This article comprises the study of three-dimensional squeezing flow of (CNT-SiO₂/H₂O) hybrid nanofluid. The flow is confined inside a rotating channel whose lower wall is stretchable as well as permeable. Heat transfer with viscous dissipation is a main subject of interest. We have analyzed mathematically the benefits of hybridizing ${\mathrm{SiO}}_2$ -based nanofluid with carbon nanotubes ( $\mathrm{CNTs})$ nanoparticles. To describe the effective thermal conductivity of the $\mathrm{CNTs}$ -based nanofluid, a renovated Hamilton–Crosser model (RHCM) has been employed. This model is an extension of Hamilton and Crosser’s model because it also incorporates the effect of the interfacial layer. For the present flow scenario, the governing equations (after the implementation of similarity transformations) results in a set of ordinary differential equations (ODEs). We have solved that system of ODEs, coupled with suitable boundary conditions (BCs), by implementing a newly proposed modified Hermite wavelet method (MHWM). The credibility of the proposed algorithm has been ensured by comparing the procured results with the result obtained by the Runge-Kutta-Fehlberg solution. Moreover, graphical assistance has also been provided to inspect the significance of various embedded parameters on the temperature and velocity profile. The expression for the local Nusselt number and the skin friction coefficient were also derived, and their influential behavior has been briefly discussed.

Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary conditions. The aim of this article is to investigate the hydrodynamical aspects of steady, axisymmetric and slow flow of a general second-order Rivlin-Ericksen fluid in a porous-walled circular tube with constant wall permeability. The governing compatibility equation have been derived and solved analytically for the stream function by applying Langlois recursive approach for slow viscoelastic flows. Analytical expressions for velocity components, pressure, volume flow rate, fractional reabsorption, wall shear stress and stream function have been obtained correct to third order. The effects of wall Reynolds number and certain non-Newtonian parameters have been studied and presented graphically. The obtained analytical expressions are in agreement with the existing solutions in literature if non-Newtonian parameters approach to zero. The solutions obtained in this article may be considered as a generalization to the existing work. The results indicate that there is a significant dependence of the flow variables on the wall Reynolds number and non-Newtonian parameters.

This article deals with the problem of finding a pricing formula for weather derivatives based on temperature dynamics through an uncertain differential equation. Weather-related derivatives are being employed more frequently in alternative risk portfolios with multiple asset classes. We first propose an uncertain process that uses data from the past to describe how the temperature has changed. Despite this, pricing these assets is difficult since it necessitates an incomplete market framework. The volatility is described by a truncated Fourier series, and we provide a novel technique for calculating this constant using Monte Carlo simulations. With this approach, the risk is assumed to have a fixed market price.

Robotics systems deal with uncertainties and nonlinearities of robot manipulator dynamics, such as the mass of the payload, which is an unmodeled dynamic uncertainty, and external disturbances caused by fluctuations from external sources. Hence, it has huge industrial applications. This study examines the use of a new combination of the optimal integral sliding mode control (OISMC), on 3‐DoF robot manipulators subject to external perturbation. The investigation is divided into two parts. The first step involves optimal control with appropriate weights without considering external disturbances, while the second stage employs integral sliding mode control to manage dynamic responses to disruptions. The model calculations are carried out using Mathematica software, and the study of a 3R joint SCARA‐type robot exhibits the robustness of the methodology. The convergence of the method is proven through Lyapunov candidate function analysis and a further novel theoretical insight is provided for the stability of the system through the phase portrait of the sliding variables. The performance of the control system was evaluated using two time‐domain metrics—RMS, and ISU—to validate the convergence of the simulations, while the chattering effect is mitigated by a saturation function.