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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Exploring MHD Free Convection in a Vertical Channel: Analytical and Numerical Solutions for Oldroyd-B Fluids and Temperature Driven Walls

Journal of Applied Nonlinear Dynamics 15(4) (2026) 805--826 | DOI:10.5890/JAND.2026.12.003

Lipika Panigrahi$^{1}$, Shankar Rao Munjam$^{2}$, J. P. Panda$^{3}$, G. C. Dash$^{4}$

$^{1}$ Department of Mathematics, C. V. Raman Global University Bhubaneswar, Odisha, India

$^{2}$ School of Technology, Woxsen University, Hyderabad-502345. Telangana, India

$^{3}$ Department of Mathematics, Veer Surendra Sai University of Technology,Burla, Orissa-768018, India

$^{4}$ Department of Mathematics, Siksha 'O' Anusandhan (Deemed to be University), Bhubaneswar, Orissa-751003, India

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Abstract

We derived an approximate analytical solution of the coupled highly nonlinear equation by a newly proposed method of directly defined inverse mapping (MDDiM) and analytically by Cardan's method to the boundary value problem bringing out the effects of important parameters. Then we considered the hydromagnetic flow of Oldroyd-B Model, (an experimentally supported realistic fluid model) through a vertical channel with both electrically conducting and non-conducting walls having asymmetric wall temperatures. The viscoelastic flow subjected to the transverse magnetic field with Hall current and induced magnetic field (IMF) considered. Subsequently, for engineering interest, the skin friction, mass flux and induced current density for relevant parameters were analyzed. The Mathematica 10.0 software is used for plotting graphs and tables. The novel findings reported here in may be useful in the design of heat ex-changers. There exists a threshold value of the Hall parameter when it is exceeded, flow reversal occurs; the primary as well as magnitude of secondary velocity increase with the higher values of stress relaxation time; the effects of strain retardation time on velocity component and It is seen that the Hall current enhances the velocity at all points in the flow domain, whereas, the Hartman number reduces it, it is revealed that the secondary velocity profile has an inverted structure with a sharp increase in magnitude of $u_{y} $ for an increase in Hall current, whereas in the case of primary velocity, no flow reversal is marked. An opposite effect is marked with reference to stress relaxation time.

Acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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