Basics of Fluid Mechanics, 2014a

11.9. RAYLEIGH FLOW 471
Table -11.6. Fanno Flow Standard basic Table (continue)
M
4fL
D
P
P ∗ P 0
P 0
∗
ρ
ρ ∗
U
U ∗
T
T ∗
60.00 0.82052 0.000680 3.6E+6 0.40853 2.448 0.00166
65.00 0.82066 0.000579 5.4E+6 0.40849 2.448 0.00142
70.00 0.82078 0.000500 7.8E+6 0.40846 2.448 0.00122
11.9 Rayleigh Flow
Rayleigh flow is a model describing a frictionless flow with heat transfer through a
pipe of constant cross sectional area. In practice, Rayleigh flow isn’t a really good
model to describe real situations. Yet, Rayleigh flow is practical and useful concept in
a obtaining trends and limits such as the density and pressure change due to external
cooling or heating. As opposed to the two previous models, the heat transfer can be in
two directions not like the friction (there is no negative friction). This fact creates a
different situation as compared to the previous two models. This model can be applied
to cases where the heat transfer is significant and the friction can be ignored. Flow of
steam in steam boiler is good examle where Rayleigh flow can be used.
11.10 Introduction
½
È ½
Ì ½
Fig. -11.37.
Flow.
flow
direction
É
heat transfer
(in and out)
¾
È ¾
Ì ¾
The control volume of Rayleigh
The third simple model for 1–dimensional
flow with a constant heat transfer for frictionless
flow. This flow is referred to in
the literature as Rayleigh Flow (see historical
notes). This flow is another extreme
case in which the friction effects are neglected
because their relative magnitute is
significantly smaller than the heat transfer
effects. While the isothermal flow model
has heat transfer and friction, the main
assumption was that relative length is enables
significant heat transfer to occur between the surroundings and tube. In contrast,
the heat transfer in Rayleigh flow occurs between unknown temperature and the tube
and the heat flux is maintained constant. As before, a simple model is built around the
assumption of constant properties (poorer prediction to case where chemical reaction
take a place).
This model is used to roughly predict the conditions which occur mostly in situations
involving chemical reaction. In analysis of the flow, one has to be aware that
properties do change significantly for a large range of temperatures. Yet, for smaller
range of temperatures and lengths the calculations are more accurate. Nevertheless,