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Lattice Boltzmann method’s ability to calculate entropy during MHD non-Newtonian ferrofluid-free convection under volumetric radiation and heat generation/absorption

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Abstract

The capability of LBM in the determination of entropy during power-law ferrofluid-free convection in the presence of effective factors is depicted in this research. Uniform absorption/production of heat and magnetic field in different types/angles affects the current inside a 2D chamber. Evaluation of the influence of thermal radiation through modeling with three separate distribution functions on the characteristics of the flow within the chamber with variable aspect ratio under various internal and external factors is among the features of this research, which has not been inquired so far. Application in the design of electronic coolers and solar collectors is one of the practical cases of this numerical evaluation. According to the results, the improvement in heat transfer due to the imposition of radiation on the system is more evident for fluid with higher viscosity. The enhancement of the power-law coefficient, further reducing the average Nusselt number value, diminishes the effectiveness of the magnetic field in reducing the entropy and the heat transfer rate. It is possible to achieve the current strength and the mean Nusselt value up to 40% and 61% more, respectively, by exerting a vertical magnetic field in a non-uniform type. Although for the generation of heat, there will be the lowest value of the thermal performance index and the average Nusselt number value, the greatest influence of the magnetic field is observed. The effectiveness of the addition of nanoparticles on the system thermal characteristics is more evident in cases where the conductivity effects are greater, such as the strong presence of the magnetic field in the high viscosities of the fluid. One of the effective ways to reduce the effect of the phenomenon of heat absorption/production is exposing the system to the shear thickening fluid. With this action, the changes in the average Nusselt number value for increasing the value of the heat absorption/generation parameter is about 59% lower than when a shear thinning fluid is considered. By designing the chamber in a smaller aspect ratio, in addition to enhancing the thermal performance system index, it is also feasible to decline the Bejan number.

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Abbreviations

∆:

Heat absorption/production index in dimensionless form

\(\beta_{{\text{R}}}\) :

Mean absorption coefficient (m−1)

λ :

Magnetic field angle (°)

\(\varepsilon\) :

Emissivity of radiative wall

θ :

Dimensionless temperature

φ :

The percentage of nanoparticles

ζ :

Chamber aspect ratio

\(\gamma\) :

Shear rate (s−1)

\(\tau\) :

Stress (pa)

\(\upsilon\) :

Kinematic viscosity (m2 s−1)

\(\mu\) :

Dynamic viscosity (Pa s)

ω :

Weighting factor

Ψ :

Stream function

B :

Strength of magnetic field (T)

Be:

The Bejan number

c :

Discrete velocity

f :

Distribution function related to the density field

F :

External force (Pa m2)

h :

Distribution function related to the energy field

H :

Dimensions (length and height) of the chamber (m)

Ha:

The Hartmann number

I :

Distribution function related to the radiation

MFT:

Magnetic field type

n :

Coefficient of power-law

Nu:

The Nusselt number

p :

Pressure (Pa)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{Q}\) :

Volumetric heat absorption/production index (W m−3)

\(q_{{\text{R}}}\) :

Volumetric radiation (W m−3)

Ra:

The Rayleigh number

RP:

Radiation parameter

S :

Total entropy (W K−1)

T :

Temperature (K)

TPI:

Coefficient of thermal performance

u/v :

Horizontal/vertical velocity (m s−1)

x/y :

Horizontal/vertical coordinate (m)

b:

Repeating variable

BF:

Base fluid

cold:

The lowest system temperature

eq:

Equilibrium

ff:

Fluid friction

hot:

The highest system temperature

ht:

Heat transfer

i:

Lattice direction

mf:

Magnetic field

NF:

Nanofluid

NP:

Nanoparticle

R:

Radiative

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Authors and Affiliations

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

    Mohammad Nemati & Mohammad Sefid

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

    D. Toghraie

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  1. Mohammad Nemati
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  2. Mohammad Sefid
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  3. D. Toghraie
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Correspondence to D. Toghraie.

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Nemati, M., Sefid, M. & Toghraie, D. Lattice Boltzmann method’s ability to calculate entropy during MHD non-Newtonian ferrofluid-free convection under volumetric radiation and heat generation/absorption. J Therm Anal Calorim 149, 3759–3779 (2024). https://doi.org/10.1007/s10973-024-12916-z

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