat transfer to several parameters is studied. We conclude by showing that the model presented here is particularly well-suited to study heat and mass transfer in porous media with many applications. Key words: Lattice Boltzmann equation (GLBE and SLBE), porous media, thermal incompressible flow, convection, hot obstacleDetailed instructions for preparing your paper submitted to International Journal of Heat and Technology are given as follows. Please be responsible for the quality and appearance of your work.It's strongly recommended that you directly type over the template or just cut and paste from another document and use markup styles. Please keep in mind all the way through the preparation, do not modify page setup in this template, such as fonts, font sizes, line spacing, margin, uppercase and lowercase, the order of sections, etc. The abstract section is mandatory, with a word limit of 200 words. The scope, aims, results and conclusions may be summarized here. Avoid inserting any reference in this section. In the Keywords section, please capitalize the initial letter of each keyword. Enter the words or phrases in alphabetical order, separated by commas. There is a maximum of 5 keywords. [Abstract style: Times New Roman 9, justified]

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Section: Mathematical Equations and Lbm Implementationmentioning

confidence: 99%

Section: Mathematical Equations and Lbm Implementationmentioning

confidence: 99%

Section: Code Validation: Poiseuille Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fluid Flow and Heat Transfer in Porous Media and Post Heated Obstacle: Lattice Boltzmann Simulation

Chatti¹,

Ghabi²,

Mhimid³

2016

IJHT

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“…The lattice Boltzmann method is a numerical method that has been recently developed and obtained acceptable results in simulation of complex phenomena in fluid mechanics research areas such as two phase flow [8], nanofluid [9], and porous media [10][11][12]. Guo and Zhao [10] applied the lattice Boltzmann method to simulate heat transfer and fluid flow in porous media.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann Simulation of Heat Transfer Enhancement in a Cold Plate Using Porous Medium

Mehrizi¹,

Farhadi²,

Sedighi³

et al. 2013

Journal of Heat Transfer

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The computational study of heat transfer and fluid flow in a porous media cold plate was investigated using lattice Boltzmann method. The study was carried out on a heat exchanger including two adiabatic inlet and outlet conduit and three hot fins with constant temperature. The porous medium is positioned between the fins to enhance heat transfer rate. The local thermal equilibrium assumption between the fluid and solid phases and the Brinkman-Forchheimer extended Darcy equation was used to simulate the porous domain. The effect of porosity on heat transfer from the fins surfaces was studied at different Reynolds and Prandtl numbers. Results show that by decreasing the porosity, the heat transfer rate increases and the fluid bulk temperature grows at less time for different Reynolds and Prandtl numbers.

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Numerical study of Prandtl effect on MHD flow at a lid‐driven porous cavity

Hasanpour

Farhadi

Sedighi

et al. 2011

Numerical Methods in Fluids

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SUMMARY In this paper, the lattice Boltzmann method is used to study the Prandtl number effect on flow structure and heat transfer rates in a magnetohydrodynamic flow mixed convection in a lid‐driven cavity filled with a porous medium. The right and left walls are at constant but different temperatures (θh and θc), while the other walls are adiabatic. Gallium and salt water (0.02 < Pr < 13.4) are used as samples of the electroconducting fluids in the cavity. Typical sets of streamlines and isotherms are presented to analyze the flow patterns set up by the competition among the forced flow created by the lid‐driven wall, the buoyancy force of the fluid and the magnetic force of the applied magnetic field. Mathematical formulations in the porous media were constructed based on the Brinkman–Forchheimer model, while the multidistribution‐function model was used for the magnetic field effect. Numerical results were obtained and the effects of the Prandtl number and the other effective parameters such as Richardson, Hartman, and Darcy numbers were investigated. It was found that the fluid fluctuations within the cavity were reduced by increasing the Hartman number. A similar pattern was observed for the Darcy number reduction. Heat transfer was essentially dominated by the conduction for the low Prandtl number and forced convection dominated as the Prandtl number increased. Also, the average Nusselt number was raised by increasing the Prandtl number. It was discovered that a remarkable heat transfer enhancement of up to 28% could be reached by increasing the Prandtl number (from 0.02 to 13.4) at constant Richardson and Darcy numbers. Copyright © 2011 John Wiley & Sons, Ltd.

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Thermal Lattice Boltzmann Model for Incompressible Flows through Porous Media

Cited by 28 publications

References 21 publications

Fluid Flow and Heat Transfer in Porous Media and Post Heated Obstacle: Lattice Boltzmann Simulation

Fluid Flow and Heat Transfer in Porous Media and Post Heated Obstacle: Lattice Boltzmann Simulation

Lattice Boltzmann Simulation of Heat Transfer Enhancement in a Cold Plate Using Porous Medium

Numerical study of Prandtl effect on MHD flow at a lid‐driven porous cavity

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