Self-similar Solution of a Cylindrical Shock Wave under the Action of Monochromatic Radiation in a Rotational Axisymmetric Dusty Gas

Abstract

A self-similar flow behind a cylindrical shock wave is studied under the action of monochromatic radiation in a rotational axisymmetric dusty gas. The dusty gas is taken to be a mixture of small solid particles and perfect gas, and solid particles are continuously distributed in the mixture. The similarity solutions are obtained and the effects of the variation of the radiation parameter, the ratio of the density of solid particles to the initial density of the gas, the mass concentration of solid particles in the mixture and the index for the time dependent energy law are investigated. It is observed that an increase in the radiation parameter has decaying effect on the shock waves; whereas the shock strength increases with an increase in the ratio of the density of solid particles to the initial density of the gas or the index for the time dependent energy law. Also, it is found that an increase in the radiation parameter has effect to decrease the flow variables except the density and the azimuthal component of fluid velocity. A comparison is also made between rotating and non-rotating cases.

Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimuthal or Axial Magnetic Field

“…The adiabatic compressibility of the mixture of non-ideal gas and small solid particles may be calculated as (cf. Nath and Sahu [32,33], Moelwyn-Hughes [50])…”

“…The study of shock waves in a mixture of a gas and small solid particles of micro-size is of great importance due to its applications to nozzle flow, lunar ash flow, bomb blast, coal-mine blast, underground, volcanic and cosmic explosions, metalized propellant rocket, supersonic flight in polluted air, the collision of coma with a planet and many other engineering problems (see refs. [23][24][25][26][27][28][29][30][31][32][33][34][35][36]). There are many research papers which concern the study of characteristics of molecular-dust clouds.…”

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

“…In Eulerian coordinates, the system of equations of gas dynamics describing the unsteady, adiabatic and spherically symmetric one-dimensional flow of dusty gas under the action of gravitational field and monochromatic radiation, can be expressed as (c.f. Khudyakov, [8] Nath and Takhar, [10−11] Nath and Sahu, [16] Pai et al, [18] Vishwakarma and Nath, [33] Zedan, [38] Nath [39] )…”

“…where r and t are independent space and time coordinates; w is the fluid velocity, ρ is the density, p is the pressure, e m is the internal energy per unit mass, m is the mass of the heavy nucleus at the center, Ḡ is the gravitational constant, j be monochromatic radiation at radial distance r and time t, and K is the absorption coefficient. Equation of state for the mixture of perfect gas and small solid particles may be written as (Nath and Sahu, [16] Pai et al, [18] Vishwakarma and Nath [33] )…”

“…Nath and Takhar, [10−11] Nath, [12] Vishwakarma and Pandey, [13] Nath and Sahu [14] ) have investigated the motion of a gas under the action of monochromatic radiation when the medium is ideal or non-ideal gas. Singh, [15] Nath and Sahu, [16] Sahu [17] have studied the motion of a gas under the influence of monochromatic radiation when the medium is mixture of gas and small solid particles.…”