The Soret and Dufour effects have significant importance in several practical scenarios, especially in the domain of fluidic mass and temperature transfer. Nanofluidics, biological systems, and combustion processes are all areas where these consequences are crucial. Because of its distinct geometry, a wedge-shaped structure has aerodynamics, production, and engineering applications. Wedge shapes are used in aerodynamics for analyzing and improving airflow across various objects. Nanofluids increase thermal conductivity over traditional fluids making them ideal for cooling high-power electronics, boosting temperature transfer efficiencies, and boosting the solar energy system output. This work is of critical importance since it examines the consequences of a heat source/sink, the Soret impact and the Dufour impact, on the movement of a ternary nanofluid over a wedge. This work uses appropriate similarity constraints to reduce the complexity of the underlying governing equations, allowing for fast computational solutions with the Runge–Kutta–Fehlberg 4–5^th order method (RKF-45). Analysis of these phenomena helps determine their possible real-world applications across various engineering fields, by presenting numerical results through plots. The results reveal that adjusting the moving wedge factor lessens the temperature profile, improving the magnetic constraint increases the velocity, and modifying the heat source/sink, Dufour, and Soret factors increases the temperature and concentration profiles. Dufour and heat source/sink constraints speed-up the heat transmission rate. In all cases, ternary nano liquids show significant performance over hybrid nano liquids.

Due to the necessity of creating customized nanomaterial designs, advanced coating processes have been developed on the surface of an isothermal sphere. To achieve accuracy in these processes, it is necessary to understand thermodynamic behavior, the rheology of materials, and the chemical reactions involved. The novelty of the present research is analyzing heat transfer in dusty fluid flow over a heated surface in the cross section of the cylinder. We develop a mathematical model including these factors for both phases and demonstrate how these factors affect the flow field. Thermal radiation propagation is simulated using Rosseland's flux diffusion model. Equations describing flow transport and magnetic body force are expressed using a Cartesian coordinate system. A set of boundary conditions has been established for momentum, thermal energy, and concentration particles to formulate conservation equations for the surface of an isothermal sphere. Using a nonsimilar transform, nonlinear partial differential equations (PDEs) are transformed into dimensionless PDEs. Using the PDSolve technique, dimensionless PDEs are solved. A significant factor in coating engineering is analyzing and calculating velocity distributions, mass, and heat transfers, which were the results of this research. The calculation is carried out using MAPLE 2024, a computational software tool. A deep neural network program was designed, which emphasizes machine learning for predicting the nature of physical phenomena for fluid applications. As part of the validation process of the proposed research, some statistical metrics were taken to assess the degree of error between true values and anticipated values. Based on the results presented, the presented approach is the most efficient method to predict physical quantities for the surface of an isothermal sphere. These results are therefore recommended for the development of industrial device setups.

Numerous researchers have been interested in nanofluids because of their improved thermal characteristics and heat transmission capabilities. Recently, it has been possible to create a novel nanofluid with exceptional thermal properties by combining ternary nanoparticles of various shapes. In this respect, it is believed that the thickness of the fin will change with the length of the fin and that the impacts of thermal radiation, convection on a heat transfer mechanism, and internal heat production in a fin wetted with ternary hybrid nanofluid will depend on the length of the fin. As a result, several fin profiles, including triangular, convex, and rectangular, have been taken into consideration. This study also investigates the comparison of heat and thermal energy fluctuations in both wet and dry conditions. In order to examine the porous nature, Darcy's model is required. With the aid of the Maple computer program, the resultant nonlinear partial differential equation and boundary conditions are non-dimensionalized and numerically resolved using the implicit finite difference approach, the graphic explanation of fin efficiency, and transient thermal response for different values of the essential parameters. The investigation yielded the novel discovery that the effectiveness of the fins is enhanced by the presence of a ternary hybrid nanofluid. Three fins with varied shapes have been compared in both wet and dry circumstances. The study has discovered that triangular fins have a quicker rate of temperature decline, whereas rectangular fins have a greater efficiency. The investigation's results have a significant impact on improving heat transmission in industrial operations.