Effect of thermal radiation on the propagation of plane acoustic waves

Abstract

A study is made of the propagation of acoustic waves in a semi-infinite expanse of radiating gas on one side of an infinite, plane, radiating wall. A solution is found, in particular, for the case of sinusoidal oscillations in both position and temperature of the wall. The solution is based on a single linear integro-differential equation that plays the same role here as does the classical wave equation in equilibrium acoustic theory. The solution is applicable throughout the range from a completely transparent to a completely opaque gas and from very low to very high temperatures. The solution appears, in general, as the sum of two types of travelling waves: (1) an essentially classical sound-wave, but with a slightly altered speed and a small amount of damping and (2) a radiation-induced wave whose speed and damping may be either large or small, depending on the temperature and absorptivity of the gas. Since the waves are coupled, both types will usually be present together, even in the special cases of pure motion or pure temperature variation of the wall.

On the Nonlinear Distortions of Sound and its Coupling with Other Modes in a Gaseous Plasma with Finite Electric Conductivity in a Magnetic Field

“…The conclusions concern also conducting liquids. Equations (24), (25), (26) are longer valid with γ denoting the adiabatic coefficient of liquid. As for mercury, a magnetic flux density H of 2.4 teslas yields absorption maximum about 0.5 nepers per wavelength at 5 · 10 5 Hz.…”

“…We do not consider dispersion caused by external forces or specific heating/cooling which make the background of wave propagation non-uniform either. These effects are well-studied in the context of MHD and have been discussed in many papers, see for example (Anand, Yadav, 2014;Vincenti, Baldwin Jr, 1962;Ponomarev, 1961;Fabian et al, 2005).…”

Effect of Conducting and Radiating Gases on the Growth and Decay of Weak Magnetogasdynamic Waves

“…(6) with the help of Eq. (7) differentiated partially with respect to t and the jumps are taken across S(1), we find, using G = c/ 3 and compatibility conditions [9], that Equation (22) is the differential equation governing the growth and decay of a radiation induced wave. The mean curvature at any point of the wave surface has the representation [18]:…”

“…Nariboli and Secrest [6] extended the analysis of Thomas to magnetogasdynamic flows with finite electrical conductivity. During the last two decades several investigation [7][8][9][10] studied thermal radiation effects on the propagation of small disturbances in gas flows under steady state conditions. The growth and decay properties of the weak waves in radiation gasdynamics have been discussed by Srinivasan and Ram [11], Ram [12], Ram and Pandey [13].…”

“…In the above studies, the approximation to the radiative heat transfer equation is too strong and the gas is assumed optically thin or thick. Most of the authors [7][8][9][10][11][12][13][14][15] have neglected the time dependence in the radiative heat transfer equations. The neglect of the time derivative of the radiation field amounts to the suppression of one mode of wave propagation excited by radiation and, therefore, the exact behaviour of waves in radiation gasdynamics is not fully understood.…”