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Hybrid nanofluid models have the potential to significantly enhance heat transport in many applications, like coolant of electric devices, thermal energy storage, and heat exchangers. Therefore, the existing problem deals with the simulation of heat and mass transport due to the three-dimensional hybrid nanoliquid flow amid two gyrating disks containing silver Ag and titanium oxide TiO2 nanoparticles. Further, a magnetic field is employed normally to flow’s direction. Applications of Darcy–Forchheimer law are discussed in terms of the porous medium. The utilization of the Cattaneo–Christov model is considered for analyzing heat and mass transmission. Additionally, the influence of thermal radiation, non-uniform heat sink/source, and Brownian diffusivity are discussed in the flow analysis. The problem is designed on the basis of the higher-order nonlinear PDEs which are then converted to ODEs using appropriate variables. Using the numerical technique known as the shooting technique in MATLAB, the reduced mathematical structure is solved numerically. From this study, it is analyzed that the axial velocity profile is weakened near the upper disk but the axial velocity profile is amplified near the lower for upsurge in the magnetic factor and porosity parameter. Hybrid nanofluid concentration is lower for higher Schmidt numbers. [ABSTRACT FROM AUTHOR]

In numerous real-world applications, transverse vibrations of beams are nonlinear in nature. It is a task to solve nonlinear beam systems due to their substantial dependence on the 4 variables of the system and the boundary conditions. To comprehend the nonlinear vibration characteristics, it is essential to do a precise parametric analysis. This research demonstrates an approximation solution for odd and even nonlinear transverse vibrating beams using the Laplace-based variation iteration method, and the formulation of the beams depends on the Galerkin approximation. For the solution of the nonlinear differential equation, this method is efficient as compared to the existing methods in the literature because the solutions exactly match with the numerical solutions. The Laplace-based variation iteration method has been used for the first time to obtain the solution to this important problem. To demonstrate the applicability and precision of the Laplace-based iteration method, several initial conditions are applied to the governing equation for nonlinearly vibrating transverse beams. The natural frequencies and periodic response curves are computed using Laplace-based VIM and compared with the Runge–Kutta RK4 method. In contrast to the RK4, the results demonstrate that the proposed method yields excellent consensus. The Lagrange multiplier is widely regarded as one of the most essential concepts in variational theory. The result obtained are displayed in the table form. Highlights The highlights of the solution of the Euler–Bernoulli beam equation with quintic nonlinearity using Lagrange multiplier are: 1. Introducing the constraint of the boundary conditions into the equation using Lagrange multipliers. 2. Formulating the equations for the Lagrange multipliers and the deflection of the beam. 3. Solving the resulting system of algebraic equations using numerical methods. 4. Obtaining the deflection of the beam as a function of its length and the applied load. 5. Analyzing the behavior of the beam under different loads and boundary conditions. [ABSTRACT FROM AUTHOR]

Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring (SPM), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive EWMA (AEWMA) control chart is a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical EWMA charts. In this study, we propose an enhanced AEWMA chart, termed the EAEWMA chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed E A E W M A chart enhances the existing AEWMA chart using the shift estimator, based on the hybrid EWMA (HEWMA) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The E A E W M A chart is compared with various existing charts, including A E W M A , H E W M A , E W M A , A C S U M , and I A C C U S U M , in zero- and steady-state scenarios. Conclusively, two practical applications of the EAEWMA chart are presented, demonstrating its value for practitioners and engineers and illustrating its efficacy in real-world scenarios. [ABSTRACT FROM AUTHOR]