Hydromagnetic Thermosolutal Instability of an Oldroyd Nanofluid in a Porous Medium

Abstract

The onset of double-diffusive convection of an Oldroyd nanofluid fluid saturated in a porous medium, heated and soluted from below, is examined both analytically and numerically under the linear stability analysis in the presence of a horizontal magnetic field and physically realistic boundary condition on the volume fraction of nanoparticles. The resulting eigenvalue problem is solved numerically by employing Galerkin method. We recover the important works of Umavathi and Prathap Kumar (J. C. Umavathi and J. Prathap Kumar, J. Heat Transfer 139, 012401 (2017)), Jaimala et al. (R. Jaimala, Singh, and V. K. Tyagi, Int. J. Heat Mass Transfer 111, 451 (2017); Jaimala, R. Singh, and V. K. Tyagi, Int. J. Heat Mass Transfer 125, 290 (2018)) and Kuznetsov and Nield (A. V. Kuznetsov and D. A. Nield, International Journal of Thermal Sciences 77, 126 (2014)) as special cases. The important findings include: (i) the independence of thermal Rayleigh-Darcy number for stationary convection upon relaxation and retardation parameters, (ii) the parameters Rn, Rs, Le, NA and λ1 (absent in case of stationary convection) enhance both the stationary and oscillatory convections and the parameter Q, ε and λ2 (absent in case of stationary convection) delay the occurrence of both convections, (iii) instability first sets in as oscillatory convection and (iv) a number of sufficient conditions for the existence and also for the non-existence of oscillatory convection are obtained analytically but only stated (without proof).