SAMS Subject Classification Number: 23

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 the minimal truncated double Fourier series which gives rise to the nonlinear Lorenz type equations. A local quasilinearization block hybrid method (LQBHM) is used 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.