Ternary hybrid nanofluids (THNFs) are modern fluids introduced to enhance the performance of conventional hybrid nanofluids (HNFs). Their unique properties make them suitable for diverse applications, ranging from heat exchangers to advanced industrial and medical treatments. Due to the practical applications and innovative features of THNFs, this paper aims to analyze the performance of these fluids to improve the efficiency of modern devices. The THNF is formulated by adding nanoparticles of three different kinds of aluminum oxide (Al ₂ O ₃ ), silicon dioxide (SiO ₂ ), and copper (Cu) into water (H ₂ O) based ethylene glycol (C ₂ H ₆ O ₂ ). The momentum equation is formulated considering the influences of Darcy Forchheimer, permeability, and magnetic field. Thermal radiation, intermolecular friction force, and Joule heating effects are accounted in the thermal field equation. Mass concentration relation is acquired considering binary chemical reaction and activation energy (AE). Additionally, the influence of stratifications (thermal and solutal) at the boundary of the cylinder is considered. The physical phenomenon representing partial differential equations is reduced into ordinary ones utilizing the transformations and then solved via Runge–Kutta Fehlberg (RKF‐45) numerical scheme in Mathematics. Influence of involved sundry variables on HNF and THNF velocity, thermal field, mass concentration, surface drag force (skin friction coefficient), mass, and heat transfer rates were examined. The results showed that the velocity fields of THNF and HNF decay through variables Darcy Forchheimer, porosity, and Hartman number. Thermal field of THNF and HNF improves via radiation parameter, Eckert number, and Hartman number. Local heat transfer rate upsurges versus curvature variable and Prandtl number.

Entropy generation (EG) is intrinsically linked with irreversibilities present within a thermodynamical system, signifying energy losses, mainly in the context of fluid friction and heat transfer. In systems characterized by nanofluid flow, such as those utilized in cooling applications, microelectronics, and heat exchangers, the reduction of EG is essential for augmenting energy efficiency by alleviating these losses. In this communication, mixed convection flow of Sutterby nanoliquid by a porous stretched sheet along with irreversibility is analyzed. The momentum equation is reported by taking mixed convection and magnetic field impacts. Dissipation, Lorentz force, and radiation influences are taken in the development of heat transport relation. The expression for concentration is described by taking the chemical reaction effect. Thermodynamics second law is employed to describe entropy. The partial differential equations (PDEs) indicating the flow phenomenon are altered into self‐similar form via transformations. The NDSolve function of Mathematica package is availed to solve the self‐similar system. The impact of sundry variables on concentration, velocity, Bejan quantity, irreversibility, and thermal field is analyzed graphically. Engineering quantities are discussed numerically. The results reveal that the velocity profile upsurges for higher thermal buoyancy parameter, while it decays for raising magnetic variable. For raising values of Eckert number temperature upsurges, while it decays for an upturn in Prandtl number. Entropy is more for superior values of diffusion and radiation variables.

This paper presents a novel approach for analyzing functionally graded beams with porosity on elastic foundations. A new first-order shear mixed beam eleme

This study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two nodes and two degrees of freedom in each node of the new beam element. The suggested element is free of shear locking, without the need for reduced or selective integrations, because of the mixed finite element formulation. Comparative results demonstrate high accuracy in computations, even with both regular and irregular meshes, as well as coarse and fine discretization. Because of its rapid convergence rate, the proposed element is an excellent tool for analyzing beam structures with complex geometries and load conditions. Several examples are provided to demonstrate the accuracy and high convergence of the proposed beam element. Additionally, the effects of various parameters, such as the power-law index and thickness-to-length ratio, on the bending behavior of functionally graded beams are investigated. The findings highlight the robustness and versatility of the developed beam element, which makes it a useful contribution to research into the computational mechanics of beam structures.