Momentum balance ideal fluids

It has been seen in deriving equations 4.33 to 4.38 that for a small disturbance the velocity of propagation of the pressure wave is equal to the velocity of sound. If the changes are much larger and the process is not isentropic, the wave developed is known as a shock wave, and the velocity may be much greater than the velocity of sound. Material and momentum balances must be maintained and the appropriate equation of state for the fluid must be followed. Furthermore, any change which takes place must be associated with an increase, never a decrease, in entropy. For an ideal gas in a uniform pipe under adiabatic conditions a material balance gives ... 

Different expressions are reported in the literature to evaluate the effective radial thermal conductivity [5] and the heat transport coefficient in the first layer near the tube wall fiw [6-9] for the pseudo-homogeneous fluid/solid phase. For ideal models, momentum balance is expressed as ... 

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