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Influences of electrical MHD and Hall current on squeezing nanofluid flow inside rotating porous plates with viscous and joule dissipation effects

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Abstract

Nanofluids have the ability to flow smoothly in micro-cavities in addition with scattering of the nanoparticles. Because of the good convection between nanoparticles and the base fluid, nanofluids can achieve a good thermal conductivity. The main advantages of adding nanosize particles with base fluid are to improve the ability of storing heat, effective surface area, heat transmission, collisions and interaction among the nanoparticles. The main aim of this research work is to examine the steady and incompressible nanofluid flow between parallel rotating plates. Viscose and joule dissipation effects are taken into account. To our knowledge, impact of electrical MHD and Hall effect with Cattaneo–Christov heat flux on the squeezing 3-D flow nanofluid between parallel rotating plates are not examined yet. Heat in the form of Cattaneo–Christov heat flux is applied. We used similarity transformations to transform the primary equations to a system of ordinary differential equations (ODEs). These ODEs are then solved through the standard procedure of homotopy analysis technique. The skin friction and Nusselt number are numerically tabulated under the influence of some focused parameters. The effects produced by different parameters on the velocity (components) and temperature profiles are graphically depicted and explained in a bit detail.

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Abbreviations

\(A_{1},A_{2},A_{3},A_{4}\) :

Nanofluid constants

\(\hbox{Nu}_{{\mathrm{x}}}\) :

Local Nusselt number

\(\hbox{Re}_{{\mathrm{x}}}\) :

Local Reynolds number \(\delta\) Suction parameter

\(\gamma\) :

Thermal relaxation parameter

\(C_{{\mathrm{f}}}\) :

Skin friction coefficient

\(\rho\) :

Density (\(\hbox{kg}\,\hbox{m}^{-3}\))

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

Specific heat (\(\hbox{J}\,{\hbox{kg}^{-1}\,\hbox{K}^{-1}}\))

\(f, g, \theta\) :

Dimensionless velocities

\(\sigma _{{\mathrm{nf}}}\) :

Electrical conductivity of nanofluid

\(k^{\star }\) :

Mean absorption coefficient

\(k_{{\mathrm{nf}}}\) :

Nanofluid thermal conductivity

\(E_{{\mathrm{I}}}\) :

Electric field parameter

\(\alpha\) :

Rotation parameter

\(\kappa\) :

Vortex viscosity

\(\lambda\) :

Heat flux relaxation

\(\mu _{{\mathrm{f}}}\) :

Base fluid dynamic viscosity

\(\infty\) :

Condition at infinity

x, y and z :

Coordinates m

B :

Magnetic parameter T

\(P_{{\mathrm{r}}}\) :

Prandtl number

\(\beta\) :

Squeezing parameter

\(U_{{\mathrm{w}}}\) :

Stretching velocity (\(\hbox{m}\,\hbox{s}^{-1}\))

T :

Fluid temperature (K)

\(\mu\) :

Dynamic viscosity (mPa)

E :

Electric field (\(\hbox{N}\,\hbox{C}^{-1}\))

t :

Time (s)

M :

Magnetic parameter Teslas

\(E_{{\mathrm{c}}}\) :

Eckert numbers

\(k_{{\mathrm{f}}}\) :

Base fluid thermal conductivity

m :

Hall parameters

\(\varphi\) :

volume fraction

\(\zeta\) :

Independent variable

S :

Suction injection parameter

\(\mu _{{\mathrm{nf}}}\) :

Nanofluid fluid dynamic viscosity

0:

Reference condition

\(B_{0}\) :

Magnetic field strength

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Acknowledgements

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah under grant no. (RG-85-130-38). The authors, therefore, acknowledge with thanks DSR for technical and financial support.

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Authors and Affiliations

  1. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Zahir Shah

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    Ebraheem O. Alzahrani & Malik Zaka Ullah

  3. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, P. O. Box 80221, Jeddah, 21589, Saudi Arabia

    Wajdi Alghamdi

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  1. Zahir Shah
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  2. Ebraheem O. Alzahrani
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  4. Malik Zaka Ullah
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Correspondence to Zahir Shah.

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Shah, Z., Alzahrani, E.O., Alghamdi, W. et al. Influences of electrical MHD and Hall current on squeezing nanofluid flow inside rotating porous plates with viscous and joule dissipation effects. J Therm Anal Calorim 140, 1215–1227 (2020). https://doi.org/10.1007/s10973-019-09176-7

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