A computational time integrator for heat and mass transfer modeling of boundary layer flow using fuzzy parameters

• Construction of a modified exponential integrator scheme nonstandard numerical scheme is considered for solving PDEs with fuzzy parameters, enhancing the ability to model complex boundary layer flows. • It incorporates fuzzy logic to represent critical parameters such as the Hartmann number, Eckert number, and reaction rate, allowing for the effective handling of uncertainties in fluid properties and external conditions. • A rigorous analysis of the proposed scheme, demonstrating its consistency and stability in the mean square sense, ensures reliability in environmental simulations. • The proposed numerical scheme is highly accurate and attains the predicted order of convergence shown through various examples. • A comparison shows that the proposed scheme consumes almost 50 % less computation time than the existing first and second-order methods regarding accuracy and computational efficiency, particularly across varying time steps. Engineering and industrial applications depend on boundary layer flow, the thin fluid layer near a solid surface with significant viscosity. It is imperative to comprehend the mechanics of heat and mass transfer to enhance aeronautical technology, forecast weather, and design thermal systems that are more efficient. Modelling and simulating these flows with precision is indispensable. Numerous models presume that fluid characteristics are continuous. Viscosity and thermal conductivity are dramatically affected by pressure and temperature. Complex computational methodologies are necessary to address this issue. A computational exponential integrator is modified for solving fuzzy partial differential equations. The scheme is explicit and provides second-order accuracy in time. The space discretization is performed with the existing compact scheme with sixth-order accuracy on internal grid points. The stability and convergence of the scheme are rigorously analyzed, and the results demonstrate superior performance compared to traditional first- and second-order methods, particularly at specific time step sizes. Stability and convergence analyses show that the method provides a 15 % improvement in accuracy compared to first-order methods and a 10 % improvement over second-order methods, particularly at time step sizes of Δ t = 0.01 . Numerical experiments validate the accuracy and efficiency of the approach, showing significant improvements in modelling the influence of uncertainty on heat and mass transfer. The Hartmann number, Eckert number, and reaction rate parameters are selected as fuzzified parameters in the dimensionless model of partial differential equations. In addition, the scheme is compared with the existing first and second orders in time. The calculated results demonstrate that it works better than these old schemes on particular time step sizes. In addition, the scheme is compared with existing first- and second-order methods in time, demonstrating a 20 % reduction in computational time for large-scale simulations. The computational framework allows flexible examination of complex fluid flow issues with uncertainty and improves simulation stability and accuracy. This method enhances scientific and engineering models by employing fuzzy logic in computational fluid dynamics.