Numerical simulation of unsteady MHD natural convection of CNT-water nanofluid in square cavity heated sinusoidally from below

Numerical unsteady natural convection flow in a square cavity in the presence of uniform magnetic field is investigated. The cavity is filled with CNT-water nanofluid and heated from below with sinusoidal temperature distribution. This study has been conducted for the certain pertinent parameters of Rayleigh number Ra, Hartmann number Ha and the CNT volume fraction from ??=?0 to 0.12. The results indicate, that for large values of Ha, increasing ? results in an increase of the normalized average Nusselt number. The rate corresponding to CNT- volume fraction nanoparticles of 10% ensures an enhancement about 50% of the heat transfer rate compared to the standard case. The flow undergoes a period bifurcation at a Rayleigh number beyond the value 10(6). A critical Rayleigh number Ra-c of 1.077???10(6) is then computed. Finally, a correlation giving the average Nusselt number as a function of the frequency of the periodic regime is established.