Natural Convection in a Vertical Microannulus with Superhydrophobic Slip and Temperature Jump

Abstract

Analytical solutions are derived for steady fully-developed buoyancy-driven flow in a vertical annular microchannel, of which either the inner or outer wall exhibits superhydrophobic velocity slip and temperature jump, and the inner wall is maintained either at constant wall temperature or constant heat flux. For the four possible cases of hydrodynamic and thermal boundary conditions, we determine the flow rate as a function of the core size, slip length and temperature jump coefficient. Asymptotic limits are obtained for very large slip and temperature jump. The effects of slip and temperature jump on two issues, namely, the optimum core radius for maximum flow rate and the singular increase of the flow rate for very small core radius, are investigated in particular.

Inertial effects on thermal transport in superhydrophobic microchannels

“…The effects of gas cavities with finite thermal conductivity [37] and evaporation at the menisci [38] have been explored for rib/cavity surfaces and both effects tend to reduce the effective temperature jump length. A few studies have also investigated the thermal transport for scenarios with imposed hydrodynamic and thermal slip lengths [39][40][41][42].…”

Natural Convection for Slip Flow in a Vertical Polygonal Duct

“…From what has been found by Wang [12,13] and Ng and Wang [9], there always exists an optimum core size for maximum flow in natural convection in a duct with a heated core. This paper aims to determine the optimum core size as a function of the following: (i) slip length, (ii) temperature jump coefficient, (iii) number of sides of the polygon, and (iv) whether the heated core is at UWT or UHF.…”

“…They found that there exists a critical value of the temperature jump coefficient, which is a function of the slip length, above which the flow rate will be larger by heating the no-slip surface than by heating the superhydrophobic surface, whether the heated surface is at UWT or at UHF. Ng and Wang [9] further examined free convection in a vertical micro-annulus with superhydrophobic slip and temperature jump. They determined the optimum core radius for maximum flow rate, and investigated the singular increase of the flow rate for very small core radius, as functions of the velocity slip and temperature jump.…”

Free Convection in a Vertical Slit Micro-channel with Super-hydrophobic Slip and Temperature Jump Conditions

“…Le et al [3] are discussed and Modified the conditions for temperature jump and viscous heat generation. Ng and Wang [4] discussed about buoyancy-based flow in a vertical annular microchannel where the inner or either outer wall exhibits superhydrophobic velocity slip and also temperature jump, while the inner wall is maintained keeping a constant temperature. Kim [5] focused on operational design methodologies to arrive at the relevant dimensions for an optimal heat sink.…”