Thermal instability in electrically conducting nanoliquid filled in Hele-Shaw cell under 3-types of rotational-speed modulation with impact of through-flow and magnetic-field

Due to the great significance of rotational-speed modulation in various areas of science and technology as well as in day-to-day life, our aim, in this study, is to perform linear/nonlinear studies to examine the impacts of sinusoidal like sine waveform and non-sinusoidal like square and triangular waveforms of rotational-speed modulation in nanoliquid (electrically-conducting) filled within a Hele-Shaw cell with through-flow and magnetic-field. The applied rotational-speed modulation has periodic components that are both constant and time-dependent and changes sinusoidally over time. The linear analysis is done using Galerkin's approach while the nonlinear analysis is done using truncated Fourier series method. The results of Mathematica's built-in NDSolve tool are validated using the Runge-Kutta-Fehlberg technique. Hele-Shaw num-ber, Taylor-number, nanoliquid magnetic number and frequency of rotational-speed modulation have a stabilising impact on the system, whereas through-flow, magnetic Prandtl-number, nanoliquid Prandtl-number and amplitude of rotational-speed modulation have destabilising impact on the system. Additionally, it has been found that rotational-speed modulation can be utilised to efficiently increase or decrease heat and mass movement. Square-waveform is most efficient for both heat and mass transport in compression of sinusoidal and triangular waveforms.