(untitled) (Journal of Naval Architecture and Marine Engineering, 2025)
The thermal-material transport in boundary-layer flows has significant implications for industries such as petroleum and agricultural engineering, gas turbines, nuclear power facilities, heat exchangers, cooling systems, and chemical processing. This particular investigation seeks to understand how thermal and solute buoyancy forces impact the fluctuating flow of a boundary layer over an upright permeable flat sheet with heat generation. It is crucial across various fields, advancing scientific understanding and practical engineering applications. This analysis requires modifying the nonlinear and time-varying partial differential equations (PDEs) to address the continuity, momentum, energy, and concentration balance equations. After developing a mathematical model, the explicit finite difference method (EFDM) is utilized to solve a set of nonlinear dimensionless partial differential equations along with the suitable boundary conditions (BCs). The EFDM technique is thoroughly described in a step-by-step manner, tailored to the specific model being analyzed. The stability, convergence, finding a suitable uniform meshing, steady-state condition, and code validation are conducted. This study focuses on velocity, temperature, and concentration distributions that are affected by incoming physical forces, such as buoyancy force and heat production. It analyzes the mean and local rates of skin friction coefficient and heat-material transports. The findings demonstrate that as buoyancy increases, fluid velocity rises, and that increasing heat generation increases heat-mass heat transmission rates. The practical behavior is a result of the pressure gradient caused by thermal buoyancy force. Two novel linear regression equations with multiple variables are derived from the outputs. By combining advanced modeling techniques, incorporating variable properties, applying unsteady analysis, considering surface porosity, and examining heat generation, and thermal-solutal buoyancy force effects, this study provides a comprehensive and versatile framework for enhancing understanding and optimizing boundary-layer flows in numerous practical applications. Journal of Naval Architecture and Marine Engineering, 22(1), 2025, pp. 21-40