Analytical Solution of Steady Air Flow in Tube with Friction and Heat Transfer

Thermodynamic and mechanical properties are intimately interrelated. The pressure loss due to viscosity causes the decrease of pressure and inevitably the expansion of volume, which naturally accompanies the increase of velocity and the decrease of temperature estimated by adiabatic expansion. The viscosity causes dissipation of kinetic energy as well, which partly causes, same as heat input, an increase in temperature. When the air temperature in a tube and that of environment are different, heat transfer occurs and this is another cause of temperature change. Analytical relations were known for isothermal and adiabatic cases. This paper presents a general relation describing the case with temperature change and heat transfer.