Free convection around a vertical isothermically heated plate of finite length at large prandtl numbers

Abstract

A free convection boundary layer arises because of the appearance of viscosity forces near a solid boundary. For high viscosity fluids the viscosity is significant over the whole flow region, and the thermal boundary layer which forms because of the restriction of heat diffusion from a heated wall by convection is characterized by the ratio between the coefficients of viscosity and thermal diffusivity, i.e., the Prandtl number. The divergence between the theoretical [1–4] and experimental data [5, 6] for the velocity profiles of free convective flow around a vertical surface at large Prandtl nunbers is due to an insufficiently clear distinction between the physical laws mentioned. In the present study the form of the velocity and temperature profiles is determined more accurately on the basis of an asymptotic analysis of the complete Navier-Stokes equations and energy equation with Prandtl number Pr → ∞ and Grashof numbers of the order of unity.