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The present study highlights the flow of an incompressible nanofluid following the non-Newtonian flow. The non-Newtonian fluid behavior is characterized by the Casson prototype. The flow occupies the conical gap between the rotating/stationary surfaces of the cone and the horizontal disc. Heat and mass transfer is also considered. The novelty of the proposed mathematical model is supplemented with the impacts of a uniform magnetic field imposed vertically upon the flow together with Ohmic dissipation and chemical reactions. The constitutive equations of the Casson fluid have been interpreted along with the cylindrical coordinates. The governing partial differential equations of momentum, energy, and concentration are converted into a set of nonlinear ordinary differential equations via appropriate similarity transformations. This scheme leads to a set of coupled nonlinear ordinary equations concerning velocity, temperature, and nanoparticles concentration distributions. These equations are analytically solved by means of the Homotopy perturbation method (HPM). The theoretical findings are presented in both graphical and tabular forms. The main objective of this study is to discuss the effects of the rotations of both cone and disc and the effects of the other parameters in the two cases of rotation alternatively. Additionally, the effect of the angle between the cone and the disk is one of our interesting points because of the importance of its effect in some engineering industry applications. The rotation parameters are found to have reduction effects on both the temperature and the radial velocity of the fluid, while they have an enhancing effect on the azimuthal velocity. The effects of other parameters with these rotations are found to be qualitatively the same as some earlier published studies. To validate the current mathematical model, a comparison with the previous scientific reports is made.

The key objective of the current examination is to examine a symmetrically peristaltic movement of microorganisms in a Rabinowitsch fluid (RF). The Boussinesq approximation, buoyancy-driven flow, where the density with gravity force term is taken as a linear function of heat and concentrations, is kept in mind. The flow moves with thermophoretic particle deposition in a horizontal tube with peristalsis. The heat distribution and volume concentration are revealed by temperature radiation and chemical reaction characteristics. The originality of the existing study arises from the importance of realizing the benefits or the threats that nanoparticles, microbes, and bacteria cause in the flow inside peristaltic tubes. The results are an attempt to understand what factors perform additional advantages and or reduce damages. The controlling nonlinear partial differential equations (PDEs) are made simpler by employing the long wavelength (LWL) and low-Reynolds numeral (LRN) approximations. These equations are subjected to a set of non-dimensional transformations that result in a collection of nonlinear ordinary differential equations (ODEs). By employing the Homotopy perturbation method (HPM), the configuration of equational analytical solutions is examined. Analytical and graphical descriptions are provided for the distributions of axial speed, heat, microbes, and nanoparticles under the influence of these physical characteristics. The important findings of the current work may help to comprehend the properties of several variations in numerous biological situations. It is found that the microorganisms condensation decays with the rise of all the operational parameters. This means that the development of all these factors benefits in shrinking the existence of harmful microbes, viruses, and bacteria in the human body’s peristaltic tubes, especially in the digestive system, and large and small intestines.

The current work scrutinizes a non-Newtonian nanofluid free convective flow induced by a rotating stretchable disc. The examination surveys the Stefan blowing and Cattaneo–Christov mass and heat fluxes, as a precise illustrative model. The innovative aspects of the ongoing project include the analysis of the border sheet nanofluid flow near a revolving disc through thermophoresis, Reiner–Rivlin prototype features, and random nanoparticle motion. The Reiner–Rivlin non-Newtonian model is considered together with the effect of an unvarying axial magnetic strength. The constitutive formulae of a Reiner–Rivlin liquid have been reproduced in the cylindrical coordinates. Through implementing the applicable relationship transformations, the controlling partial differential equations are transferred to ordinary differential equations (ODE). This procedure yields a group of coupled nonlinear ordinary differential equations in relation to speed, heat, and nanoparticle concentration profiles that are impacted by several physical characteristics. These equations are analyzed by using the homotopy perturbation method (HPM). Due to the analytical solution given by HPM, the current work enables us to take the infinity of the layer as a parameter of the problem and discuss its variation in the obtained distributions. Consequently, a physical significant graphical visualization of the data is emphasized. The rates of mass and temperature transmission are examined to understand if any of the relevant parameters may improve these rates. Additionally, the Stefan blowing causes extra particles diffusion, which enhances heat transfer and raises the nanoparticles concentration and could be useful in some medical therapies. Furthermore, the stretching of the rotating disc is concluded, which improves the fluid heat transfer.

The principal purpose of the current investigation is to indicate the behavior of the tangent-hyperbolic micropolar nanofluid border sheet across an extending layer through a permeable medium. The model is influenced by a normal uniform magnetic field. Temperature and nanoparticle mass transmission is considered. Ohmic dissipation, heat resource, thermal radiation, and chemical impacts are also included. The results of the current work have applicable importance regarding boundary layers and stretching sheet issues like rotating metals, rubber sheets, glass fibers, and extruding polymer sheets. The innovation of the current work arises from merging the tangent-hyperbolic and micropolar fluids with nanoparticle dispersal which adds a new trend to those applications. Applying appropriate similarity transformations, the fundamental partial differential equations concerning speed, microrotation, heat, and nanoparticle concentration distributions are converted into ordinary differential equations, depending on several non-dimensional physical parameters. The fundamental equations are analyzed by using the Rung-Kutta with the Shooting technique, where the findings are represented in graphic and tabular forms. It is noticed that heat transmission improves through most parameters that appear in this work, except for the Prandtl number and the stretching parameter which play opposite dual roles in tin heat diffusion. Such an outcome can be useful in many applications that require simultaneous improvement of heat within the flow. A comparison of some values of friction with previous scientific studies is developed to validate the current mathematical model.

