Effect of radiative heat transfer on the growth and decay of acceleration waves

The propagation of acceleration waves has been studied along the characteristic path by using the characteristics of the governing quasilinear system as the reference coordinate system. It is shown that a linear solution in the characteristic plane can exhibit non-linear behaviour in the physical plane. As an application of the theory the point is determined where the wave will break down, provided the breaking occurs at the wave front. It is investigated as for how the radiative heat transfer effects under optically thin limit will influence the process of steepening or flattening of acceleration waves with planar, cylindrical and spherical symmetry. The critical time is obtained when all the characteristics will pile up at the wave front to form a shock wave. The critical amplitude of the initial disturbance has been determined such that any compressive disturbance with an initial amplitude greater than the critical one always terminates into a shock wave, while an initial amplitude less than the critical one results in a decay of the disturbance. The radiative heat transfer effects delay the formation of a shock wave and has a stabilizing effect in the sense that not all compressive acceleration waves will grow into shock waves. A non-linear steepening and a radiative heat transfer provide a particular answer to the substantial question as for when a shock wave will be formed.Nomenclature density of the gas - u gas velocity - t time - x spacial coordinate - p gas pressure - a _R the Stefan-Boltzmann constant - D _R the Rossland diffusion coefficient of radiation - T temperature K - U a column matrix - B a column matrix - A a square matrix of order 3 - time-derivative operator as observed from the wave front - Z] symbol for jump in the enclosed quantity - 0 a null column vector - I an identity matrix of order 3 - c sound velocity - J Jacobian of transformation - c _v specific heat at constant volume - (t) wave front - dimensionless parameter of wave amplitude - dimensionless parameter of time - dimensionless parameter of radiative heat effects - dimensionless parameter of initial acceleration - W() an integral function - parameter of symmetry - ratio of specific heats - wave tag - particle tag Exceptions are c critical value - * initial wave label - 0 state ahead of the wave