Convective heat transport

Abstract

In Sect. 3.2 we saw that when a hot (or cold) fluid flows past a cold (or hot) body of size L, with a characteristic velocity U such that the Peclet number is large, i.e., (Formula presented.), then the convective heat flux is in general much larger than is diffusive counterpart. This is true everywhere, with the exception of a thin layer near the surface of the body of thickness δT, called thermal boundary layer. In fact, although far from the walls convection prevails, at the wall the fluid velocity is null and therefore heat is exchanged only by diffusion. Therefore, at a certain distance from the walls, convective and diffusive effects must balance each other: this is what defines the thickness δT of the thermal boundary layer. Although the amount of fluid contained in the thermal boundary layer is but a tiny fraction of the total fluid volume, it nevertheless plays a very important role, as it regulates the heat exchange between fluid and body, which is what concerns us the most. In this chapter, after investigating the scaling of the problem in Sect. 13.1, thermal boundary layer is studied in Sect. 13.2, determining its dependence on the fluid velocity and its physical properties. Finally, in Sect. 13.3, the Colburn-Chilton analogy between heat and momentum transport is analyzed, showing that the properties of one of the two transport phenomena can be determined, once the other is known.