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Fractional‐order ray equations and fractional Duffing‐van der Pol oscillator equations are relationships utilized as a reliable means of modeling some phenomena in optics and engineering. The main motivation of this study is to introduce a new hybrid technique utilizing Chelyshkov wavelets and least squares‐support vector regression (LS‐SVR) for determining the approximate solution of fractional ray equations and fractional Duffing‐van der Pol oscillator equations (D‐v POEs). With the help of the Riemann‐Liouville operator for Chelyshkov wavelets and LS‐SVR (called Chw‐Ls‐SVR), the mentioned problems transform into systems of algebraic equations. The convergence analysis is discussed. Finally, the numerical results are proposed and compared with some schemes to display the capability of the numerical technique proposed here. [ABSTRACT FROM AUTHOR]

The improve design and enhanced thermal management systems nowadays depends upon the enhanced heat transfer capabilities of hybrid nanofluids and their wide range of applications. These lead to efficient cooling in electronic devices, thermal control in chemical processing, and several many industrial as well as biomedical applications. The proposed study aims to enrich the heat transfer characteristic of methanol-based hybrid nanofluid comprising CuO and MgO nanoparticles in convergent and divergent channels. The study focuses on the Jeffery–Hamel flow via porous medium where the impact of heat source is analyzed. The flow behavior is characterized by the role of several pertinent factors those are derived by the implementation of similarity variables in the governing equations. These rules help in transforming the dimensional form of set of equations into non-dimensional form. Numerical solution is presented for the set of equations by using bvp4c routine function in MATLAB particularly utilizing Runge–Kutta fourth-order. However, the investigation explores the key factors such as particle concentration, Reynolds number, Darcy parameter and heat source affecting various flow characteristic. The important results indicate that the existence of CuO and MgO nanoparticles significantly overshoots the conductivity and heat transfer rate in comparison with the base fluid. Further, the fluid velocity is significantly controlled by the increasing Reynolds number. [ABSTRACT FROM AUTHOR]

The investigation of velocity slip combined with the dissipative heat corresponds to the non-Newtonian Williamson hybrid nanofluids utilizing the "Cattaneo-Christov heat flux model" is crucial in advanced applications in several sectors. The proposed analysis focuses on the hybrid nanofluid comprised of magnesium oxide (MgO) and zirconium dioxide (ZrO2) in water which boosts the thermal conductivity along with the performance of the fluid. The magnetized Williamson fluid is a particular type of non-Newtonian fluid that exhibits essential applications to biomedical engineering. The insertion of magnetization along with porosity suggests considering the dissipative heat impact associated with Joule and Darcy which energies the heat transport phenomena. The limitation of classical Fourier laws is addressed by the consideration of the Cattaneo–Christov heat flux framework along with the thermal radiation. The designed flow model with dimensional terms is transformed into a corresponding non-dimensional form by implementing similarity functions. Further, these transmuted equations are solved numerically via the shooting-based Runge–Kutta technique. The parametric analysis of the flow phenomena is obtained and arranged graphically. The validation with earlier investigation displays a valid association in particular scenarios. The main outcomes reveal that the resistivity characteristics produced by the interplay between permeability and magnetization regulate fluid velocity, especially when combined with the non-Newtonian Williamson parameter. Furthermore, in both nanofluid and hybrid nanofluid scenarios, the fluid temperature is greatly raised by the effects of thermal radiation and the Eckert number. [ABSTRACT FROM AUTHOR]

A broad and impactful application in designing and optimizing thermal system in engineering is due to the utility of the nanoparticles. These include advanced cooling technologies in electronics and enhanced recovery processes where managing heat flow in porous medium. Based on the above-mentioned features and utilities, a study is carried out in examining the flow characteristics involving the Marangoni convection of a radiative tri-hybrid nanofluid passing via a Riga plate by considering the variable thermal conductivity and the effect of Darcy–Forchheimer inertial drag. The incorporation of heat source/sink relating to both space and temperature dependent with the imposition of a magnetic field enriches the flow phenomena of a nanofluid consisting of composite nanoparticles. The thermal properties combined with the effect of thermal conductivity, density, etc., enrich the transport phenomena. The utilization of the specific similarity rules is effective in transforming the designed model into a dimensionless. Further, a numerical technique is introduced for the solution of these transmuted equations and the numerical values correlating to the established results show a good relationship in a particular case. The important characteristics of several factors about the flow phenomena are presented briefly through graphs. The observations reveal that the enhanced Hartmann number gives rise to increase the fluid velocity and the radiative heat for the inclusion of thermal radiation also favours in enhancing the fluid temperature. [ABSTRACT FROM AUTHOR]

