Two-Dimensional Convective Heat/Mass Transfer for Low Prandtl and Any Peclet Numbers

Abstract

This paper introduces the complex variable approach to heat or mass transfer by two-dimensional fluid flows at low Prandtl and arbitrary Peclet numbers as applied to several important problems in mathematical physics. The approach using conformal mapping allows one to derive accurate analytic solutions to two-dimensional problems of heat/mass convection flows for any Peclet number and an arbitrary shape of a streamlined contour. As a sample problem, heat transport from an arbitrary cylinder in a saturated porous medium as a result of heat-conductive fluid flow in the medium around the cylinder is considered at a prescribed constant temperature of the cylinder. Asymptotic solutions for high and low Peclet numbers are individually studied by routine methods and compared with the exact solution. Heat and mass transfer in fluidized or packed beds of chemical reactors as well as catalytic converters, flow of liquid metals, heat and mass transfer through a leak in a wall, planar void growth in fine lines in mic...