Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization.

By using the power-exponential function method and the extended hyperbolic auxiliary equation method, we present the explicit solutions of the subsidiary elliptic-like equation. With the aid of the subsidiary elliptic-like equation and a simple transformation, we obtain the exact solutions of Hirota equation which include bright solitary wave, dark solitary wave, bell profile solitary wave solutions and Jacobian elliptic function solutions. Some of these solutions are found for the first time, which may be useful for depicting nonlinear physical phenomena. This approach can also be applied to solve the other nonlinear partial differential equations.

Instability analysis for MHD boundary layer flow of nanofluid over a rotating disk with anisotropic and isotropic roughness.

The study focuses on the instability of local linear convective flow in an incompressible boundary layer caused by a rough rotating disk in a steady MHD flow of viscous nanofluid. Miklavcic and Wang's (Miklavcic and Wang, 2004) [9] MW roughness model are utilized in the presence of MHD of Cu-water nanofluid with enforcement of axial flows. This study will investigate the instability characteristics with the MHD boundary layer flow of nanofluid over a rotating disk and incorporate the effects of axial flow with anisotropic and isotropic surface roughness. The resulting ordinary differential equations (ODEs) are obtained by using von Kàrmàn (Kármán, 1921) [3] similarity transformation on partial differential equations (PDEs). Subsequently, numerical solutions are obtained using the shooting method, specifically the Runge-Kutta technique. Steady-flow profiles for MHD and volume fractions of nanoparticles are analyzed by the partial-slip conditions with surface roughness. Convective instability for stationary modes and neutral stability curves are also obtained and investigated by the formulation of linear stability equations with the MHD of nanofluid. Linear convective growth rates are utilized to analyze the stability of magnetic fields and nanoparticles and to confirm the outcomes of this analysis. Stationary disturbances are also considered in the energy analysis. The investigation indicates the correlation between instability modes Type I and Type II, in the presence of MHD, nanoparticles, and the growth rates of the critical Reynolds number. An integral energy equation enhances comprehension of the fundamental physical mechanisms. The factors contributing to convective instability in the system are clarified using this approach.

Entropy generation for exact irreversibility analysis in the MHD channel flow of Williamson fluid with combined convective-radiative boundary conditions.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall.

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique ([Formula: see text] as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

Fractional Nadeem trigonometric non-Newtonian (NTNN) fluid model based on Caputo-Fabrizio fractional derivative with heated boundaries.

The fractional operator of Caputo-Fabrizio has significant advantages in various physical flow problems due to the implementations in manufacturing and engineering fields such as viscoelastic damping in polymer, image processing, wave propagation, and dielectric polymerization. The current study has the main objective of implementation of Caputo-Fabrizio fractional derivative on the flow phenomenon and heat transfer mechanism of trigonometric non-Newtonian fluid. The time-dependent flow mechanism is assumed to be developed through a vertical infinite plate. The thermal radiation's effects are incorporated into the analysis of heat transfer. With the help of mathematical formulations, the physical flow system is expressed. The governing equations of the flow system acquire the dimensionless form through the involvement of the dimensionless variables. The application of Caputo-Fabrizio derivative is implemented to achieve the fractional model of the dimensionless system. An exact solution of the fractional-based dimensionless system of the equations is acquired through the technique of the Laplace transform. Physical interpretation of temperature and velocity distributions relative to the pertinent parameters is visualized via graphs. The current study concludes that the velocity distributions exhibit an accelerating nature corresponding to the increasing order of the fractional operator. Moreover, the graphical results are more significant corresponding to the greater time period.

A new type of radial basis functions for problems governed by partial differential equations.

The aim of this paper is to introduce a novel category of radial basis functions that incorporate smoothing techniques. Initially, we employ the power augmented and shape parameter schemes to create the radial basis functions. Subsequently, we apply the newly-constructed radial basis functions using the traditional collocation method and singular values decomposition algorithm to solve the corresponding linear system equations. Finally, we analyze several pairs of radial basis functions in depth to address physical problems linked to thermal science that are governed by partial differential equations. The numerical results demonstrate that the radial basis functions constructed using the power augmented and shape parameter schemes exhibit remarkable performance.

