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Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al2O3 free convection in entropy determination

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Abstract

The simultaneous investigation on the parameters affecting the flow of electrically conductive fluids such as volumetric radiation, heat absorption, heat generation, and magnetic field (MF) is very vital due to its existence in various sectors of industry and engineering. The present research focuses on mathematical modeling to simulate the cooling of a hot component through power-law (PL) nanofluid convection flow. The temperature reduction of the hot component inside a two-dimensional (2D) inclined chamber with two different cold wall shapes is evaluated. The formulation of the problem is derived with the lattice Boltzmann method (LBM) by code writing via the FORTRAN language. The variables such as the radiation parameter (0–1), the Hartmann number (0–75), the heat absorption/generation coefficient (−5−5), the fluid behavioral index (0.8–1.2), the Rayleigh number (103–105), the imposed MF angle (0°–90°), the chamber inclination angle (−90°–90°), and the cavity cold wall shape (smooth and curved) are investigated. The findings indicate that the presence of radiation increases the mean Nusselt number value for the shear-thickening, Newtonian, and shear thinning fluids by about 6.2%, 4%, and 2%, respectively. In most cases, the presence of nanoparticles improves the heat transfer (HT) rate, especially in the cases where thermal conduction dominates convection. There is the lowest cooling performance index and MF effect for the cavity placed at an angle of 90°. The application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical research.

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Abbreviations

α :

thermal diffusivity (m2/s)

β R :

mean absorption coefficient (1/m)

ε :

thermal performance index

ε*:

emissivity of radiative wall

σ R :

scattering coefficient

Δ:

dimensionless heat absorption/generation coefficient

λ:

magnetic field angle (°)

Γ:

chamber inclination angle (°)

θ :

dimensionless temperature

φ :

nanoparticle volume concentration

τ :

stress tensor

τ f :

relaxation time for velocity field

τ h :

relaxation time for thermal field

τ R :

relaxation time for radiation

γ :

shear rate tensor (1/s)

ψ:

dimensionless stream function

ω :

weighting coefficient

B :

magnetic field strength (T)

Be :

Bejan number

c :

discrete velocity

f :

distribution function related to velocity field

F :

external force (Pa · m2)

g :

acceleration of gravity (m/s2)

h :

distribution function related to temperature field

H :

length and height of the chamber (m)

Ha :

Hartmann number

I :

distribution function related to radiation

n :

coefficient of power-law fluid

Nu :

Nusselt number

\(\widetilde{Q}\) :

volumetric heat absorption/generation coefficient (W/m3)

q R :

radiative heat flux (W/m3)

Ra :

Rayleigh number

R P :

radiation parameter

S :

entropy (W/K)

T :

temperature (K)

u, v :

velocity components (m/s)

w R :

scattering albedo

x, y :

lattice coordinates (m).

0:

Newtonian fluid

b:

black body

f*:

fluid friction

ht:

heat transfer

i :

lattice direction

mf:

magnetic field

NF:

nanofluid

NP:

nanoparticle

PF:

pure fluid

R:

radiative.

r :

solution step

eq:

equilibrium

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Yazd University, Yazd, 8915818411, Iran

    M. Nemati & M. Sefid

  2. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131, Iran

    A. Karimipour

  3. Faculty of Engineering, Kuwait College of Science and Technology, Doha, 35004, Kuwait

    A. J. Chamkha

Authors
  1. M. Nemati
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  2. M. Sefid
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  3. A. Karimipour
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  4. A. J. Chamkha
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Correspondence to M. Sefid.

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Citation: NEMATI, M., SEFID, M., KARIMIPOUR, A., and CHAMKHA, A. J. Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al2O3 free convection in entropy determination. Applied Mathematics and Mechanics (English Edition), 45(6), 1085–1106 (2024) https://doi.org/10.1007/s10483-024-3117-8

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Nemati, M., Sefid, M., Karimipour, A. et al. Lattice Boltzmann method formulation for simulation of thermal radiation effects on non-Newtonian Al2O3 free convection in entropy determination. Appl. Math. Mech.-Engl. Ed. 45, 1085–1106 (2024). https://doi.org/10.1007/s10483-024-3117-8

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  • DOI: https://doi.org/10.1007/s10483-024-3117-8

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