The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell

In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number HS, the modified diffusive ratio NA and the nanoparticle Rayleigh number RN is to quicken the convective motion, while the Lewis number Le has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number Pm is not greater than unity.