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Using lattice Boltzmann method to control entropy generation during conjugate heat transfer of power-law liquids with magnetic field and heat absorption/production

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Abstract

Installation of electronic components in a confined space makes the issue of heat transfer and cooling inside shaped chambers of great importance. Investigation of the entropy generated in the equipment is considered as an important approach in the optimal design of devices in which heat transfer occurs. The innovation of the present work is the modeling of non-uniform magnetic field with heat absorption/production in the determination of the amount of entropy produced arising from conjugate heat transfer of power-law liquid inside the K-shaped cavity that has not been studied. The main variables of this study are Rayleigh number (103 and 105), Hartmann number (0, 15, 30 and 45), heat absorption/production (−7, 0 and +7), thermal conductivity ratio (1, 10 and 50), cavity aspect ratio (0.2, 0.4 and 0.6), type of magnetic field and kind of fluid (Pseudoplastic, Newtonian and Dilatant fluids). The obtained outcomes revealed that: The power of the current and the amount of heat transfer can be controlled by applying magnetic field. Less reduction of the mean Nusselt number and current strength is achieved by applying magnetic field non-uniformly. Enhancement of the heat absorption/production coefficient leads to a decrement of the mean Nusselt number, which this impact increases with augmenting Hartmann number. Enhancement of the cavity aspect ratio reduces the influence of magnetic field, flow strength, mean Nusselt number and entropy produced, which this effect is negligible for dilatant fluid. Heat transfer is a function of the ratio of thermal conductivity and Rayleigh number so that as these two values increase, the influence of enhancement of the Hartmann number is more pronounced. The influence of increment of the Hartmann number on the entropy production: increasing up to 30% in heat production mode and decreasing up to 10% in heat absorption mode. Entropy production increases with increasing Rayleigh number and heat absorption/production coefficient. The influence of magnetic field on entropy production for pseudoplastic fluid is most significant. Generally, the influence of variations thermal conductivity ratio and Hartmann number on the dilatant fluid is insignificant.

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Abbreviations

AR:

Cavity aspect ratio

B:

Magnetic field strength (T)

Be:

Bejan number

c :

Discrete lattice velocity (m s−1)

F :

External force (N)

f:

Density distribution function

feq :

Equilibrium density distribution function

g:

Energy distribution function

geq :

Equilibrium energy distribution function

g :

Gravity force (m s−2)

h:

Magnetic field distribution function

heq :

Equilibrium magnetic field distribution function

H:

Cavity height and length (m)

Ha:

Hartmann number

HAP:

Heat absorption/production

HAPC:

Heat absorption/production coefficient

k:

Thermal conductivity (W m−1 K−1)

MF:

Magnetic field

n:

Power-law index

Nu:

Nusselt number

p:

Pressure (Pa)

Pr:

Prandtl number

Q:

Volumetric heat absorption/production (W K−1)

Ra:

Rayleigh number

S:

Total entropy (kJ kg−1 K−1)

SF :

Entropy production arising from fluid friction (kJ kg−1 K−1)

SM :

Entropy production arising from magnetic field (kJ kg−1 K−1)

SH :

Entropy production arising from heat transfer (kJ kg−1 K−1)

T:

Temperature (K)

TCR:

Thermal conductivity ratio \(\left( {\frac{{{\text{k}}_{{\text{s}}} }}{{{\text{k}}_{{\text{f}}} }}} \right)\)

TMF:

Type of magnetic field

W:

Thickness of conductive wall (m)

u (u, v):

Macroscopic velocities (m s−1)

x(x,y):

Lattice coordinates (m)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

τ * :

Flow field relaxation time

τ ** :

Temperature field relaxation time

τ *** :

Magnetic field relaxation time

υ :

Kinematic viscosity (m2 s−1)

θ:

Dimensionless temperature

ρ :

Density (kg m−3)

µ :

Dynamic viscosity (pa s)

ψ :

Stream function (m2 s−1)

ω :

Weighting factor

c:

Cold

f:

Fluid

h:

Hot

s:

Solid

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

    Mohammad Nemati

  2. School of Mechanical Engineering, Arak University of Technology, Arak, 38181-41167, Iran

    Somayeh Davoodabadi Farahani

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Correspondence to Mohammad Nemati.

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Nemati, M., Farahani, S.D. Using lattice Boltzmann method to control entropy generation during conjugate heat transfer of power-law liquids with magnetic field and heat absorption/production. Comp. Part. Mech. 10, 331–354 (2023). https://doi.org/10.1007/s40571-022-00497-3

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