An Investigation of Sound Vibrations in a Tube Containing a Heat Source

The aerothermodynamic process inside a tube in which is placed heat source and through which air is flowing is investigated theoretically. The formulation is based partly on the assumption that the average state of the medium inside may be approximated by a step distribution in the gas variables, simplifying hypothesis suggested by experimental observations by Lehmann (see reference 4). The zeroth‐order (mean hydrodynamic flow) and first‐order (acoustic) solutions inside the tube are first obtained using a heat transfer law for the heater which depends on some arbitrary function of the local values of the gas variables, velocity‐gradient, and source temperature. Upon the basis of a few hypotheses regarding turbulent flow and turbulent heat transfer, the possible existence of heaters whose heat transfer rate depends essentially on the negative of the velocity gradient of the flow through them is demonstrated. The solution is then specialized to those types of heaters, and it is shown that, in agreement wit...