Thermal transport due to liquid jet impingement on superhydrophobic surfaces with isotropic slip: Isoflux wall

Abstract

Thermal transport due to a liquid water jet impinging an isoflux superhydrophobic surface with isotropic slip was modeled analytically. An integral analysis of the transport equations resulting in a system of ordinary differential equations was solved numerically. Impingement on superhydrophobic surfaces greatly reduces the heat transfer that occurs relative to a smooth surface due to gas trapped in cavities on the surface. This results in an apparent slip velocity and temperature jump at the surface. Local and average Nusselt numbers are presented as a function of radial position (0 to 45 jet radii), jet Reynolds number (3×103 to 1.5×104), liquid Prandtl number (2 to 11), normalized slip length (0 to 0.2), and normalized temperature jump length (0 to 0.2). All results are compared to classical (no-slip, no temperature jump) behavior on a smooth surface. Although local Nusselt numbers for the isoflux scenario are greater than the corresponding isothermal case, the difference in Nusselt number between these two heating conditions becomes negligible as the temperature jump length increases to quantities realizable on superhydrophobic surfaces. These results may be utilized to explore heat transfer degradation in applications where smooth surfaces are replaced by superhydrophobic surfaces to avoid fouling.