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

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Abstract

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.

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Abbreviations

c i :

Lattice velocity

c s :

Speed of sound

K :

Thermal conductivity (W m−1 K−1)

k b :

Boltzmann constant

qr:

Radiation source term

f i :

Particle density distribution function

\(f_{\text{i}}^{\text{eq}}\) :

Equilibrium particle density distribution function

g i :

Particle energy distribution function

\(g_{\text{i}}^{\text{eq}}\) :

Equilibrium particle energy distribution function

g y :

Gravitational acceleration (m s−2)

L :

Length of channel (m)

Num :

Mean Nusselt number

Nuy :

Local Nusselt number (h.x/k)

Pe:

Peclet number (Re.Pr)

Pr:

Prandtel number (υ/α)

Ra:

Rayleigh number (g.β.ΔT.L3/υ.α)

Re:

Reynolds number (u.L/υ)

T h :

Wall temperature (K)

T c :

Internal dimensionless temperature (K)

RP:

Radiation overall parameter

C D :

Drag coefficient

C L :

Lift coefficient

u, v :

Velocity vectors (m s−1)

x, y :

Coordinates (m)

n1, n2 :

Relaxation time constants

α :

Thermal diffusivity (m2 s−1)

µ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

β :

Thermal expansion coefficient (1/K)

τ v :

Relaxation time relating to flow field

τ c :

Relaxation time of temperature field

υ :

Kinematic viscosity (m2 s−1)

θ:

Dimensionless temperature

ΔT :

Temperature difference (K)

i:

Direction of lattice link

t:

Top

b:

Bottom

l:

Left

r:

Right

h:

Hot

D:

Drag

L:

Lift

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

    Mohammad Mohsen Peiravi & Javad Alinejad

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  1. Mohammad Mohsen Peiravi
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Correspondence to Javad Alinejad.

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Peiravi, M.M., Alinejad, J. Hybrid conduction, convection and radiation heat transfer simulation in a channel with rectangular cylinder. J Therm Anal Calorim 140, 2733–2747 (2020). https://doi.org/10.1007/s10973-019-09010-0

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