Oblique stagnation point flow of magnetized Maxwell fluid over a stretchable Riga plate with Cattaneo-Christov heat flux and convective conditions.

The current work deals with the oblique stagnation point flow phenomenon of a rate-type Maxwell fluid with the significance of the Cattaneo-Christov double diffusion theory. The Cattaneo-Christov theory is illustrated through the modified form of Fourier's and Fick's laws. The steady magnetized flow mechanism is observed in two dimensions through a stretchable convective Riga plate. In the mass and heat transfer analysis, the consequences of chemical reactions and thermal radiation are also incorporated. With the contribution of relevant dimensionless quantities, the setup of dimensionless equations is acquired which further takes the form of nonlinear equations. The physical significance of the numerous parameters on different features of the flow phenomenon is graphically exhibited. The interesting physical quantities are computed and numerically evaluated relative to the pertinent parameters. This study reveals that the thermal relaxation time parameter lowers the rate of heat transfer, and the thermal Biot number enhances the rate of heat transport. Moreover, the Deborah number minimizes the flow field of both tangential and axial velocities.

Effects of variable magnetic field and partial slips on the dynamics of Sutterby nanofluid due to biaxially exponential and nonlinear stretchable sheets.

Based on both the characteristics of shear thinning and shear thickening fluids, the Sutterby fluid has various applications in engineering and industrial fields. Due to the dual nature of the Sutterby fluid, the motive of the current study is to scrutinize the variable physical effects on the Sutterby nanofluid flow subject to shear thickening and shear thinning behavior over biaxially stretchable exponential and nonlinear sheets. The steady flow mechanism with the variable magnetic field, partial slip effects, and variable heat source/sink is examined over both stretchable sheets. The analysis of mass and heat transfer is carried out with the mutual impacts of thermophoresis and Brownian motion through the Buongiorno model. Suitable transformations for both exponential and nonlinear sheets are implemented on the problem's constitutive equations. As a result, the nonlinear setup of ordinary differential equations is acquired which is further numerically analyzed through the bvp4c technique in MATLAB. The graphical explanation of temperature, velocity, and concentration distributions exhibits that the exponential sheet provides more significant results as compared to the nonlinear sheet. Further, this study revealed that for the shear thickening behavior of Sutterby nanofluid, the increasing values of Deborah number increase the axial velocity.

The flow of an Eyring Powell Nanofluid in a porous peristaltic channel through a porous medium.

In a porous medium, we have examined sinusoidal two-dimensional transport enclosed porous peristaltic boundaries having an Eyring Powell fluid with a water containing [Formula: see text]. The determining momentum and temperature equations are solved semi-analytically by using regular perturbation method and Mathematica. In present research only free pumping case and small amplitude ratio is studied. Mathematical and pictorial consequences are investigated for distinct physical parameters of interest like porosity, viscosity, volume fraction and permeability to check the effects of flow velocity and temperature.

CFD analysis on blood flow inside a symmetric stenosed artery: Physiology of a coronary artery disease.

