Hybrid conduction, convection and radiation heat transfer simulation in a channel with rectangular cylinder

  • Mohammad Mohsen Peiravi
  • Javad AlinejadEmail author


The innovation of this study is to investigate the combination effect of thermal radiation and convection in the hybrid heat transfer between solid and fluid in a channel. The lattice Boltzmann method based on the D2Q9 scheme has been utilized for modeling fluid and temperature fields. Streamlines, isotherms, vortices and Nusselt numbers along the wall surfaces have been investigated for different Reynolds numbers (Re = 10, Re = 60, Re = 133.3), Peclet numbers (Pe = 7.1, Pe = 42.6, Pe = 94.7), the emission coefficients (ε = 0.3, ε = 0.7, ε = 1), radiation coefficients (RP = 0.010, RP = 0.015, RP = 0.020) and diffusion coefficients (αs = αf, αs = αf/2, αs = 2αf). The mean Nusselt number (Num) fluctuations have been analyzed for different cases to predict optimal levels of effective factors of this simulation in order to maximize and minimize the heat transfer rate. The results show that by increasing the Reynolds number to Re = 133.3, the maximum average Nusselt number can be changed by more than 9.249 time. Also by increasing the thermal diffusion coefficient to αs = 2αf, the minimum average Nusselt number can be changed by less than − 0.687 time.


Channel internal flow Hybrid heat transfer Lattice Boltzmann method Rectangular cylinder Thermal radiation 

List of symbols


Lattice velocity


Speed of sound


Thermal conductivity (W m−1 K−1)


Boltzmann constant


Radiation source term


Particle density distribution function


Equilibrium particle density distribution function


Particle energy distribution function


Equilibrium particle energy distribution function


Gravitational acceleration (m s−2)


Length of channel (m)


Mean Nusselt number


Local Nusselt number (h.x/k)


Peclet number (Re.Pr)


Prandtel number (υ/α)


Rayleigh number (g.βT.L3/υ.α)


Reynolds number (u.L/υ)


Wall temperature (K)


Internal dimensionless temperature (K)


Radiation overall parameter


Drag coefficient


Lift coefficient

u, v

Velocity vectors (m s−1)

x, y

Coordinates (m)

n1, n2

Relaxation time constants

Greek letters


Thermal diffusivity (m2 s−1)


Dynamic viscosity (kg m−1 s−1)


Density (kg m−3)


Thermal expansion coefficient (1/K)


Relaxation time relating to flow field


Relaxation time of temperature field


Kinematic viscosity (m2 s−1)


Dimensionless temperature


Temperature difference (K)



Direction of lattice link

















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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Sari BranchIslamic Azad UniversitySariIran

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