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Lattice Boltzmann method to study free convection and entropy generation of power-law fluids under influence of magnetic field and heat absorption/generation

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Abstract

The aim of this present work assesses heat transfer and entropy generation arising from free convection of power-law fluids in a trapezoidal chamber under the effect of uniform and non-uniform magnetic field with heat absorption/generation by using LBM. The impact of Rayleigh number (103, 104 and 105), wall slope (11.5°, 26.5° and 38.5°), power-law index (0.75, 1.0 and 1.25), Hartmann number (0, 15, 30 and 45), type of magnetic field applied (uniform and non-uniform) with heat absorption/generation (− 10, − 5, 0, + 5 and + 10) on fluid flow and heat transfer characteristics has been evaluated. By enhancement of the Rayleigh number and decreasing wall slope of the chamber, the flow strength, the rate of heat transfer and entropy generation increase and the effect of the magnetic field becomes more remarkable. By applying a magnetic field non-uniformly, the flow strength and heat transfer rate can be grown to about 25% and 15%, respectively. At higher Hartmann and Rayleigh numbers, the effect of changing the type of magnetic field applied is more notable. By increasing the heat absorption/generation coefficient, the average Nusselt number decreases and the effect of the magnetic field increases. In the heat generation mode, the total entropy generation increases with increasing Hartmann number, while in the heat absorption mode, the opposite effect was obvious. A salient and distinctive feature of the present work compared to previous studies is the application of non-uniform magnetic field (specific type of application) in the presence of heat absorption/generation for non-Newtonian fluids, which is not researched.

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Abbreviations

B :

Magnetic field strength/T

Be:

Bejan number

c :

Discrete particle speeds for D2Q9/m s−1

C p :

Specific heat at constant pressure/kJ kg−1 K−1

f :

Density distribution function

f eq :

Functions of density distribution/kg m−3

F :

External force/N

g :

Energy distribution function/K

g eq :

Equilibrium energy distribution function/K

g :

Acceleration of gravity/m s−2

h :

Function of magnetic field distribution/T

h eq :

Magnetic field equilibrium function/T

Ha:

Hartmann number

k :

Thermal conductivity/W m−1 K−1

L :

Length and height of the chamber/m

q :

Dimensionless heat absorption/generation coefficient

Ra:

Rayleigh number

S :

Entropy generation/kJ kg−1 K−1

S F :

Entropy generation arising from fluid friction/kJ kg−1 K−1

S M :

Entropy generation arising from magnetic field/kJ kg−1 K−1

S T :

Entropy generation arising from heat transfer/kJ kg−1 K−1

T :

Temperature/K

TMFA:

Type of magnetic field applied

u (u,v):

Velocity components/m s−1

x (x,y):

Cartesian coordinates/m

α :

Thermal diffusivity/m2 s−1

β :

Thermal expansion coefficient/K−1

\(\tau_{\rm f}\) :

Lattice relaxation time for the flow field

\(\tau_{\rm g}\) :

Lattice relaxation time for the temperature field

\(\tau_{\rm h}\) :

Lattice relaxation time for the magnetic field

ρ :

Density/kg m−3

υ :

Kinematic viscosity/m2 s−1

µ :

Dynamic viscosity/pa s

φ :

Slope of the wall/Degrees

θ :

Dimensionless temperature

γ :

Shear rate/s−1

η :

Magnetic resistivity

ψ :

Stream function/m2 s−1

ω :

Weighting factor

c:

Cold

h:

Hot

i:

Move direction of single particle

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Authors and Affiliations

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

    Mohammad Nemati & Mohammad Sefid

  2. Department of Nutrition, Cihan University-Erbil, Kurdistan Region, Iraq

    S. Mohammad Sajadi

  3. Department of Phytochemistry, SRC, Soran University, KRG, Iraq

    S. Mohammad Sajadi

  4. Department of Chemical and Process Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia (UKM), 43600, Bangi, Selangor, Malaysia

    Ferial Ghaemi

  5. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  6. Institute of Space Sciences, Magurele, Romania

    Dumitru Baleanu

  7. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Dumitru Baleanu

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  1. Mohammad Nemati
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  2. Mohammad Sefid
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  3. S. Mohammad Sajadi
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  4. Ferial Ghaemi
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  5. Dumitru Baleanu
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Nemati, M., Sefid, M., Mohammad Sajadi, S. et al. Lattice Boltzmann method to study free convection and entropy generation of power-law fluids under influence of magnetic field and heat absorption/generation. J Therm Anal Calorim 147, 10569–10594 (2022). https://doi.org/10.1007/s10973-022-11271-1

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