This research article interprets the computational fluid dynamics analysis on blood flow inside a symmetric stenosed artery. The current problem models the blood flow inside the left coronary artery as having a symmetric stenosis in the central region. A comprehensive physiological examination of coronary artery disease is numerically evaluated by using the computational fluid dynamics toolbox Open-Field Operation And Manipulation. There are no assumptions of mild stenosis taken into account since the considered stenosis has an exactly measured length, height and position, etc. The blood flow problem is modeled for the non-Newtonian Casson fluid with unsteady, laminar, and incompressible flow assumptions. The underlying problem is solved numerically in its dimensional form. A thorough graphical analysis is provided on the blood flow simulations, pressure profile, velocity line graphs, pressure line graphs, and streamlines for the left coronary artery having a symmetric stenosis formation. The considered artery is divided into three sections, i.e. pre-stenosis, post-stenosis, and stenosis region, and the velocity and pressure line graphs are plotted for these considered regions. The graphical illustrations provide a detailed analysis of how the blood flow is affected inside the left coronary artery due to coronary artery disease. These pre- and post-stenosis velocity line graphs reveal two intriguing results: In the pre-stenosis zone, the velocity increases with increasing axial coordinate length, whereas in the post-stenosis region, the velocity decreases with rising axial coordinate length. It is evident that as the flow moves toward the stenosis region, the flow profile rises; yet, after passing through the stenosis zone, the flow profile begins to fall as the flow moves away from the stenosis region.

Bismuth-Rich Co/Ni Bimetallic Metal-Organic Frameworks as Photocatalysts toward Efficient Removal of Organic Contaminants under Environmental Conditions.

Active photocatalysts with an efficiency of 99% were prepared for the degradation of the industrial dye, methylene blue (MB), under visible light irradiation. These photocatalysts comprised Co/Ni-metal-organic frameworks (MOFs), to which bismuth oxyiodide (BiOI) was added as a filler to prepare Co/Ni-MOF@BiOI composites. The composites exhibited remarkable photocatalytic degradation of MB in aqueous solutions. The effects of various parameters, including the pH, reaction time, catalyst dose, and MB concentration, on the photocatalytic activity of the prepared catalysts were also evaluated. We believe that these composites are promising photocatalysts for the removal of MB from aqueous solutions under visible light.

Source, occurrence, distribution, fate, and implications of microplastic pollutants in freshwater on environment: A critical review and way forward.

The generation of microplastics (MPs) has increased recently and become an emerging issue globally. Due to their long-term durability and capability of traveling between different habitats in air, water, and soil, MPs presence in freshwater ecosystem threatens the environment with respect to its quality, biotic life, and sustainability. Although many previous works have been undertaken on the MPs pollution in the marine system recently, none of the study has covered the scope of MPs pollution in the freshwater. To consolidate scattered knowledge in the literature body into one place, this work identifies the sources, fate, occurrence, transport pathways, and distribution of MPs pollution in the aquatic system with respect to their impacts on biotic life, degradation, and detection techniques. This article also discusses the environmental implications of MPs pollution in the freshwater ecosystems. Certain techniques for identifying MPs and their limitations in applications are presented. Through a literature survey of over 276 published articles (2000-2023), this study presents an overview of solutions to the MP pollution, while identifying research gaps in the body of knowledge for further work. It is conclusive from this review that the MPs exist in the freshwater due to an improper littering of plastic waste and its degradation into smaller particles. Approximately 15-51 trillion MP particles have accumulated in the oceans with their weight ranging between 93,000 and 236,000 metric ton (Mt), while about 19-23 Mt of plastic waste was released into rivers in 2016, which was projected to increase up to 53 Mt by 2030. A subsequent degradation of MPs in the aquatic environment results in the generation of NPs with size ranging from 1 to 1000 nm. It is expected that this work facilitates stakeholders to understand the multi-aspects of MPs pollution in the freshwater and recommends policy actions to implement sustainable solutions to this environmental problem.

Reynolds nano fluid model for Casson fluid flow conveying exponential nanoparticles through a slandering sheet.

