MAGNETO-CONVECTION IN A VISCOELASTIC FLUID SATURATED DEVELOPING SOLUBLE ANISOTROPIC POROUS MEDIUM
By
Monal Bharty1 , Atul K. Srivastava2 and Hrishikesh Mahato3
1Faculty of Engineering and IT, ARKA JAIN University, Jamshedpur, Jharkhand India-831001
2Department of Mathematics, AIAS, Amity University, Ranchi, Jharkhand India-835303
3Department of Mathematics, Central University of Jharkhand, Ranchi, Jharkhand India-835222
Email: priyabharty58@gmail.com, atulshaswat@gmail.com, hrishikesh.mahato@cuj.ac.in
(Received: July 30, 2024; In format: September 16, 2024; Revised: November 18, 2025; Accepted: December 02, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55212
Abstract
We consider the thermo-solutal magneto-convection in a horizontal anisotropic porous medium, saturated with viscoelastic fluid, which is heated and salted from below. Here, the chemical equilibrium is on the bounding surfaces, and the solubility of the dissolved components depends on temperature. The aim is to determine the criteria for the onset of magneto-convection by finding the critical Rayleigh number and wave number. Also, heat and mass transfer phenomena are captured by studying Nusselt and Sherwood numbers. The extended Darcy model is used to express the momentum equation for Oldroydtype viscoelastic fluid with an externally imposed vertical magnetic field. Due to viscoelastic behaviour of the fluid, the convection is set in through oscillatory rather than stationary. An entire investigation has been done in two parts: (i) linear stability analysis and (ii) weakly non-linear stability analysis. The effect of main controlling parameters, such as the magnetic field parameter (Chandrashekhar number Q), viscoelastic parameters (relaxation (λ1) and retardation (λ2) parameters), and effective chemical reaction (i.e. Damk'ö'hler number, (χ)), on the stability of the system are investigated. Q, λ2 are found to delay the oscillatory convection whereas λ1 and χ speed up the onset of oscillatory convection. The non-linear theory based on the truncated representation of the Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motion. The effect of the above-mentioned parameters on heat and mass transfer is also discussed.
2020 Mathematical Sciences Classification: 12E20; 94A60
Keywords and Phrases: Anisotropy porous medium, Darcy model, external Magnetic field, Rayleigh Number, Chemical reaction, Viscoelastic fluid.