Heat and mass transfer over slippery, superhydrophobic surfaces

The classical Graetz-Nusselt problem is extended to describe heat and mass transfer over heterogeneously slippery, superhydrophobic surfaces. The cylindrical wall consists of segments with a constant temperature/concentration and areas that are insulating/impermeable. Only in the case of mass transport do the locations of hydrodynamic slip and mass exchange coincide. This makes advection near the mass exchanging wall segments larger than near the heat exchanging regions. Also the direction of radial fluid flow is reversed for heat and mass transport, which has an influence on the location where the concentration or temperature boundary layer is compressed or extended. As a result, mass transport is more efficient than heat transfer. Also the influence of axial diffusion on the Nusselt and Sherwood numbers is investigated for various Péclet numbers Pe. When Pe < 102, which is characteristic for heat transfer over superhydrophobic surfaces, axial conduction should be taken into account. For Pe ≥ 102, which are typical numbers for mass transport in microfluidic systems, axial diffusion can be neglected.