Nanofluids with their augmented thermal characteristics exhibit numerous implementations in engineering and industrial fields such as heat exchangers, microelectronics, chiller, pharmaceutical procedures, etc. Due to such properties of nanofluids, a mathematical model of non-Newtonian Casson nanofluid is analyzed in this current study to explore the steady flow mechanism with the contribution of water-based Aluminum oxide nanoparticles. A stretchable surface incorporating variable thickness is considered to be the source of the concerning fluid flow in two-dimension. An exponential viscosity of the nanofluid is proposed to observe the fluid flow phenomenon. Different models of viscosity including Brinkman and Einstein are also incorporated in the flow analysis and compared with the present exponential model. The physical flow problem is organized in the boundary layer equations which are further tackled by the execution of the relevant similarity transformations and appear in the form of ordinary nonlinear differential equations. The different three models of nanofluid viscosity exhibit strong graphical and tabulated relations with each other relative to the various aspects of the flow problem. In all concerned models of the viscosity, the deteriorating nature of the velocity field corresponding to the Casson fluid and surface thickness parameters is observed.

Numerical simulation for peristalsis of Quemada fluid: A dynamic mesh approach.

INTRODUCTION: Flow dynamics due to the peristaltic pumping has been the topic of great interest for the researchers. But numerical and analytical analyses for the peristaltic motion are limited where flow domain is deformed real-time. Research on peristalsis has a limitation where theoretical aspects of walls motion are considered, neglecting the real time deformation of the walls. OBJECTIVES: This paper aims to propose a more reliable and accurate numerical methodology for peristaltic motions to address the above-mentioned challenge. Stream traces, velocities, and pressure drops along the tube is to be visualized more accurately. METHODS: In present study a finite volume based dynamic mesh motion method is adopted to analyze the peristaltic motion of a non-Newtonian Quemada fluid in an axisymmetric channel. The walls and interior domain of the channel is dynamically deformed for a sinusoidal wave traveling on boundary. RESULTS: Simulation of unsteady flow behavior for time t=0s to 2s and amplitude ratio Φ=0.2,0.4,and0.6. predicts fluid trapping phenomenon. Rotation of fluid particles is more prominent for higher amplitude ratios. Pressure gradient increases with increasing amplitude ratios. CONCLUSION: A novel dynamic mesh method is proposed for peristaltic pumping. It provides more accurate and more physical results for stream traces; pressure drops and velocities along the tube. A limited case of the study validates the theoretical and analytical results already presented in literature; hence the method is reliable.

Correction: CO2 free production of ethylene oxide via liquid phase epoxidation of ethylene using niobium oxide incorporated mesoporous silica material as the catalyst.

[This corrects the article DOI: 10.1039/D2RA07240H.].

CO2 free production of ethylene oxide via liquid phase epoxidation of ethylene using niobium oxide incorporated mesoporous silica material as the catalyst.

Ethylene Oxide (EO) is an essential raw material used in various consumer products like different glycol derivatives, ethoxylates, and polymers. We hydrothermally synthesize niobium oxide incorporated with mesoporous silica material (Nb/MSM), an efficient catalyst for CO2 free-ethylene oxide (EO) production via partial oxidation of ethylene. The structural properties of Nb/MSM catalysts were characterized using XRD, TEM, and N2 adsorption-desorption. The catalytic activity of synthesized materials in liquid phase epoxidation (LPE) of ethylene was evaluated in the presence of peracetic acid (PAA) as an oxidant to avoid the production of CO2 and also minimize metal leaching. GC chromatography was used to investigate the successful production of EO, and a peak with a retention time (RT) of 9.01 min served as confirmation. Various reaction parameters viz. temperature, catalyst concentration, ethylene to PAA molar ratio, and solvent effect were investigated in order to optimize the reaction conditions for enhancing the ethylene conversion and selectivity for EO production. By this approach, the challenges of greenhouse gas production and metal leaching were addressed which were associated with previously reported catalysts.

Carbon Nanotube Fiber-Based Flexible Microelectrode for Electrochemical Glucose Sensors.

