Visualization and analysis of magnetothermal convection of paramagnetic liquid in the Rayleigh-Benard model

Abstract

We examined the heat transfer of magnetothermal convection in a Rayleigh-Benard model (height 9.2 mm, vessel diameter 20 mm, aspect ratio 2.17). The working fluid was an aqueous gadolinium nitrate solution of 0.15 mol/kg ($\mathrm{pH}=4.52$ at 305.5 K, paramagnetic substance). Not only the magnetic body force but also the temperature dependence of paramagnetic susceptibility according to Curie's law provides the driving body force of convection and exerts a decisive influence over the heat transfer performance. The visual observation of the isothermal contour of convection was realized by the addition of a thermochromic liquid crystal (TLC). Using a large upward magnetic body force, i.e., $(\stackrel{P\vec}{b}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{\ensuremath{\nabla}})\phantom{\rule{0.16em}{0ex}}{b}_{z}=83.31\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{2}/\mathrm{m}$ at the vessel center, we succeeded in visualizing the horizontal isothermal illuminant of the TLC, which revealed the realization of a quasiweightless condition in the Rayleigh-Benard model. The heat transfer on convection was analyzed by the method of Churchill and Ozoe. Its performance was enhanced by the downward magnetic body force and was suppressed by the upward magnetic body force, as compared with Rayleigh-Benard convection. The convective flows in the experiment ($\mathrm{Prandtl}\phantom{\rule{0.16em}{0ex}}\mathrm{number}=5.17$, $\mathrm{Ra}=1.53\ifmmode\times\else\texttimes\fi{}1{0}^{5}$, aspect ratio 2.0) were numerically simulated by three-dimensional computation. All the experimental and numerical results were arranged by Rayleigh number (Ra) and Nusselt number (Nu). In addition, we introduced the magnetic Rayleigh number (${\mathrm{Ra}}_{\mathrm{m}}$) instead of Ra. The results of Nu plotted versus the ${\mathrm{Ra}}_{\mathrm{m}}$ were closely distributed in the vicinity of the Silveston curve. This relationship reveals that the heat transfer on magnetothermal convection is controlled by the use of ${\mathrm{Ra}}_{\mathrm{m}}$.