The current study explores nonlinear stability in vessels with roll-damping to ensure safety in realistic maritime conditions, thereby expanding stability. It develops a generalized model that considers operating situations, nonlinearities, and hydrodynamic factors. One degree of freedom (1DOF) of nonlinear ship dynamics is included in the exiting model. The prototypical incorporates inertia, damping, restoring forces, and external forces. The objective is to examine the responsible non-perturbative method (NPA) in determining periodic response of a damped and conservative coupled system. In contrast to all other traditional perturbation techniques, NPA’s goal is to convert a weakly oscillator of nonlinear of ordinary differential equation (ODE) into a linear one without consuming Taylor expansion. A strong agreement with original numerical solution (NS) is validated. Using Galerkin technique, the inquiry produces an advanced, comparable linear ODE. Quantitative comparisons verify that final solution agrees with advanced solution. The resonance area, situated within stability zone and exhibiting complex relationships between forces in the system, is influenced by all physical properties. An approximate solution up to the second order is found by applying the multiple-time scales method (MTSM), which evaluates the system’s stability configuration and highlights both the stable and unstable features. Changes in bifurcation parameters have an impact on curvature of the bifurcation curve. Additionally, phase portraits, Poincaré maps, and bifurcation diagrams are used to perform a bifurcation analysis of the designated models and identify the different motions of the system.

The inspection of a cantilever beam subjected to parametric stimulation is essential in engineering structures such as bridges, aircraft wings, and micro electromechanical systems (MEMS). It is demonstrated that nonlinearities restrict the rise in accessibility. The existing issue mitigates vibrations in a structure exposed to primary parametric stimulation. It utilizes knowledge to develop a simple nonlinear feedback law designed to reduce vibrations of the first mode of a cantilever beam. The fundamental methodology relies on the non-perturbative approach (NPA), which is grounded in He’s frequency formula (HFF). This approach simply converts a weakly nonlinear oscillator of a second nonlinear ordinary differential equation (ODE) into a linear one. Consequently, the goal is to depart from traditional perturbation methods and get unrestricted approximation solutions of small amplitude parametric components. Furthermore, the method is extended to find the best solutions for large amplitude nonlinear fluctuations of coupled system. The generated parametric equation shows good agreement with the original equation when validated using the Mathematica Software (MS). The stability behavior is investigated across several contexts. The current methodology is founded on explicit principles, is suitable, user-friendly, and yields remarkably high numerical precision. The present approach reduces the mathematical difficulty, making it beneficial of the mathematical execution of nonlinear parametric issues. It is found that the system is stable with the increase of both linear and nonlinear damping coefficients, while it becomes less stable as excitation force’s parameters increase. Furthermore, the Poincaré map, phase portrait, and bifurcation are analyzed, which collectively provide a comprehensive depiction of the system’s behavior at different phases.

In this work, we studied the peristaltic motion of steady non-Newtonian nanofluid flow with heat transfer through a non-uniform inclined channel. The flow in this discussion obeys the power law model through a non-Darcy porous medium. Moreover, the effects of thermal radiation, heat generation, Ohmic dissipation and a uniform external magnetic field are taken in consideration. The governing equations that describe the velocity, temperature and nanoparticles concentration are simplified under the assumptions of long wave length and low-Reynolds number. These equations have been solved numerically by using Runge–Kutta–Merson method with the help of shooting and matching technique. The solutions are obtained as functions of the physical parameters entering the problem. The effects of these parameters on the obtained solutions are discussed and illustrated graphically through a set of figures. It is found that as Brownian motion parameter increases, the axial velocity decreases, whereas the nanoparticles concentration increases and it has a dual effect on the temperature distribution. Moreover, the axial velocity and temperature increase as Prandtl number increases, while the nanoparticles decrease.

