Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Hamila, Rihab; Chaabane, Raoudha; Askri, Faouzi; Jemni, Abdelmajid; Nasrallah, Sassi Ben

doi:10.18280/ijht.350212

Cited by 13 publications

(2 citation statements)

References 16 publications

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“…In the foregoing analysis of variable profile graded longitudinal fin, LBM for transient homogeneous fin reported by Sahu and Bhowmick 38,39 is modified. Furthermore, the concept of equilibrium distribution function, 50 relaxation time, 51 and source term 52 is observed to play a crucial role while embedding inhomogeneity parameter in LBM. Moreover, Walther et al 32,33 reported LBM for homogeneous and heterogeneous method wherein nonnegativity of equilibrium distribution function and the safe usage of LBM had been discussed, to have a stable solution the value of relaxation frequency (ω) must lies in between 0 and 2.…”

Section: Transient Response Under Step Change In Base Heat Fluxmentioning

confidence: 99%

Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

Sahu

Bhowmick

2022

Heat Trans

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Graded materials (GM) possess superior thermo‐mechanical properties, which are not feasible to obtain with homogeneous materials (HM), and hence in this paper, the transient response of a longitudinal fin of varying geometry made up of GM is reported. The temperature‐dependent convection coefficient and heat generation parameters are considered to account for real‐world high‐temperature applications of fins. Fin material properties such as density and specific heat remain constant while thermal conductivity is assumed to vary axially based on four different physically possible variations namely, linear, quadratic, power, and exponential variations. The typical nonlinear differential equation obtained for fins was solved by using a mesoscopic scale‐based particle tracking method called the Lattice Boltzmann method. The Lattice Boltzmann solver has been implemented in form of an in‐house MATLAB code and validated with existing results, thereafter it is developed for solving the foregoing problems. The results obtained are reported for rectangular, triangular, convex, and concave profiles under step change in base temperature and base heat flux. The performance of graded fins is investigated in terms of time required to attain steady‐state and fin tip temperature which are inherent design parameters in the case of the transient fin. Inhomogeneity index and profile function have a significant effect on the performance of fin in terms of resistance to heat flow. Hereby, in comparison with HM fins, GM fins have lower resistance to heat flow irrespective of fin profiles. Concurrently, comparative analysis for fins of different profiles made of HM and GM is also done to facilitate the designer in selecting the most appropriate fins.

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Section: Transient Response Under Step Change In Base Heat Fluxmentioning

confidence: 99%

Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

Sahu

Bhowmick

2022

Heat Trans

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“…After flame stabilization, the flow controllers are set to the desired equivalence ratio. The measurement procedure is performed after the thermal equilibrium of the system occurs [67]. Three thermocouples perform thermal monitoring, so this balance is considered when all temperatures do not vary by more than 2°C over 10 minutes.…”

Section: Figure 1 Drawing Of the Porous Burnermentioning

confidence: 99%

Experimental Assessment of Thermal Radiation Behavior Emitted by Solid Porous Material

Caetano¹,

Lorenzini²,

Lhamby³

et al. 2020

IJHT

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Porous media burners have been the focus of many studies due to the advantage in different applications in industry, which exhibit a directional emission of thermal radiation and low emission of pollutants. Indeed, these characteristics yields benefits regarding productivity by an environment friendly process. Thus, this work analyzes the behavior of radiation heat flux emitted by materials of different linear densities and porosities, varying the rate of air/fuel mixture and the flame power. In this way, was constructed an experimental setup that consists in a supply system of air/fuel, data acquisition, burner support for the radiation sensor, and the radiometer. This structure enables the displacement from 0°C to 90°C allowing the analysis of radiation in the area of a semisphere. The results shown that the silicon carbide has higher radiation efficiency than zirconia, due the higher thermal conductivity and emissivity. However, the silicon carbide degraded in one of the measurements. The ZrO2 media has proved challenging to stabilize for equivalence ratios below 0.6. Regarding the porosity, it is concluded that the higher the porosity, the greater the radiation efficiency, the expected result because there is a larger contact area for the reaction to occur within the pores.

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Modeling of magnetohydrodynamic free convection in an enclosure having elliptical sinks using lattice Boltzmann method

Raoudha

2024

Heat Trans

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This paper adopted the Lattice Boltzmann Method (LBM) to compute a two‐dimensional incompressible convective flow field with two isothermal elliptical sinks attached vertically to the horizontal bottom north side of the enclosure, which is subjected to a horizontal magnetic field. The attained results show that LBM can effectively capture vortex shedding structures and other features inside such complex flow. Also, the Hartmann numbers with a panoply of heated sinks location were studied, and the results showed that fluid flow and heat transfer rate depend on the Hartmann number and are greatly influenced by the heated sinks positions. The effect of the Prandtl number on the average Nusselt number is also highlighted.

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Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Cited by 13 publications

References 16 publications

Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

Experimental Assessment of Thermal Radiation Behavior Emitted by Solid Porous Material

Modeling of magnetohydrodynamic free convection in an enclosure having elliptical sinks using lattice Boltzmann method

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