Introduction

Abstract

The simplest configuration for a flow with heat transfer is a uniform external flow over a flat surface, part or all of which is at a temperature different from that of the oncoming fluid (Fig. 1.1). In slightly more complicated cases the surface may be curved and the external-flow velocity u _e may be a function of the longitudinal coordinate x, but in a large number of practical heat-transfer problems the variation of u _e with y in the external flow is negligibly small compared with the variation of velocity in a region very close to the surface. Within this region, called the boundary layer, the x-component velocity u rises from zero at the surface to an asymptotic value equal to u _e ; in practice one defines the thickness of this layer as the value of y at which u has reached, say, 0.995u _e . The temperature also varies rapidly with y near the surface, changing from the surface value T _w , (subscript w means “wall”) to the external-flow value T _e ,which, like u _e , can often be taken independent of y. This region of large temperature gradient is called the thermal boundary layer; if the fluid has high thermal conductivity, it will be thicker than the hydrodynamic (velocity) boundary layer, and if conductivity is low, it will be thinner than the hydrodynamic boundary layer. Later we shall be more precise about the meanings of “high” and “low,” which involves comparing the conduction of heat by molecular motion with the “conduction” of momentum—that is, the viscosity of the fluid, which control the rate of growth of the velocity boundary layer.