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#

The Entrance Limitation of Supersonic Branch

Situations where the conditions at the tube exit
have not arrived at the critical conditions are discussed here.
It is very useful to obtain the relationship between
the entrance and the exit condition for this case.
Denote 1 and 2 as the conditions at the inlet and exit respectably.
From equation (

8.24)

For the case that

and

equation (

8.36) is
reduced into the following approximation

Solving for

results in

This relationship shows the maximum limit that Mach number can
approach when the heat transfer is extraordinarily fast.
In reality, even small

results in a Mach number which is
larger than 4.5.
This velocity requires a large entrance length to achieve
good heat transfer.
With this conflicting mechanism obviously the flow is closer to
the Fanno flow model.
Yet this model provides the directions of the heat transfer effects
on the flow.

** Next:** Comparison with Incompressible Flow
** Up:** Isothermal Flow
** Previous:** Dimensionless Representation
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Created by:Genick Bar-Meir, Ph.D.

On:
2007-11-21