The roles of nanoparticles and geometric effects are incredible in nanotechnology. The significant prospective of nanoparticles can be found in the manufacturing of machineries, heating/cooling of nuclear reactors, chemical and thermal engineering, mechanical and aerodynamics, etc. Thus, the current model study is performed for the heat transport mechanism in a newly engineered ternary nanofluid model for sinusoidal surface. The conventional model was updated via influences of ternary nanoparticles, transient phenomena, radiation and heat generation effects, convective and thermal slip impacts. The primary governing laws are reduced into the desired model form via transient similarity expressions and ternary nanoliquid models. Afterward, the shooting scheme supportive by RK technique is endorsed for physical configuration of the model dynamics under multiple ranges of the parameters. The outcomes revealed that both the components of velocity showed different behaviors for nodal and saddle points against the nodal-saddle parameter s1 that is, in the saddle case the velocity is decreased while in the nodal case its value is boosted when the value of s1 is slightly increased. Further, the temperature of the fluid is increased when Q1 and Rd varied from 0.1 to 0.7. Further, the skin friction augments from 119.5% to 121.55%, 121.54% to 129.15% when s1 and st vary from 0.1 to 0.5, respectively. The Nusselt number improved from 12.2124% to 12.218% (for nanoparticles concentration), 11.9109% to 11.7996% (for heating source Q1 from 0.2 to 0.5) and increased from 22.3815% to 47.5804% (for Biot number variations from 0.2 to 0.5). Hence, the Biot number highly contributes to the heat transfer rate than other parameters. [ABSTRACT FROM AUTHOR]

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of a model called the (2 + 1) q -deformed tanh-Gordon model. This model is particularly useful for studying physical systems with violated symmetries, as it provides insights into their behavior. To solve the (2 + 1) q -deformed equation for specific parameter values, the (H + G ′ G 2) -expansion approach is employed. This technique generates analytical solutions that reveal valuable information about the system's dynamics and behavior. These solutions offer insights into the underlying mathematics and deepen the understanding of the system's properties. To validate the accuracy of the analytical solutions, the finite difference technique is also used to find a numerical solution to the q -deformed equation. This numerical approach ensures the correctness of the solutions and enhances the reliability of the results. Tables and graphics are presented in the publication to aid comprehension and comparison. These visuals improve the clarity and interpretability of the data, allowing readers to better understand the similarities and differences between the analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of TiO 2 and Fe 3 O 4 nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the Fe 3 O 4 nanoparticles. The HNF ( TiO 2 + Fe 3 O 4 ∕ H 2 O) exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid ( Fe 3 O 4 ∕ H 2 O) for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement. [ABSTRACT FROM AUTHOR]

The study of squeezing fluids is considered to be one of the most important areas of scientific research due to its various engineering and bioapplications such as the squeezing processes that occur in the brake mechanisms in trucks and Piston’s systems, liquid metal lubrication systems, polymer processing and compression/injection molding as well as the contraction processes in the arteries and veins. This work deals with the study of one of these applications through modeling using the basic equations governing the squeezing fluids and their boundary conditions, and the presence of some external thermal influences such as the magnetic field and linear/nonlinear thermal radiation in its basic form as a nonlinear partial differential equations system, then converting this system into nonlinear ordinary differential equations that were solved numerically and analytically for special cases. The results focused on showing the thermal and flow behavior of the fluid at different concentrations of nanoparticles, which induce the effect of thermal forces represented by the magnetic field and thermal radiation. These results were demonstrated through a set of graphs and tables and discussed in detail, and in summary, some important results were found from the physical analysis. For some of these results, the use of different types and concentrations of particles increases the viscosity of the fluid, which causes an increase in temperature ranging between 17% and 45%. [ABSTRACT FROM AUTHOR]

An investigation is proposed for the Buongiorno model nanofluid flow within a converging as well as diverging channel which is inclined with the plane walls. The impact of magnetization is reported for the imposed of applied magnetic field along the normal direction of the flow. Additionally, the behavior of thermal radiation and the effect of binary chemical ration are implemented in the energy and concentration equation respectively. It is superimposed that both the channel walls are uniformly heated, and it is also assumed that concentration of the nanoparticles near the walls is considered as constant. However, the Cartesian coordinate system is imposed to describe the proposed designed flow problem. The formulated problem governed by nonlinear coupled partial differential equations is generalized and renovated to corresponding nondimensional form by implementing appropriate similarity rules. Further, the transformed equations are solved numerically using Runge-Kutta fourth order accompanied by shooting technique. The physical behavior of the standard factors involved in the problem is displayed graphically. Validation of the result is presented with an earlier study which shows a good correlation as well as convergence analysis of the proposed methodology. Further, the important outcomes of the proposed study are deployed as follows: the velocity distribution retards for the enhanced Reynolds number significantly; however, the Brownian motion is treated as a controlling parameter for the fluid temperature and reverse impact observed in case of fluid concentration. • The Buongiorno model nanofluid flow within a converging and diverging channel inclined with the plane walls is analysed. • The behaviour of not only thermal radiation but also the effect of binary chemical ration is implemented. • It is superimposed that both the channel walls are uniformly heated and it is also assumed that concentration of the nanoparticles near the walls is considered as constant. • The transformed equations are solved numerically using Runge-Kutta fourth-order accompanied by shooting technique. [ABSTRACT FROM AUTHOR]

