The College of Science in the Department of Mathematics discussed a seminar entitled Numerical analysis of compressible inelastic fluid flow under thermal conditions for postgraduate student Rawaa Kareem Ganem. This seminar presents a study of the fluids behavior (liquids or gases) whose density changes significantly with pressure variations. The analysis focuses on modeling non-isothermal non-Newtonian fluid flows and the complex interaction between thermodynamics and hydrodynamic motion of the fluid using compressible Navier-Stokes equations coupled with an energy equation to describe the heat transfer problem.