Analytical Solution and Energy Behavior to a Forced Shock Wave Problem Under Dusty Gas Regime

In the presented research work, we have solved a new kind of problem of forced shock waves in a compressible inviscid perfect gas having dirty (dust) particles of small size in a one-dimensional unsteady adiabatic flow. The approach that we have used is referred to as the generalized geometry approach. Here, we investigated how the density of the zone, which is undisturbed, changes as a function of the position from the point of the source of explosion. In addition, we have obtained analytically a novel solution to the problem in the form of a new rule of power of time and distance. Further, we have investigated the energy behavior of forced shock waves and interaction within the environment containing dust particles. Also, the behavior of the entire energy of a forced shock wave is expounded at different Mach numbers, respectively, for planar geometry, cylindrically symmetric geometry, and spherically symmetric geometry under a dusty gas medium. Furthermore, the findings show that dust particles in a gas produce a more sophisticated representation rather than the standard gas dynamics.