A numerical study of double-diffusive convection in the anisotropic porous layer under rotational modulation with internal heat generation

Abstract

Double-diffusive convection in a non-uniformly rotating anisotropic fluid layer with internal heating is investigated. The normal mode technique is used to obtain the critical stationary and oscillatory Rayleigh numbers. The analysis for the nonlinear case is based on minimal truncated double Fourier series which gives rise to the nonlinear Lorenz type equations. A local quasilinearization block hybrid method (LQBHM) is employed to solve the coupled nonlinear Lorenz type equations. The solution obtained using this method is compared with solutions obtained using the ode45 solver. The numerical results indicate that the LQBHM is accurate, efficient, and flexible. A weakly nonlinear analysis is used to investigate the rate of heat and mass transfer in the fluid system. The effects of time varying rotation, internal heat generation, anisotropy parameters, concentration Rayleigh, Vadasz, and Lewis numbers on the heat and mass transfer are shown graphically. Among other results, the quantitative relationships for rotational modulation amplitude and internal heat generation are [Nu/Sh]δ1=0.2<<[Nu/Sh]δ1=1.1 and [Nu/Sh]Ri=5<<[Nu/Sh]Ri=30 respectively. Therefore, modulation amplitude and internal heating have been found to enhance the rate of heat mass transfer hence advancing the onset of thermal convection in the system.