Explore the principles of computational fluid dynamics $($CFD$)$ and its applications in chemical engineering simulations. Discuss the governing equations of fluid flow and heat transfer, such as the Navier$-$Stokes equations, and explain the numerical methods used to solve these equations in CFD simulations. Analyze the role of CFD in the design and optimization of chemical processes, such as reactor design, heat exchanger performance, and mixing studies, emphasizing its importance in reducing experimental costs and accelerating process development.