Equations for flow in a duct subject to heat exchange

3 Equations for flow in a duct subject to heat exchange 

The dynamic mass balance for a duct of uniform cross-sectional area is given by equation (3.57), repeated below  

The flow dynamics will be very much faster than the temperature dynamics that will be our primary concern. Hence we may assume that the flow is in an evolving steady state, which allows us to set the time differential to zero. But by equation (3.57), the space differential must also be zero  

Since the cross-sectional area of the heat exchanger duct. A, will be unchanged with distance, equation (20.1) implies that the mass flow will be the same at all points along the heat exchanger duct, as can be seen from  

It is normally reasonable for both liquids and gases to calculate the flow through each heat exchanger duct using a steady-state flow equation of the form  

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