Thermal flux in unsteady Rayleigh-B\'{e}nard magnetoconvection

Abstract

We present results of numerical investigation on thermal flux in Rayleigh-B\'{e}nard magnetoconvection in the presence of a uniform vertical magnetic field. We have studied thermal flux in different viscous fluids with a range of Prandtl number ($0.1 \le \mathrm{Pr} < 6.5$) and a range of Chandrasekhar number ($50 \le \mathrm{Q} \le 2.5 \times 10^4$). The power spectral density of the Nusselt number varies with frequency $f$ approximately as $f^{-2}$. The probability distribution function of the fluctuating part of the Nusselt number is nearly normal distribution with slight asymmetric tails. For a fixed value the Rayleigh number $\mathrm{Ra}$, the time averaged Nusselt number $\langle \mathrm{Nu} (\mathrm{Q})\rangle$ decreases logarithmically with Chandrasekhar number for $\mathrm{Q} > \mathrm{Q}_c$, which depends on $\mathrm{Ra}$ and $\mathrm{Pr}$. The reduced Nusselt number $\mathrm{Nu_r}$ $=$ $\langle \mathrm{Nu}(\mathrm{Q})\rangle/{\langle \mathrm{Nu}(0)\rangle}$ rises sharply, reaches a maximum slightly above unity and then start decreasing very slowly to unity as the value of a dimensionless parameter $\sqrt{\mathrm{Ra/(Q~Pr)}}$ is raised. The probability distribution function of the local thermal flux in the vertical direction is found to be asymmetric and non-Gaussian with a cusp at its maximum.