Study of Thermal Instability in Magneto-Convection Nanoliquid Confined within Hele-Shaw Cell Under Three Types of Thermal/Gravity Modulation

In the present paper, we investigate a thermal instability of magneto-convection in an electrically conducting nanoliquid confined within Hele-Shaw cell, subjected to an applied time-periodic boundary thermal (ATBT) or gravitational modulation (ATGM), and surrounded by a constant vertical magnetic field. A steady portion and a time-dependent oscillatory portion constitute the temperature gradient seen between liquid layer's walls in the context of ATBT. In this scenario, both walls' temperatures are modulated. The liquid layer oscillation can be used to realise the externally applied time periodic component of the gravity field that is present in the ATGM problem. The perturbation is described in terms of the power series of the assumed-small convective amplitude. The impact of modulations on heat/mass transfer are examined utilising Ginzburg-Landau (GBL) approach. The impact of different parameters on the transportation of mass and heat is also explored. Additionally, we observe that gravitational modulation is very much effective than thermal modulation. Lewis-number, modified-diffusivity ratio and concentration Rayleigh-number increase heat and mass transport in the system.