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Heat transfer across the dynamics of water conveying alumina nanoparticles subject to Lorentz force in a rectangular cavity with various aspect ratios

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Abstract

Heat transfer in cavities under the influence of magnetic field is very important in industry. The effect of the presence of a magnetic field on the behavior of heat transfer in closed cavities (electrical transformers) is inevitable, which is addressed in this research. The present study is about the heat transfer of water/alumina nanofluid in a rectangular cavity. The cavity has two insulated walls in front of each other, a constant temperature warm wall at an angle of zero with the horizontal and a constant temperature cold wall. A constant magnetic force with Hartmann number of Ha = 0–45 is applied, which has a zero angle with respect to the horizontal line. The Rayleigh number is Ra = 105, and the problem is solved for various length-to-width cavity aspect ratios of AR = 1–6. In this paper, the solution method uses a finite volume discretization with a pressure-based and segregated algorithm. Results revealed that for AR = 1, the temperature contours have a decreasing trend from top to bottom, as it experiences the maximum and minimum temperatures near the warm and cold walls. For this aspect ratio, the minimum dimensionless temperature occurs at the dimensionless position of X = 0.7–0.8 for various Hartmann numbers, which also coincides with the maximum Nusselt number. For the aspect ratio of AR = 2, increasing the magnetic force results in a higher Lorentz force, which opposes the buoyancy force, reducing the local Nusselt number. However, for AR = 4, increasing the magnetic force creates straight isothermal lines. For this aspect ratio, the isothermal lines are close to each other near the warm wall at two points of X = 0.3 and 0.7, with a slight temperature difference, thereby maximizing the Nusselt number. For AR = 6 and all Hartmann numbers, the Nusselt number is maximum at two points of X = 0.34 and 0.65, while the minimum is located at X = 0.2, 0.5, and 0.8.

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Abbreviations

\(T_{c}\) :

Cold surface temperature/K

\(T_{\text{h}}\) :

Warm surface temperature/K

L :

Length scale/m

H :

Distance between the cold and warm walls/m

G :

Acceleration of gravity/ms−2

T :

Fluid temperature/K

X, Y :

Cartesian coordinates/Dimensionless

U :

Velocity in the x-direction/Dimensionless

V :

Velocity in the y-direction/Dimensionless

\({\text{B}}_{0}\) :

Applied magnetic field/T

B :

Induced magnetic field/T

\({\text{Re}}_{{\text{m}}}\) :

Magnetic Reynolds number/Dimensionless

Ha:

Hartmann number/Dimensionless

AR:

Cavity aspect ratio

β :

Coefficient of thermal expansion/K−1

P :

Pressure/Dimensionless

\(Q\) :

Heat transfer/W

H :

Convective heat transfer coefficient/Wm−2 K−1

A :

Heat transfer surface area/m2

L :

Distance between two insulated walls/m

k :

Thermal conduction coefficient/Wm−1 K−1

\(C_{\text{p}}\) :

Constant pressure specific heat/JKg−1 K−1

x, y :

Cartesian coordinates/m

\(U\) :

Fluid velocity in the x-direction/ms−1

V :

Fluid velocity in the y-direction/ms−1

J:

Electric current density/ Am−2

\( F_{{\text{L}}} \) :

Lorentz force/N

Gr:

Grashof number/Dimensionless

Nu:

Grashof number/Dimensionless

Pr:

Prandtl number/Dimensionless

P :

Pressure/Pa

E :

Electric field/V

β :

Coefficient of thermal expansion/K−1

\(\mu_{0}\) :

Magnetic permeability coefficient/NA−2

\(\rho\) :

Fluid density/Kgm−3

\(\psi\) :

Stream function

\({\Psi }\) :

Stream function/Dimensionless

\(\sigma\) :

Fluid’s electrical conduction coefficient/Ωm−1

\(\mu\) :

Dynamic viscosity/Pas−1

\(\vartheta\) :

Kinematic viscosity/m2s−1

\(\alpha\) :

Thermal diffusivity coefficient/m2s−1

\(\theta\) :

Temperature/Dimensionless

H:

Hot

Nf:

Nanofluid

C :

Cold

F :

Fluid

P :

Nanoparticles properties

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Sayed Hamid Bahreini, Mohsen Saghafian & Omid Ali Akbari

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  1. Sayed Hamid Bahreini
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Correspondence to Mohsen Saghafian.

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Bahreini, S.H., Saghafian, M. & Akbari, O.A. Heat transfer across the dynamics of water conveying alumina nanoparticles subject to Lorentz force in a rectangular cavity with various aspect ratios. J Therm Anal Calorim 148, 2251–2264 (2023). https://doi.org/10.1007/s10973-022-11902-7

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