Bistable Heat Transfer in a Nanofluid

Heat convection in water can be suppressed by adding a small amount of highly thermophilic nanoparticles. We show that such suppression is not effective when a suspension with uniform concentration of nanoparticles is suddenly heated from below. At Rayleigh numbers smaller than a sample dependent threshold ${\mathrm{Ra}}^{*}$ we observe transient oscillatory convection. Unexpectedly, the duration of convection diverges at ${\mathrm{Ra}}^{*}$. Above ${\mathrm{Ra}}^{*}$ oscillatory convection becomes permanent and the heat transferred exhibits bistability. Our results are explained only partially and qualitatively by existing theories.

Figure 1

Nusselt number plotted as a function of Ra. Squares and downward pointing triangles represent reference data on water [8] and liquid helium [9], respectively. Upward pointing triangles represent data for water taken by us. The vertical dotted line marks the threshold for RB convection ${\mathrm{Ra}}_c$. Circles represent measurements on the MFA NF performed by starting with a uniform concentration of NP; open circles represent data taken during transient convection, while solid circles represent measurements taken at steady state. The data clearly show a discrete jump of Nu in correspondence of the transition from transient to permanent convection at ${\mathrm{Ra}}^{*}\approx 3400$. Diamonds represent measurements on the MFA NF performed by starting in the presence of a fully developed concentration profile. At variance with a simple fluid, above ${\mathrm{Ra}}_c$ the conductive branch is stable for a highly thermophilic NF heated from below [1, 2, 3]. The horizontal dashed line represents the conductive regime $\mathrm{Nu}=1$.

Figure 2

(a) Power $Q_S$ transferred by the sample as a function of the time elapsed from the imposition of the temperature difference. $Q_S$ remains stable at 6.76 W for about $5.5\times {10}^4\mathrm{s}$. After this transient the convective heat transfer stops suddenly and $Q_S$ drops to 5.39 W. (b) Time evolution of the rms average of shadowgraph images. During the oscillating convective regime $I_{\mathrm{rms}}$ exhibits large fluctuations generated by the propagating convective patterns.

Figure 3

Open circles represent the time $t_e$ needed for transient oscillatory convection to end as a function of Ra. The time $t_e$ diverges as ${\mathrm{Ra}}^{*}\approx 3400$ (vertical dotted line) is approached from below. Full circles represent experimental runs where oscillatory convection survived indefinitely, until it was stopped after 1 week. Regions I and II mark the transient and permanent oscillatory convective regimes.