Ultrasound Doppler velocimetry study of magnetoconvection on the heated vertical flat plate at low Hartmann number

Using Ultrasound Doppler Velocimetry (UDV), magnetoconvection on a heated vertical flat plate is investigated with and without the influence of a transverse applied magnetic field, created by two strong permanent magnets placed sidewise to the plate. The relative positions of the two magnets lead to a configuration wherein the resultant magnetic field is in a direction that is normal to the temperature gradient field as well as to the flow. The working fluid is an aqueous salt solution ($\mathrm{NaCl}$ concentration of 5 % by weight) prepared in de-ionized water. In the measurement region, a quasi-uniform magnetic field distribution of 281 $\mathrm{mT}$ was obtained with the magnets in a custom-built magnet holder. COMSOL-based simulations were carried out for the experimental configuration to confirm the magnetic field distribution. To the best of our knowledge, the present study is the first attempt to successfully demonstrate the use of UDV for the non-intrusive mapping of the velocity boundary layer (VBL) in the vicinity of the heated flat plate, under a transverse magnetic field for a $Pr>1$ fluid. Simultaneously, a thermal probe (k-type thermocouple) is used to obtain the temperature profile inside the boundary layers. Measurements are carried out for a range of temperature differences ($\Delta T$ = 5, 10, and 15 °C), corresponding to Rayleigh numbers (Ra) between 5.22 × 10⁷ to 2.11 × 10⁸, and Hartmann number ($\mathrm{Ha}$) of $2.3$. Experimental observations reveal the maximum velocity near the hot wall and an increase in the average Nusselt number (Nu) due to the effect of the externally applied magnetic field, even at low $\mathrm{Ha}$. A plausible explanation for the observed trend has been provided based on the measurements made. The experimentally measured average Nusselt numbers compare well with standard correlations available in the open literature.