A green, rapid, and simple RP-UPLC method was developed and optimized by full factorial design for the simultaneous separation of oseltamivir phosphate, daclatasivir dihydrochloride, and remdesivir, with dexamethasone as a co-administered drug. The separation was established on a UPLC column BEH C 18 1.7 µm (2.1 × 100.0 mm) connected with a UPLC pre-column BEH 1.7 µm (2.1 × 5.0 mm) at 25 °C with an injection volume of 10 µL. The detector (PDA) was set at 239 nm. The mobile phase consisted of methanol and ammonium acetate (8.1818 mM) in a ratio of 75.7: 24.3 (v/v). The flow rate was set at 0.048 mL min −1 . The overall separation time was 9.5 min. The retention times of oseltamivir phosphate, dexamethasone, daclatasivir dihydrochloride, and remdesivir were 6.323 ± 0.145, 7.166 ± 0.036, 8.078 ± 0.124, and 8.572 ± 0.166 min (eight replicates), respectively. The proposed method demonstrated linearity in the ranges of 10.0–500.0 (ng mL −1 ) and 0.5–30.0 (µg mL −1 ) for oseltamivir phosphate, 50.0–5000.0 (ng mL −1 ) for dexamethasone, 25.0–1000.0 (ng mL −1 ) and 0.5–25.0 (µg mL −1 ) for daclatasvir dihydrochlorde, and 10.0–500.0 (ng mL −1 ) and 0.5–30.0 (µg mL −1 ) for remdesivir. The coefficients of determination (R 2 ) were greater than 0.9999, with percentage recoveries greater than 99.5% for each drug. The limits of quantitation were 6.4, 1.8, 7.8, and 1.6 ng mL −1 , and the limits of detection were 1.9, 0.5, 2.0, and 0.5 ng mL −1 for oseltamivir phosphate, dexamethasone, daclatasivir dihydrochloride, and remdesivir, respectively. The proposed method was highly precise, as indicated by the low percentage of relative standard deviation values of less than 1.2% for each drug. The average content and uniformity of dosage units in the studied drugs' dosage forms were determined. The average contents of oseltamivir phosphate, dexamethasone, daclatasivir dihydrochloride, and remdesivir were nearly 93%, 102%, 99%, and 95%, respectively, while the uniformity of dosage unit values were nearly 92%, 102%, 101%, and 97%. Two novel methods were established in this work. The first method was used to assess the stability of standard solutions. This novel method was based on the slope of regression equations. The second was to evaluate the excipient's interference using an innovative instrumental standard addition method. The novel instrumental standard addition method was performed using the UPLC instrument program. It was more accurate, sensitive, time-saving, economical, and eco-friendly than the classic standard addition method. The results showed that the proposed method can estimate the tested drugs' concentrations without interference from their dosage form excipients. According to the Eco-score (more than 75), the Green Analytical Procedure Index (GAPI), and the AGREE criteria (total score of 0.77), the suggested method was considered eco-friendly.

The current study investigates the peristaltic transport of an incompressible micropolar non—Newtonian nanofluid following the Sutterby model. The heat and mass transfer inside the two-dimensional symmetric vertical channel is considered. The system is affected by a strong magnetic field together with thermal radiation, couple stress, chemical reaction, Joule heating, heat generation, Dufour, Soret and Hall current effects. The governing equations of motion are analytically solved by utilizing the long wavelength and low Reynolds number approximations. Furthermore, the resulted boundary—value problem is solved by means of the Homotopy perturbation method (HPM). An illustration of the influence of the various physical parameters in the foreign distributions; such as Hall currents, magnetic field, Sutterby, couple stress, Brownian motion, thermophoresis and slip parameters is obtained throughout a set of graphs and tables. It is observed that the axial velocity enhances with the increase in the Sutterby parameter. Furthermore, the temperature decreases with the larger values of a heat transfer Biot number. While, the concentration enlarges with the increase in the values of mass transfer Biot numbers. Moreover, the trapping phenomenon is discussed throughout a set of figures. This depicts the variation of the streamlines under the impact of couple stress, amplitude ratio, and magnetic field parameters. It is noticed that the size of the trapped bolus increases with the increase in the foregoing three parameters.

A green and simple UPLC method was developed and optimized, adopting a factorial design for simultaneous determination of oseltamivir phosphate and remdesivir with dexamethasone as a co-administered drug in human plasma and using daclatasvir dihydrochloride as an internal standard within 5 min. The separation was established on UPLC column BEH C 18 1.7 μm (2.1 × 100.0 mm) connected to UPLC pre-column BEH 1.7 μm (2.1 × 5.0 mm) at 50 °C with an injection volume of 10 μL. The photodiode array detector (PDA) was set at three wavelengths of 220, 315, and 245 nm for oseltamivir phosphate, the internal standard, and both dexamethasone and remdesivir, respectively. The mobile phase consisted of methanol and ammonium acetate solution (40 mM) adjusted to pH 4 in a ratio of 61.5:38.5 (v/v) with a flow rate of 0.25 mL min −1 . The calibration curves were linear over 500.0–5000.0 ng mL −1 for oseltamivir phosphate, over 10.0–500.0 ng mL −1 and 500.0–5000.0 ng mL −1 for dexamethasone, and over 20.0–500 ng mL −1 and 500.0–5000.0 ng mL −1 for remdesivir. The Gibbs free energy and Van't Hoff plots were used to investigate the effect of column oven temperatures on retention times. Fluoride-EDTA anticoagulant showed inhibition activity on the esterase enzyme in plasma. The proposed method was validated according to the M10 ICH, FDA, and EMA’s bioanalytical guidelines. According to Eco-score, GAPI, and AGREE criteria, the proposed method was considered acceptable green.