Variable viscosity effects in several natural convection flows

Abstract

A regular perturbation analysis is presented for three laminar natural convection flows in liquids with temperature dependent viscosity: a freely-rising plane plume, the flow above a horizontal line source on an adiabatic surface (a plane wall plume) and the flow adjacent to a vertical uniform flux surface. While these flows have well-known power-law similarity solutions when the fluid viscosity is taken to be constant, they are non-similar when the viscosity is considered to be a function of temperature. A single similar flow, that adjacent to a vertical isothermal surface, is also analyzed for comparison in order to estimate the extent of validity of the perturbation analysis. The formulation used here provides a unified treatment of variable viscosity effects on these four flows. With the exception of water, the major temperature variation of the fluid properties of common liquids is seen to be in the absolute viscosity. This has been previously recognized and utilized for other flows and is the basis for the applicability of the present analysis. Computed first-order perturbation quantities are presented for all four flows. Several interesting variable viscosity trends on flow and transport are suggested by the present results. These modifications to a constant viscosity formulation are seen to be significant even within the necessarily limited range of a first-order perturbation analysis. Heat transfer results for the isothermal and uniform heat flux surfaces are in very close agreement with the corresponding data and correlations of previous investigations. The present results also place some previous conclusions regarding plume flows in clearer perspective.