Intermittent flow regimes near the convection threshold in ferromagnetic nanofluids

The onset and decay of convection in a spherical cavity filled with ferromagnetic nanofluid and heated from below are investigated experimentally. It is found that, unlike in a single-component Newtonian fluid where stationary convection sets in as a result of supercritical bifurcation and where convection intensity increases continuously with the degree of supercriticality, convection in a multicomponent ferromagnetic nanofluid starts abruptly and has an oscillatory nature. The hysteresis is observed in the transition between conduction and convection states. In moderately supercritical regimes, the arising fluid motion observed at a fixed temperature difference intermittently transitions from quasiharmonic to essentially irregular oscillations that are followed by periods of a quasistationary convection. The observed oscillations are shown to result from the precession of the axis of a convection vortex in the equatorial plane. When the vertical temperature difference exceeds the convection onset value by a factor of 2.5, the initially oscillatory convection settles to a steady-state regime with no intermittent behavior detected afterward. The performed wavelet and Fourier analyses of thermocouple readings indicate the presence of various oscillatory modes with characteristic periods ranging from one hour to several days.

Figure 1

Schematic diagram of the density gradients $\nabla {\rho }_T$, $\nabla {\rho }_{TD}$, and $\nabla {\rho }_{gC}$ caused by thermal expansion, thermal diffusion, and gravitational sedimentation, respectively, arising in a ferromagnetic nanofluid heated from below.

Figure 2

Schematic of the experimental chamber: A—spherical cavity filled with a ferromagnetic nanofluid, B—Plexiglas plates, C—aluminum heat exchangers, D—Plexiglas inserts, 1, 2, 3, 4—thermocouples; $\Delta T$ and $\Delta T^{\prime }$ are the temperature differences between the poles of the sphere and the heat exchangers, respectively.

Figure 3

Schematic view of a base vortex: 1, 2, 3, and 4 are thermocouples located in the equatorial plane (see Fig. 2); the arrow represents a vector of angular velocity of the first base convection vortex.

Figure 4

The dependence of the Nusselt number (1) on the relative temperature difference $\Delta T/\Delta T_{\mathrm{c}}$. The solid curve shows the least-squares fit to experimental data given by $\mathrm{Nu}=1+0.44\sqrt{\Delta T/\Delta T_c-1}$. The symbols are defined in the text. The experimental error bars are not shown to improve the readability of the figure.

Figure 5

The temperature time series for a sequence of stepwise increments of the temperature difference between the poles of a sphere. Convection was first detected once the relative temperature difference of $\Delta T=1.9\Delta T_{\mathrm{c}}$ was applied.

Figure 6

The temperature time series illustrating the onset of oscillatory convection at $\Delta T=3.9\Delta T_{\mathrm{c}}$.

Figure 7

The nondimensional amplitude of the signal recorded by the equatorial thermocouples as a function of the relative temperature difference. Solid and empty circles correspond to stationary and oscillatory regimes of convection in a premixed fluid, respectively. Vertical bars show the amplitude ranges detected for oscillatory convection.

Figure 8

The temporal evolution of the temperature response at $\Delta T=1.2\Delta T_{\mathrm{c}}$.

Figure 9

The closeup of a region shown by a dashed frame in Fig. 8.

Figure 10

The orientation of the vector of the angular velocity $\mathit{\omega }$ of the convection vortex for time moments B–F in Fig. 9. The shown numerical values correspond to the thermocouple readings ${\theta }_{\mathrm{I}}$ and ${\theta }_{\mathrm{II}}$.

Figure 11

(a) The spectral density $S$ and (b) the magnitude of Morlet wavelet coefficients for the thermocouple signal ${\theta }_{\mathrm{I}}$ recorded for $\Delta T=1.2\Delta T_{\mathrm{c}}$. The darker shade corresponds to the larger value of the coefficient amplitude.

Figure 12

The temporal evolution of the temperature response ${\theta }_{\mathrm{I}}$ at $\Delta T=1.8\Delta T_{\mathrm{c}}$.

Figure 13

Same as Fig. 11 but for $\Delta T=1.8\Delta T_{\mathrm{c}}$.

Figure 14

(a) The spectral density $S$ and (b) the magnitude of Morlet wavelet coefficients for the thermocouple signal ${\theta }_{\mathrm{I}}$ recorded for $\Delta T=1.8\Delta T_{\mathrm{c}}$ for interval A (day 1) in Fig. 12. The darker shade corresponds to the larger value of the coefficient amplitude.

Figure 15

Details of the temporal evolution of the temperature response ${\theta }_{\mathrm{I}}$ and ${\theta }_{\mathrm{II}}$ at $\Delta T=1.8\Delta T_{\mathrm{c}}$ for interval A (day 1) in Fig. 12.

Figure 16

Same as Fig. 15 but for interval B (days 5–7) in Fig. 12.

Figure 17

Same as Fig. 14 but for interval B (days 5–7) in Fig. 12.

Figure 18

Same as Fig. 15 but for interval C (days 8–12) in Fig. 12.

Figure 19

Same as Fig. 14 but for interval C (days 8–12) in Fig. 12.

Figure 20

Same as Fig. 15 (only ${\theta }_{\mathrm{I}}$ is shown) but for interval D (days 15–35) in Fig. 12.

Figure 21

Same as Fig. 14 but for interval D (days 15–35) in Fig. 12.