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Heat transfer effects on electro-magnetohydrodynamic Carreau fluid flow between two micro-parallel plates with Darcy–Brinkman–Forchheimer medium

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Abstract

This article deals with heat transfer analysis on the Electro-magnetohydrodynamic Carreau fluid flow through a pair of rectangular plates. A Darcy–Brinkman–Forchheimer medium is considered for physical modeling. The flow is induced due to the Lorentz force, which occurs owing to the presence of an extrinsic imposed magnetic and electric field. The solutions are obtained with the help of numerical and semi-analytical/numerical schemes. A differential transform method (DTM) is employed to resolve the nonlinear coupled differential equations. The obtained solutions are discussed and plotted against all the physical parameters, and the Nusselt number is also addressed with the help of the table. The present outcomes are also plotted for the Newtonian fluid model as a particular case. The comparison of DTM is presented with a numerical shooting method for the Nusselt number. It is concluded from the analogy that the DTM method is very adaptive and stable to solve the nonlinear differential equations.

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  • 12 January 2021

    Journal abbreviated title on top of the page has been corrected to “Arch Appl Mech”

Abbreviations

\({\mathbf{E}}\) :

Electric fields

\({\mathbf{B}}\) :

Magnetic field

\(\bar{y},\bar{x},\bar{z}\) :

Rectangular coordinate system

\(l\) :

Microchannel length

\(w\) :

Width

\(2H\) :

Height

\({\mathbf{v}}\) :

Velocity vector

\({\mathbf{F}}\) :

Body force

\(\zeta\) :

Stress tensor

\(p\) :

Pressure

\(k\) :

Porosity parameter

\(c_{\text{F}}\) :

Forchheimer coefficient

\(\rho\) :

Density

\(\bar{t}\) :

Time

\(\lambda\) :

Relaxation time

\(\dot{\gamma }\) :

Second invariant tensor

\(\mu\) :

Dynamic viscosity

\(n\) :

Power-law index

\(\tilde{\mu }_{\inf }\) :

Viscosity at infinite shear rate

\(\sigma\) :

Electrical conductivity

\({\mathbf{j}}\) :

Local ion current density

\(T\) :

Temperature

\(c\) :

Specific heat

\(h_{\text{f}}\) :

Heat flux vector

\(\upsilon\) :

Kinematic viscosity

\({\text{Ha}}\) :

Hartmann number

\(H_{1}\) :

Electrical strength

\({\text{We}}\) :

Weissenberg number

\(k_{1}\) :

Dimensionless porosity parameter

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

Forchheimer number

\(N_{\text{n}}\) :

Nusselt number

\(T_{\text{s}} ,T_{\text{m}}\) :

Surface and mean temperatures

\(h_{\text{s}}\) :

Constant heat flux at the wall

\(B_{\text{m}}\) :

Brinkman number

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Acknowledgments

M. M. Bhatti was supported by the Cultivation Project of Young and Innovative Talents in Universities of Shandong Province [Nonlinear Sciences Research Team].

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Muhammad Mubashir Bhatti & Chaudry Masood Khalique

  2. International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho, 2735, South Africa

    Muhammad Mubashir Bhatti, Lehlohonolo Phali & Chaudry Masood Khalique

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Bhatti, M.M., Phali, L. & Khalique, C.M. Heat transfer effects on electro-magnetohydrodynamic Carreau fluid flow between two micro-parallel plates with Darcy–Brinkman–Forchheimer medium. Arch Appl Mech 91, 1683–1695 (2021). https://doi.org/10.1007/s00419-020-01847-4

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