11.1 Introduction: Sources of Heat Addition

In this chapter we examine flows in which heat addition has a major effect on the fluid motion. The situations addressed have a fractional change in bulk flow temperature which is of order unity, and we thus first inquire what circumstances lead to this occurrence.

Estimates for the magnitudes of temperature differences due to heat transfer from surfaces can be made based on the Reynolds analogy between heat and momentum transfer from a solid surface to a fluid. The physical content of this analogy, as described in a number of texts (e.g. Eckert and Drake, 1972; Kerrebrock, 1992; Schlichting, 1979; Pitts and Sissom, 1977), is that magnitude of the heat flux, q, and the shear stress, ?, (the momentum transfer per unit area across a plane parallel to the wall) arise from similar transport processes. If the two are viewed as changing in a similar manner through the boundary layer, their ratio can be approximated as constant from the wall to the free stream. Using the expressions for magnitudes of heat transfer and shear stresses in terms of gradients of velocity and temperature this ratio can be written as

In (11.1.1) the thermal conductivity, viscosity, and Prandtl number, Pr (= ?c _p /k), are interpreted as applying to a laminar or turbulent situation as appropriate.

Equation (11.1.1) can be integrated through the boundary layer, from the wall ( T = T _w, u = 0) to the free...