|Thermodynamics and Propulsion
17.1, which shows a
cross-sectional view of a turbine blade. There are three different
types of cooling indicated, all meant to ensure that the metal is
kept at a temperature much lower than that of the combustor exit
flow in which the turbine blade operates. In this case, the turbine
wall temperature is not known and must be found as part of
the solution to the problem.
To find the turbine wall temperature, we need to analyze convective heat transfer, which means we need to examine some features of the fluid motion near a surface. The conditions near a surface are illustrated schematically in Figure 17.2. In a region of thickness , there is a thin ``film'' of slowly moving fluid through which most of the temperature difference occurs. Outside this layer, is roughly uniform (this defines ). The heat flux can thus be expressed as
It cannot be emphasized enough that this is a very crude picture. The general concept, however, is correct, in that close to the wall, there is a thin layer in which heat is transferred basically by conduction. Outside of this region is high mixing. The difficulty is that the thickness of the layer is not a fluid property. It depends on velocity (Reynolds number), structure of the wall surface, pressure gradient and Mach number. Generally is not known and needs to be found and it is customary to calculate the heat transfer using . This quantity has the symbol and is known as the convective heat transfer coefficient. The units of are W/m2K. The convective heat transfer coefficient is defined by
Equation (17.2) is often called Newton's Law of Cooling. For many situations of practical interest, the quantity is still known mainly through experiments.
How do we know that is not a fluid property? (MP 17.1)