Natural convection heat transfer utilizing nanofluid in a cavity with a periodic side-wall temperature in the presence of a magnetic field

Natural convection in a square cavity filled with electrically conducting nanofluid that is driven by a periodic temperature profile along on of the vertical wall is studied numerically. The top and bottom horizontal walls are kept adiabatic. The right wall is maintained at low temperature while the temperature of the opposing vertical wall varies sinusoidally with time about a mean temperature. Flow and heat transfer performance through the enclosure is examined over a wide range of oscillation amplitudes and frequencies, Hartmann number, Rayleigh number and solid volume fraction at Prandtl number Pr = 6.2. The results show that oscillation amplitude, A, and frequency, f, of the vertical wall significantly affect the response of heat transfer inside the cavity. For A > 0.5, the forcing frequency is found to remain almost constant at f = 2.5, while it shifts towards a higher frequency f = 5 for A <= 0.5. At low Rayleigh number, Nusselt number is found to be independent of Rayleigh and Hartman numbers, while at higher Rayleigh number, convective flow dominates, and Nusselt number becomes independent of Hartmann number. In this regime, the Nusselt scaling with Rayleigh number agrees well with the exponent predicted by theory of natural convection in a cavity without magnetic field or nanoparticles, with a value of 1/4. With the increase of solid volume fraction, the heat transfer rate may increase or decrease depending on the values of Hartmann and Rayleigh numbers.