International Journal of Applied Mathematics, Computational Science and Systems Engineering
E-ISSN: 2766-9823
Volume 6, 2024
Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition
Authors: , ,
Abstract: The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), Γ (non dimensional inter phase heat transfer coefficient), λ1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, Γ and λ2 stabilize the system in oscillatory case while λ1 destabilize the system. Furthermore ξ (mechanical anisotropic parameter), $$η_s$$ (thermal anisotropic parameter for solid phase), destabilizes the system and ηf (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, λ1, λ2,Γ, ξ, $$η_f$$ and $$η_s$$ on heat transfer is also examined.
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Keywords: Extended Darcy model, An external vertical magnetic field, Rayleigh Number, Viscoelastic fluid, LTNE, Porous medium
Pages: 144-159
DOI: 10.37394/232026.2024.6.13