A novel approach for analyzing fluid flow dynamics and static pressure distributions within a convergent-divergent nozzle was presented, integrating soft computing techniques with computational fluid dynamics (CFD) simulations performed using Ansys Fluent. The study differs from traditional CFD approaches by leveraging soft computing methods to optimize simulation parameters and enhance the accuracy of predictions. Four distinct fluids—air, hydrogen, nitrogen, and helium—were analyzed across a range of inlet velocities (1 m/s to 5 m/s). The study systematically evaluates the influence of boundary conditions and flow models, including both viscous and inviscid conditions, on the flow patterns and static pressure distributions. The results highlight the substantial impact of fluid density and viscosity on the flow dynamics, particularly for lighter gases such as hydrogen and helium. These gases exhibit higher velocities and less pronounced pressure gradients due to their lower density and viscosity compared to denser fluids like air and nitrogen. Soft computing techniques improve the reliability of these findings by enhancing the predictive capability of the CFD model, allowing for more precise insights into complex fluid behaviors. The implications of these findings are significant across multiple engineering domains, such as aerospace propulsion, chemical processing, and energy systems, where optimizing fluid flow characteristics is critical. The integration of soft computing with CFD provides a robust framework for more accurate modelling of low-density, high-velocity flows and offers valuable insights for the design of more efficient systems. This study underscores the potential of advanced computational techniques in advancing both fluid dynamics research and engineering applications.

The present paper emphasizes finding the solution for a fuzzy fractional heat conduction equation using the homotopy analysis transform method (HATM). The HATM combines two powerful, well-known methods: homotopy analysis method and the Laplace transform method. The approximate solution of the fuzzy fractional heat conduction equation is obtained by using HATM. Comparison with existing methods shows that the results obtained using the proposed method are in good agreement with the exact solutions available in the literature. All the numerical computations justify the proposed method is very efficient, effective, and simple for obtaining an approximate solution of the fuzzy time-fractional heat conduction equation.