Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry – An application of the lattice Boltzmann method

Mukherjee, Aritra; Lahiri, Arnab; Mishra, Subhash C.

doi:10.1016/j.ijheatmasstransfer.2012.07.014

Cited by 35 publications

(14 citation statements)

References 24 publications

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“…Moreover, the validity of the R13 equations has been checked against direct simulation Monte Carlo data, for Couette and Poiseuille flows (Taheri et al 2009), which lends further credence to the equation proposed herein. The useful of Catteneo equation has been shown by its application to various problems (Shiomi and Maruyama 2006;Tzou and Chiu 2001;Mishra and Sahai 2012;Xu et al 2008;Antaki 2005). The purpose of this work is not to validate the model proposed in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Since no process is instantaneous, a correction is required to this law. Such a correction becomes especially pertinent in problems involving small length (Yang et al 2005;Shiomi and Maruyama 2006) or time scale (Tzou and Chiu 2001;Mishra and Sahai 2012) and for temperatures close to absolute zero (Ozisik and Vick 1984). Chester (1963) mentions that there is a critical frequency beyond which non-Fourier effects become appreciable.…”

Section: Introductionmentioning

confidence: 99%

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Higher-Order Continuum Equation Based Heat Conduction Law

Agrawal

2016

INAE Lett

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The Fourier law has the unphysical consequence of infinite speed of heat conduction. The Cattaneo modification to the heat conduction equation removes this deficiency. The modified equation however suffers from two main defects: the speed of propagation cannot be determined theoretically, and the equation can lead to results which violate the second law of thermodynamics. In this paper, we derive the Cattaneo equation starting from Grads 13-moment equations. Further, we derive a thermodynamically consistent conduction model from the regularized moment equations. The deficits in the existing models are therefore satisfactorily addressed in this work.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Higher-Order Continuum Equation Based Heat Conduction Law

Agrawal

2016

INAE Lett

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“…The LBM is a computational method based on a mesoscopic description of heat flow, which better describes and captures sharp discontinuities of physical problems than the finite difference/volume methods [11,23]. In order to simplify the energy equation with known radiative energy, we consider the dimensionless parameters as follows…”

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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“…Eq. (5) has been widely studied to description mass and heat transport phenomena 19,18,20 . Considering a initial distribution as Dirac delta, D = 0.01 and τ = 0.1, Figure 1 shows the comparing distributions of Fick and Telegraph's diffusion, where it is interesting note that the frontal edge of telegraph frequency distribution is abrupt, unlike that for Fick' diffusion.…”

Section: Telegraph Reaction-diffusion Equationmentioning

confidence: 99%

Spatiotemporal Dynamics of Telegraph Reaction-Diffusion Predator-Prey Models

et al. 2013

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Reaction-diffusion (RD) equations are commonly used to describe the propagation effects in population interactions in ecology. RD system are described by parabolic partial differential equations (PDE), based on the Fick diffusion equation, hence arbitrary large population speeds are involved. To avoid this unrealistic situation, we introduce the Cattaneo's diffusion in spatiotemporal models of prey-predator interactions, which leads to more realistic and interesting interactions between populations and can be useful to gain insights to the understanding of food-chain dynamics. The resulting model is the so-called telegraph RD model. Numerical simulations on a predator-prey model with Holling type II functional response and cross-diffusion show the effects of the relaxation time in the dynamic of population interactions.

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Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry – An application of the lattice Boltzmann method

Cited by 35 publications

References 24 publications

Higher-Order Continuum Equation Based Heat Conduction Law

Higher-Order Continuum Equation Based Heat Conduction Law

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

Spatiotemporal Dynamics of Telegraph Reaction-Diffusion Predator-Prey Models

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