Analysis and Simulation of Heat Transfer in a Superhydrophobic Microchannel

The transport behavior of a superhydrophobic Hele-Shaw channel subject to arbitrary velocity slip, temperature slip, and constant heat flux boundary conditions is analyzed, resulting in a general expression for the Nusselt number. The results of a scaling analysis and numerical simulation are then presented characterizing the thermal behavior of an idealized pillar-structured superhydrophobic surface in the low pillar concentration limit that treats the trapped vapor region as adiabatic. When thermal behavior is uncoupled from the flow, the temperature slip length is shown to follow the same ..1=2 s dependency on pillar solid fraction as the velocity slip length. Further analysis and simulation including the effects of Marangoni stress, so that the thermal and flow fields are no longer decoupled, yields a further geometric scaling parameter. It is demonstrated that the apparent slip length may be increased against an adverse channel temperature gradient due to the local non-equilibrium of temperature in the vicinity of each pillar.