Effect of the radial temperature gradient on resonant oscillations of gas in a closed tube

Resonant oscillations of gas in a closed tube with a heat source are studied. The amplitude-frequency characteristics and spatial distributions of pressure and velocity amplitudes in a tube with a radial temperature gradient are calculated. It is shown that a radial temperature gradient leads to the radial dependence of the oscillation velocity in the flow core and reduces the average value of the momentum source due to viscosity. Together with the temperature dependence of the viscosity, this leads to the amplification of resonant gas oscillations in a tube with a heat source. The influence of the heat source on the resonant gas oscillations is determined by the radial temperature gradient and the square of the reduced oscillation frequency.