Analytical investigation for the propagation of planar shock waves in a dust-filled van der Waals gas under the action of the magnetic field

• Main Authors: Husain, Akmal, Haider, S. A., Singh, V. K.
• Format: Conference Proceeding
• Language: English
• Subjects: Boundary conditions; Closed form solutions; Dust; Exact solutions; Explosions; Flow profiles; Ideal gas; Magnetic fields; Parameters; Shock waves; Velocity distribution
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0201495

The current study aims to formulate an analytical solution to a one-dimensional planar blast wave proliferation problem in a non-ideal gas filled with small solid dusty particles under the action of the magnetic field. For this, a relation has been established between thermodynamic flow quantities subject to Rankine–Hugoniot jump boundary conditions. By considering the simple analytical technique proposed by Murata, a closed-form explicit solution has been obtained for the physical flow parameters and the radius of the shock front; which expounds the dependence on time-space. Simultaneously, an analytical investigation of the total energy (released during the propagation of the strong discontinuity from the center of the explosion) has also been carried out in the medium of non-ideal gas filled with dusty particles. Furthermore, the impacts of the dust particles and non-ideal parameters in the presence of a magnetic field (modeled in the form of Shock-Cowling number) on the behavior of physical flow profiles and total energy have been examined, and the results are depicted graphically. From the outcomes, it is worthwhile noting that the closed form (precise) solutions obtained for the flow-field variables: density, pressure, and magnetic pressure, are spaciously affected by the magnetic field; however, shock front radius and velocity profile remains unaltered under the impact of the magnetic field, whereas the effect of non-ideal and dust-loading parameters significantly appear.