Electrochemical sensors are gaining significant demand for real-time monitoring of health-related parameters such as temperature, heart rate, and blood glucose level. A fiber-like microelectrode composed of copper oxide-modified carbon nanotubes (CuO@CNTFs) has been developed as a flexible and wearable glucose sensor with remarkable catalytic activity. The unidimensional structure of CNT fibers displayed efficient conductivity with enhanced mechanical strength, which makes these fibers far superior as compared to other fibrous-like materials. Copper oxide (CuO) nanoparticles were deposited over the surface of CNT fibers by a binder-free facile electrodeposition approach followed by thermal treatment that enhanced the performance of non-enzymatic glucose sensors. Scanning electron microscopy and energy-dispersive X-ray analysis confirmed the successful deposition of CuO nanoparticles over the fiber surface. Amperometric and voltammetric studies of fiber-based microelectrodes (CuO@CNTFs) toward glucose sensing showed an excellent sensitivity of ∼3000 µA/mM cm2, a low detection limit of 1.4 µM, and a wide linear range of up to 13 mM. The superior performance of the microelectrode is attributed to the synergistic effect of the electrocatalytic activity of CuO nanoparticles and the excellent conductivity of CNT fibers. A lower charge transfer resistance value obtained via electrochemical impedance spectroscopy (EIS) also demonstrated the superior electrode performance. This work demonstrates a facile approach for developing CNT fiber-based microelectrodes as a promising solution for flexible and disposable non-enzymatic glucose sensors.

Entropy analysis for a novel peristaltic flow in a curved heated endoscope: an application of applied sciences.

Entropy interpretation with a descriptive heat generation analysis is carried out for the heated flow between two homocentric and sinusoidally fluctuating curved tubes. A novel peristaltic endoscope is considered for the first time inside a curved tube with evaluation of heat transfer and entropy. This flexible and novel endoscope with peristaltic locomotion is more efficient for endoscopy of complex mechanical structures and it is more comfortable for patients undergoing the endoscopy of a human organs. A comprehensive mathematical model is developed that also completely evaluates the heat transfer analysis for this novel endoscope. Certain and systematic computations are performed with the help of Mathematica software and exact mathematical as well as graphical solutions are obtained. Entropy has a lower rate that is almost zero entropy in the central region of these two curved tubes, but maximum entropy is noted near the sinusoidally deformable walls of both the endoscope and channel.

Photocatalytic degradation of industrial dye using hybrid filler impregnated poly-sulfone membrane and optimizing the catalytic performance using Box-Behnken design.

Mixed Matrix Membranes have gained significant attention over the past few years due to their diverse applications, unique hybrid inorganic filler and polymeric properties. In this article, the impregnation of nano-hybrid filler (polyoxometalates (∼POMs) encapsulated into the metal-organic framework (MOF) âˆ¼ PMOF) on the polysulfone membrane (∼PSF) was done, resulting in a mix matrix membrane (∼PMOF@PSF). The developed structure was characterized by Fourier transform infrared (FT-IR), powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), scanning electron microscopy (SEM), and transmission electron microscopes (TEM). The results confirmed that the nano-hybrid filler was successfully fabricated on the surface of PSF. Different loading ratios of nano-hybrid filler (5%, 10%, 20%, 30%, and 40%) were used for impregnation. The study's objective was to enhance catalytic performance using optimization curves designed using a three-level Box-Behnken Design (BBD) simulation. The photodegradation of Methylene Blue (∼MB) was studied against PMOF@PSF30% and was found to perform optimally when the concentration of catalyst, time of degradation, and temperature were 0.05-0.15 gm, 40-120 min, and 30-70 °C respectively. These experiments were replicated 15 times, and obtained results were further processed using a two-quadratic polynomial model to develop response surface methodology (RSM), which allowed for a functional relationship between the decolorization and experimental parameters. The optimal performance of the reaction mixture was calculated to be 0.15 gm for concentration, 70 °C for temperature, with an 80 min reaction time. Under these optimal conditions, the predicted decolorization of MB was 98.09%. Regression analysis with R2 > 0.99 verified the fit of experimental results with predicted values. The PMOF@PSF PSF30% demonstrated excellent reusability as its dye degradation properties were significantly unaffected after ten cycles.