Research Projects

Shock waves are sudden and powerful disturbances that travel faster than sound and can cause serious damage as they move through air. In many real-life situations such as factory explosions, mining accidents, gas leaks, or defense-related blasts, shock waves often pass through air that is not ideal but contaminated with dust, smoke, or pollutants especially in cities and industrial zones. These particles, along with high pressures and temperatures, make shock waves stronger and more complex, making them harder to predict or control. This issue is particularly relevant in India’s coal mining regions like Jharkhand and Chhattisgarh, where dust-laden air can amplify shock waves, increasing the risk of collapse and fatalities. During spacecraft re-entry, strong shock waves encounter the dusty, ionized upper atmosphere, known as the plasma sheath. Similar interactions occur in industrial dust explosions, solar flare emissions, and volcanic eruptions, all involving dusty, viscous, and magnetized environments. While current safety standards and simulation tools offer useful insights using ideal gas assumptions, their accuracy can be significantly enhanced by incorporating the effects of non-ideal dusty gas behavior, especially for complex real-world scenarios. This project proposes a mathematical analysis of magnetogasdynamic shock wave propagation in a dust-contaminated, viscous, non-ideal gaseous medium governed by quasilinear hyperbolic PDEs. Objectives: 1.Obtain similarity solution for strong magnetogasdynamic shock in a viscous flow of non-ideal dusty gas using the method of Lie group of transformation. 2.Analyze the flow-field behind a magnetogasdynamic shock wave in a viscous non-ideal dusty gas with radiation heat flux and obtain self-similar solution. 3.Use perturbation method to obtain a global solution to the problem of imploding strong shock waves collapsing at the axis of symmetry in a non-ideal MGD with the effects of viscosity and dust particles. 4.Obtain an approximate analytical solution for the problem of shock wave in a viscous flow of non-ideal dusty gas using the power series method. 5.Analyze the evolutionary behavior of shock waves of arbitrary strength in a viscous flow of non-ideal dusty gas. Expected Output: •Self-similar solution under various physical effects •Profiles for flow variables and shock structure •Parametric analysis Expected Outcomes: •Deeper understanding of shock wave behavior in complex environments •Applications in aerospace, safety engineering, and planetary science •Theoretical progress in solving non-linear PDEs using different approaches If successful, the research will offer a more realistic and predictive model for shock waves in plasma-aerosol environments. This will advance fundamental understanding in magnetogasdynamics and could significantly benefit applied fields like space vehicle re-entry modeling, dust-laden plasma control in fusion reactors, and explosion dynamics in dusty industrial settings.