On the Thermofluidics of a Steady Laminar Jet Impacting on a Rotating Hot Plate: An ab-initio Scaling Perspective

TL;DR

This paper develops an ab-initio scaling analysis for the liquid film thickness and Nusselt number of a steady laminar jet impacting a rotating heated plate, incorporating evaporative effects and boundary layer dynamics.

Contribution

It introduces new scaling laws that account for evaporation and rotation effects, validated against experimental data.

Findings

Evaporative effects significantly influence film thickness beyond a critical radius.

Scaling laws align with experimental observations.

Critical length impacts thermal and hydrodynamic boundary layers.

Abstract

We provide an ab-initio scaling analysis for liquid film thickness and Nusselt number of a steady laminar jet impacting a rotating heated plate. The limiting scaling regimes incorporating the evaporative effects along the liquid-vapor interface have been probed. The dependence of liquid film thickness and Nusselt number on Reynolds, Rossby, and Prandtl number have 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 were compared with existing experimental data available in the literature, and the trends predicted were consistent.