Thermally fully developed pipe flows of active liquids

Active matter laden active liquids define a unique class of liquids, whose extremely rich dynamics can be captured only by appropriately considering the contribution of active matter induced stresses. In this paper, we develop analytical solutions for studying the effect of a background active fluid flow in the temperature distribution and the Nusselt number in a thermally fully developed pipe flow with constant surface heat flux. Specifically, we consider the flow of an active liquid consisting of active particles demonstrating vortex defects: consequently, in the presence of an axial gradient in activity, there occurs an induced pressure-driven flow in a pipe that has a profile different from the Hagen-Poiseuille flow profile in non-active pressure-driven flow. We find that the Nusselt number for the case of the background active flow is 3.83, which is smaller than the classical value of 4.36 observed for the non-active liquids with background pressure-driven flow (with constant heat flux). We justify this decrease by noting that for the case where the activity gradient (for active flows) is identical to the pressure gradient (for non-active pressure-driven flows), the overall flow strength is smaller for the active flows: such reduced flow strength causes a reduced convective heat transfer triggering a decrease in the Nusselt number for the case of the background active flows. This reduced convective heat transfer also causes a smaller temperature away from the wall (for the case where the wall temperature is greater than the mean temperature) for the case of the background active flows.