Perturbation solutions for blast waves with convective and radiative heat transfer

Summary The non-self-similar point explosion problem is investigated, taking into accont internal heat transfer effects. The conductive heat flux is expressed in terms of Fourier's law and radiation is considered to be of the diffusion type.A co-ordinate expansion based on the reciprocal of the square of the shock Mach number is employed to obtain solutions for the initial stages of blast waves with non-zero counter-pressure for either planar, cyclindrical or spherical symmetry. The first approximation that corresponds to the self-similar problem and the second approximation are discussed. Since both formulations imply a two-point boundary-value problem with a singularity at the centre of symmetry an iterative shooting technique is applied to determine the correct solutions. The comparison of our results with those of other authors is presented.