Singular surface and steepening of waves in a non-ideal gas with dust particles

Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

“…The system of partial differential equations representing the one-dimensional, unsteady flow of a dusty relaxing gas with planar (m = 0) and non-planar, i.e. cylindrical symmetry (m = 1) or spherical symmetry (m = 2) with the assumptions made for dust particles in [36,37] is given by:…”

“…Further, eliminating ρ, α (1) and ξ from (10) we obtain the following Bernoulli type of transport equation [6] for α (1) 2 dα (1) dt +…”

“…, a * 0 = a 0 a 0e , θ * = ρ 0e θ, (α (1) ) * = t 0e α (1) , and then suppressing the asterisk sign, the transport (11) reduces to 2 dα (1) dt +…”

“…Singular surface theory of the first order uses the approach that the functions itself are continuous and undergo jump discontinuity in at least one of its first order derivatives. In a recent paper, this theory was used to study wave propagation and its termination into discontinuities in three different contexts of flow of a non-ideal dusty gas, and further among other results, the effects of the ratio of species densities and the ratio of specific heat on shock formation were shown [1]. The nonlinear theory of wave propagation was discussed by Varley and Cumberbatch [2] and the propagation of weak discontinuities in different materials using singular surface theory has been studied by many authors from an applicative point of view [3][4][5].…”

“…In this paper, we discuss the interaction of a singular surface with a characteristic shock in a relaxing gas with dust particles. It is imperative to highlight some of the assumptions being made to formulate the system of the fluid flow [33][34][35][36]. It is considered that the solid particles are spherical in nature with uniform size and the specific heat of the gas and the dust particles are constant.…”