Effect of Three Types of Magnetic-Field Modulation and Different Shapes of Nanoparticles on the Instability of Nanofluid (Al2O3 + H2O) Saturated Porous Medium with Internal Heating

Abstract

In this article the authors investigate the effect of three different types of magnetic-field modulation namely triangular-wave form, sine-wave form, and square-wave form on the instability of nanofluid (Al2O3 + H2O) saturated porous medium with internal heating. Linear stability analysis is done analytically using the normal mode approach, whereas nonlinear stability analysis is done by using the truncated Fourier series method. We obtained that the internal heating parameter destabilizes the system, whereas Darcy number and magnetic Chandrasekhar number stabilizes the system. The impact of three different shapes (Sphere/Bricks/Cylinder) of nanoparticles over instability is also analyzed, and it is found that the system is most stable for sphericalshaped nanoparticles while least stable for cylindrical-shaped nanoparticles. Mass/heat transfer in the system is analyzed by two different approaches, Mathematica NDSolve and Runge-Kutta-Fehlberg method (RKF-45), and it is found that the rate of mass/heat transfer is exactly the same in both cases. The internal heating and magnetic Chandrasekhar number play a crucial role in the heat/mass transfer in the system. Moreover, it is also noticed that heat and mass transfer start earliest in the case of triangle-waveforms as compared to other types of magnetic-field modulations.