Effect of three types of magnetic field modulation on the instability of heat transfer in micropolar nanofluid filled within Hele-Shaw cell

Abstract

This article investigates the impact of three different types of magnetic field modulation on the instability of micropolar nanofluid filled within Hele-Shaw cells applying both nonlinear and linear approaches. The truncated Fourier series approach is used to analyze nonlinear stability, while the analytical evaluation of linear stability is performed using the normal mode methodology. All the results are graphically demonstrated. Based on the outcomes, the micropolar parameter, magnetic Chandrasekhar number, Hele-Shaw number, and the coefficient of coupling between vorticity and spin effect have stabilized effects in the system. As opposed to that, nanoparticle Rayleigh number accelerate the start of convective motion inside the system. Some parameters play a significant influence in the transport of heat and mass in nonlinear analysis. The Hele-Shaw number, micropolar parameter, magnetic Prandtl number, and magnetic Chandrasekhar number perform a major contribution to the heat/mass transfer in the system. Using two different approaches, the system’s heat and mass transmission are investigated, the Runge–Kutta–Fehlberg method and Mathematica NDSolve, and It has been found that the rate of heat/mass transfer in both conditions is exactly the same. Moreover, It has been found that heat and mass transmission start earliest in the case of triangle waveforms as compared to other types of magnetic field modulations.