Fluid mechanics: Pressure and Velocity of gas flow in a heated pipe

uby

1. The problem statement, all variables and given/known data

Please note this is for my own understanding -- I am no longer in school! I simply cannot find this addressed in introductory texts.

Suppose you have a long pipe of constant cross-sectional area with a heated section in the middle. The system has flowing gas such that the pressure at the inlet (say, 1.1 atm) is slightly higher than the outlet (say, 1 atm).

Assume that the heat transfer rate to the gas is infinitely fast.

As the gas passes through the heated length of pipe, what happens to its pressure and velocity?


2. Relevant equations
Ideal gas law: PV=nRT
Conservation of mass: flux in = flux out ... (c*b)in = (c*b)out

3. The attempt at a solution
If you draw a control volume with virtual inlet prior to the heated portion of tube and virtual outlet within the heated portion, conservation of mass must be satisfied. So, the convective flux given by concentration*velocity (c*b) should be conserved. Thus, either both variables remain constant or they vary inversely to each other.

From the ideal gas law, the value n/V = concentration = P/RT. Combining with mass conservation:
(P*b/T)in = (P*b/T)out

So, as T changes, so must the product P*b. The open question is ... how do P and b vary? Is it reasonable to assume one is constant? Any ideas?