Page 210 - 48Fundamentals of Compressible Fluid Mechanics

172 CHAPTER 10. RAYLEIGH FLOW

compressible. The density change though the heat transfer (temperature change).
As appose to the Fanno flow in which the resistance always oppose the the flow di-
rection, in Rayleigh flow also cooling can be applied. The flow velocity acceleration
change the direction when the cooling is applied.

10.2 Governing Equation

flow
direction

heat transfer (in and out)

Fig. 10.1: The control volume of Rayleigh Flow

The energy balance on the control volume reads
(10.1)

I
the momentum balance reads E
(10.2)

E E

(10.3)
!
The mass conservation reads !

Equation of state #"$ "

(10.4)
!
!

There are four equations with four unknown, if the upstream conditions are known
(or downstream condition are known). Thus, a solution can be obtained. One