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A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode

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Abstract

Lattice Boltzmann method is extended to solve a combined mode of radiation and force convection heat transfer problem in a channel. Effects of different parameters such as radiation parameters, Peclet number, and emissivity on temperature distribution are investigated. To benchmark the accuracy of the LBM model, the results are compared by the published results of the same geometry modeled by the finite volume method. It is observed that there are good agreements between the LBM and FVM results for all cases. Moreover, the shares of advection, radiation and conduction terms in energy equation are 0.0024, 0.9974, and 0.0002, respectively, for the last one-third piece of the channel.

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Abbreviations

C :

Speed of light (m s−1)

\(c_{\text{p}}\) :

Specific heat capacity (J kg−1 K−1)

\(c_{k}\) :

Lattice speed (–)

\(c_{\text{s}}\) :

Sound speed (–)

\(e\) :

Discrete particle velocity (–)

\(f\) :

Stream distribution function

\(g\) :

Temperature distribution function

\(G\) :

Incident radiation (W m−2)

\(G^{{ \wedge }}\) :

Dimensionless incident radiation

\(H\) :

Channel height (m)

\(I\) :

Radiation intensity (W m−2 sr−1)

\(k\) :

Thermal conductivity (W m−1 K−1)

\(M\) :

Total number of discrete lattice direction

\(N\) :

Conduction parameter (–)

\(\vec{n}\) :

Outer unit vector normal (–)

\(P\) :

Pressure (Pa)

\(P_{\text{f}}\) :

Scattering phase function

\(Pe\) :

Peclet number (–)

\(Pr\) :

Prandtl number (–)

\(q_{\text{r}}\) :

Dimensionless radiative heat flux (–)

\({\text{RP}}\) :

Radiation parameter (–)

\(Re\) :

Reynolds number (–)

\(\vec{r}\) :

Position vector (m)

s :

Geometric distance (1/s)

\(t\) :

Time (s)

T :

Temperature (K)

\(u\) :

Length velocity (m s−1)

\(U\) :

Dimensionless × velocity (–)

\(v\) :

Height velocity (m s−1)

\(V\) :

Dimensionless y velocity (–)

\(w\) :

Weight coefficient (–)

\(x\) :

Position (m)

\(X\) :

Dimensionless coordinate (–)

\(y\) :

Position (m)

\(Y\) :

Dimensionless coordinate (–)

\(\alpha\) :

Thermal diffusivity coefficient (m2 s−1)

\(\beta\) :

Extinction coefficient (m−1)

\(\Delta t\) :

Lattice time step (–)

\(\Delta x\) :

Mesh spacing (–)

\(\gamma\) :

Polar angle (rad)

\(\delta\) :

Azimuthal angle (rad)

\(\varepsilon\) :

Emissivity coefficient (–)

\(k_{\text{a}}\) :

Absorbing coefficient (–)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\rho\) :

Density (kg m−3)

\(\sigma\) :

Stefan–Boltzmann constant (W k−4 m−2)

\(\sigma_{\text{s}}\) :

Scattering coefficient (m−1)

\(\tau\) :

Dimensionless relaxation time (–)

\(\omega\) :

Scattering albedo (–)

\(\varOmega\) :

Direction \((\delta ,\gamma )\)

\(\Delta \varOmega\) :

Solid angle (sr)

\(\theta\) :

Dimensionless temperature (–)

\(b\) :

Black body (–)

\(i\) :

Discrete velocity direction (–)

w:

Wall (–)

o:

Inter value (–)

m:

Mean value (–)

eq:

Equilibrium (–)

*:

After collision

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, 91775-1111, Mashhad, Iran

    Reza Hosseini & Javad Abolfazli Esfahani

  2. Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran

    Saman Rashidi

Authors
  1. Reza Hosseini
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  2. Saman Rashidi
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  3. Javad Abolfazli Esfahani
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Correspondence to Javad Abolfazli Esfahani.

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Technical Editor: Francis HR Franca.

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Hosseini, R., Rashidi, S. & Esfahani, J.A. A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode. J Braz. Soc. Mech. Sci. Eng. 39, 3695–3706 (2017). https://doi.org/10.1007/s40430-017-0831-8

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  • DOI: https://doi.org/10.1007/s40430-017-0831-8

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