Thermal flux in unsteady Rayleigh-Bénard magnetoconvection

Abstract

We present results of numerical investigation on thermal flux in Rayleigh-Bénard 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 $⟨\mathrm{Nu}(\mathrm{Q})⟩$ decreases logarithmically with Chandrasekhar number for $\mathrm{Q}>{\mathrm{Q}}_c$, which depends on $\mathrm{Ra}$ and $\mathrm{Pr}$. The reduced Nusselt number $\mathrm{N}{\mathrm{u}}_{\mathrm{r}}$ $=$ $⟨\mathrm{Nu}(\mathrm{Q})⟩/⟨\mathrm{Nu}(0)⟩$ rises sharply, reaches a maximum slightly above unity and then start decreasing very slowly to unity as the value of a dimensionless parameter $\sqrt{Ra/(\mathrm{Q}\mathrm{Pr})}$ 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.

11 pages, 10 figures