On the thermofluidics of a steady laminar jet impacting on a rotating hot plate: An ab initio scaling perspective

Abstract

We provide an ab initio scaling analysis for liquid film thickness and Nusselt number of a steady laminar jet impinging a rotating heated plate. We have probed the limiting scaling regimes by incorporating the evaporative effects at the liquid–vapor interface. The dependence of liquid film thickness and Nusselt number on Reynolds, Rossby, and Prandtl numbers has been unearthed using scaling analysis of the integral and differential form of the continuity, Navier–Stokes, and energy equation in a cylindrical coordinate system. Boundary layer analysis has been used to discover a critical length that plays a significant role in understanding the effect of evaporation on hydrodynamic, thermal boundary layer thicknesses, and subsequently Nusselt number. The evaporative effects on liquid film thickness become increasingly important after a certain critical radius. The scaling laws derived are compared with existing experimental data available in the literature, and the trends predicted were consistent.