Citation: Agarwal, V.; Singh, B.;
Kumari, A.; Jamshed, W.; Nisar, K.S.;
Almaliki, A.H.; Zahran, H.Y. Steady
Magnetohydrodynamic Micropolar
Fluid Flow and Heat and Mass
Transfer in Permeable Channel with
Thermal Radiation. Coatings 2022, 12,
11. https://doi.org/10.3390/
coatings12010011
Academic Editor: Rahmat Ellahi
Received: 20 November 2021
Accepted: 15 December 2021
Published: 23 December 2021
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coatings
Article
Steady Magnetohydrodynamic Micropolar Fluid Flow and Heat
and Mass Transfer in Permeable Channel with Thermal Radiation
Vandana Agarwal
1
, Bhupander Singh
2
, Amrita Kumari
3
, Wasim Jamshed
4
, Kottakkaran Sooppy Nisar
5,
* ,
Abdulrazak H. Almaliki
6
and H. Y. Zahran
7,8
1
Department of Computer Application, Raghunath Girl’s (PG) College, Meeru 250001, India;
vandanargmeerut@gmail.com
2
Department of Mathematics, Meerut College, Meerut 250003, India; bhupandersingh1969@yahoo.com
3
Department of Mathematics, AS(PG) College Mawana, Meerut 250001, India; ampanwar@gmail.com
4
Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000,
Pakistan; wasiktk@hotmail.com
5
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University,
Wadi Aldawaser 11991, Saudi Arabia
6
Department of Civil Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944,
Saudi Arabia; a.almaliki@tu.edu.sa
7
Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty
of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; heldemardash@kku.edu.sa
8
Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Metallurgical Lab. 1,
Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt
* Correspondence: n.sooppy@psau.edu.sa
Abstract: The present work is devoted to the study of magnetohydrodynamic micropolar fluid flow
in a permeable channel with thermal radiation. The Rosseland approximation for thermal radiation
is taken into account in the modelling of heat transfer. The governing equations are expressed
in non-dimensional form. The Homotopy Perturbation Method (HPM) is briefly introduced and
applied to derive the solution of nonlinear equations. The effects of various involved parameters
like Reynolds number, microrotation parameter and Prandtl number on flow and heat transfer are
discussed. Further, their effects on Nusselt and Sherwood numbers are also investigated from the
physical point of view. Analytic solutions of the problem are obtained by HPM and a numerical
technique bvp4c package MATLAB is applied to predict the graphs between different parameters.
Keywords: micropolar fluid; permeable channel; homotopy perturbation method; heat transfer;
magnetohydrodynamic; thermal radiation
1. Introduction
From the industrial point of view, the process of heat and mass transfer has a great im-
pact. Many researchers concentrate on this area. In particular, in the metallurgical industry,
an application of heat transfer criterion has been studied with magnetohydrodynamic mi-
cropolar fluid flows. Mohamed and Abo-Dahab [1], Perdikis and Raptis [2] and Raptis [3]
discussed the impact of heat and mass transfer in micropolar and magnetohydrodynamic
micropolar fluid flows in the presence of various characteristics like thermal radiation,
heat generation, and porous media. Seddeek et al. [4] obtained the analytic solution of
the problem leading to the effect of radiation on the flow of a magneto-micropolar fluid
past a continuously moving plate with suction and blowing. El-Arabawy [5] observed
the behaviour of suction and injection in his problem. On the other hand, Sharma and
Gupta [6] studied the effects of porosity and thermal convection on micropolar fluids. The
numerical simulation of the solution of micropolar fluid flows with suction and injection
has been discussed by Subhadra et al. [7], Takhar et al. [8], Kelson and Farrell [9], and
Muhammad et al. [10]. A few years ago, the flows in permeable channels and circular pipes
made a considerable impact, drawing attention to these researchers.
Coatings 2022, 12, 11. https://doi.org/10.3390/coatings12010011 https://www.mdpi.com/journal/coatings