2024/05/09 by W. Cade Reinberger, Nathaniel S. Barlow, Reinberger, W. Cade +5
Engineering · Environmental Science · #76-10 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Nanofluid Flow and Heat Transfer #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.2405.06071
openalex publication_date 2024/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of convective heat transfer across the laminar boundary-layer induced by an isothermal moving surface in a Newtonian fluid. In previous work (Barlow, Reinberger, and Weinstein, 2024, Physics of Fluids, 36 (031703), 1-3) an exact power series solution was provided for the hydrodynamic flow, often referred to as the Sakiadis boundary layer. Here, we utilize this expression to develop an exact solution for the associated thermal boundary layer as characterized by the Prandtl number (Pr) and local Reynolds number along the surface. To extract the location-dependent heat-transfer coefficient (expressed in dimensionless form as the Nusselt number), the dimensionless temperature gradient at the wall is required; this gradient is solely a function of Pr, and is expressed as an integral of the exact boundary layer flow solution. We find that the exact solution for the temperature gradient is computationally unstable at large Pr, and a large Pr expansion for the temperature gradient is obtained using Laplace's method. A composite solution is obtained that is accurate to O(10-10). Although divergent, the classical power series solution for the Sakiadis boundary layer -- expanded about the wall -- may be used to obtain all higher-order corrections in the asymptotic expansion. We show that this result is connected to the physics of large Prandtl number flows where the thickness of the hydrodynamic boundary layer is much larger than that of the thermal boundary layer. The present model is valid for all Prandtl numbers and attractive for ease of use.