Development of a thermal lattice Boltzmann method to simulate heat transfer problems with variable thermal conductivity

Varmazyar, Mostafa; Bazargan, Majid

doi:10.1016/j.ijheatmasstransfer.2012.12.014

Cited by 15 publications

(5 citation statements)

References 18 publications

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“…The results are presented for different values of the conduction radiation parameter N and scattering albedo,  . The results are in good agreement with those obtained by [23,24,3]. From Figure 10(a)-(c), in radiation domination case, the effect of thermal conductivity on temperature profiles is found more pronounced.…”

Section: Variable Thermal Conductivitysupporting

confidence: 89%

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Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Hamila¹,

Chaabane²,

Askri³

et al. 2017

IJHT

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In this paper, we investigate the effect of variation in thermal conductivity on several transient heat transfer problems with the lattice Boltzmann method (LBM). First, benchmark problems involving radiation and/or conduction with constant thermal conductivity are simulated. Then we consider the case of variable thermal conductivity with temperature in solving 2D coupled conduction-radiation heat transfer problem and natural convection in differentially heated enclosure. Both the energy equation and the radiative transfer equation (RTE) were solved using exclusively the lattice Boltzmann method. Good agreement with available data in literature was obtained.

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Section: Variable Thermal Conductivitysupporting

confidence: 89%

“…The horizontals walls are under adiabatic boundary condition. With accordance to the grid analysis sensitivity done by [23], the mesh grid adopted in this simulation is (61  61). [23] and [24] In Figure 12…”

Section: Natural Convection With Heat Generationmentioning

confidence: 99%

Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Hamila¹,

Chaabane²,

Askri³

et al. 2017

IJHT

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show abstract

“…Heat transport in boilers, furnaces, porous burners, foam insulations, and fibrous and volumetric solar receivers are few examples of conduction problems where temperature changes and thus the alteration of thermal conductivity is large. Temperature-dependent conductivity in convection heat transport phenomenon may be noticed in chilling structures of electronic devices and heat exchangers [1]. The consideration of steady thermal conductivity in reproducing such cases can consequence in significant error.…”

Section: Introductionmentioning

confidence: 99%

Application of improved Fourier’s and Fick’s laws in a non-Newtonian fluid with temperature-dependent thermal conductivity

Waqas

Hayat

Shehzad

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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An analysis is presented to report the notable features of non-Fourier's double diffusion model in stretchable flow of modified Burgers liquid. The flow phenomenon is due to impermeable stretched sheet. The energy and mass expressions are modeled utilizing concept of non-Fourier's double diffusion. Heat transfer mechanism is characterized within the frame of variable thermal conductivity. Relevant variables reduced the non-linear partial differential expressions into the ordinary differential expressions. Series solutions of established systems are obtained within the frame of homotopy concept. Convergence is attained and acceptable values are certified by expressing the so-called h curves. Temperature and concentration are further disclosed and argued for several variables through graphs. Higher values of thermal/concentration relaxation time lead to decay in temperature and concentration.

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“…For D1Q2 model, particles moves with two opposites unit velocities, 1 ⃗⃗⃗⃗ and 2 ⃗⃗⃗⃗ . The relaxation time and vectors are = ( ) + ∆ /2 [11,23,24]. After discretization, Eq.…”

Section: Lattice Boltzmann Methods Formulation (Lbm)mentioning

confidence: 99%

Analysis of Heat Transfer in the Case of Non-linear Hyperbolic Conduction Equation Coupled with Radiation or with Thermoelectricity

Lazard¹,

Ymeli²,

Kamdem³

et al. 2019

IJES

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Nonlinear hyperbolic heat conduction problems are analyzed thanks to the Cattaneo-Vernotte model, which takes what happens at very short times into account. First, the case of the coupled conductive-radiative heat transfer in planar and spherical media is considered. The accuracy of the Lattice Boltzmann heat conduction model coupled with an analytical layered spherical harmonics solution of the radiative transport equation is investigated. The effects of different parameters such as scattering albedo on both temperature and conductive heat flux distributions within the medium are studied for steady and transient states. The present predictions agree well with literature benchmarks. It is also shown that the parameters have a significant effect on both temperature profile and hyperbolic sharp wave front. Second, the non-Fourier heat conduction in a thermoelectric thin layer is investigated under several boundary conditions by performing a specific quadrupole method. The expressions of the temperature and the heat flux of the small-scale thermoelectric materials are obtained and the whole matrix formulation is given explicitly. Good agreement is observed between quadrupole temperature predictions and analytical results for the Fourier heat conduction problems.

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Development of a thermal lattice Boltzmann method to simulate heat transfer problems with variable thermal conductivity

Cited by 15 publications

References 18 publications

Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Application of improved Fourier’s and Fick’s laws in a non-Newtonian fluid with temperature-dependent thermal conductivity

Analysis of Heat Transfer in the Case of Non-linear Hyperbolic Conduction Equation Coupled with Radiation or with Thermoelectricity

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