In various industrial vis-a-vis technological applications, the study of squeezing flow of carbon nanotube (CNT) nanofluid past along the Riga surface is vital. The present article aims in examining the role of velocity slip in two distinct cases considering the flow of CNT–water and CNT–kerosene nanofluid over a Riga-squeezing surface. The Riga surface generates Lorentz force and provides a platform for enhancing heat transfer characteristics. Additionally, the inclusion of dissipative heat along with radiant heat and irregular heat supplier energies the heat transport phenomenon. The mathematical model endorsed with dimensional features is transmuted into nondimensional form by the implementation of similarity rules, and the results of several flow profiles are manipulated by employing the traditional “Runge–Kutta fourth-order” along with shooting scheme. The parametric analysis is presented through graphs, and the validation with earlier investigation is depicted via tabular form representing the numerical results in the particular case.

Summary This paper contributes to the study of a new model called the q$$ \mathfrak{q} $$‐deformed equation or the q$$ \mathfrak{q} $$‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the G′kG′+G+r$$ \left(\frac{{\mathcal{G}}^{\prime }}{k{\mathcal{G}}^{\prime }+\mathcal{G}+r}\right) $$‐expansion approach to solve the q$$ \mathfrak{q} $$‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the q$$ \mathfrak{q} $$‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The q$$ \mathfrak{q} $$‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the q$$ \mathfrak{q} $$‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of q$$ \mathfrak{q} $$‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features. [ABSTRACT FROM AUTHOR]

The conversion of heat from the mechanical energy in a fluid basically depends upon the internal friction and the effect of viscosity. Joule dissipation along with Darcy frictional force that is used as a measure of the resistance to flow in a porous medium has an important role in various systems. Therefore, the present article aims to investigate the characteristic of velocity slip considering the flow of radiative hybrid nanofluid over an elongating and contracting surface. The flow file enriches for the inclusion of both the Joule, i.e., magnetic dissipation and the Darcy dissipation, in the energy equation. The complex system then transformed to ordinary as well as nondimensional form due to the adoption of particular similarity rules. Further, a traditional numerical technique equipped with shooting-based Runge–Kutta is used for the solution of the transformed designed model. The present model is validated with the earlier established system in the particular case of base fluid water with good agreement, and the parametric behavior is projected via several graphs and streamlines. However, the important outcomes of the study are presented as the concentration of solid nanoparticles that controls the velocity profiles, whereas the reverse trend is revealed in fluid temperature. Further, suction/injection provides greater control in decelerating the fluid velocity for the interaction of velocity slip. [ABSTRACT FROM AUTHOR]

AbstractMany industrial and thermal systems regard continuous thermal propagation as vital because it may improve the efficacy of thermal engineering machinery and engines. Consequently, this is a potential development for bettering power energy through employing magnetized nanomolecules within a heat-carrying non-Newtonian fluid. This study examines nanofluids with Casson and Maxwell nanofluids by considering nonlinear radiation and heat generation because of bioconvection over a stretchable surface with a porous material. Moreover, the interaction between gyrotactic microorganisms and activation energy has been discussed in detail. The flow model under consideration is formulated via Thermophoretic diffusion and Brownian motion. Using similarity conversions, the regulating partial differential equations (PDEs) are made dimensionless, thus reducing them to ordinary differential equations. A shooting technique was employed to solve the problem; MATLAB software used RK methods combined with the shooting method to solve this problem. Many diagrams have been depicted to describe the diverse flow factors; other interesting quantities, such as motile microbes’ density and Sherwood numbers, are computed and plotted. In addition, mixed convection, buoyancy ratio, bioconvection Rayleigh constant, and resistivity due to magnetized significantly affect velocity profile through Casson–Maxwell nanofluid. It is seen that both Casson and Maxwell fluids have nonuniform boundary layers of temperature and concentration fields. Maxwell fluids’ temperature and concentration fields are more sensitive than Casson fluids toward the same parameters. [ABSTRACT FROM AUTHOR]

This paper enchases the performance of the inertial drag on the Buongirino model nanofluid flow past a curved stretching surface embedding within a permeable medium. The radiating heat transport property for the interaction linear approach of Rosseland thermal radiation vis-à-vis reacting species enriches the flow behavior. Further, this study is novel due to the consideration of convective boundary conditions for both the energy and solutal bounding surface condition in association with the slip velocity condition. In a practical situation, when the fluid and surface temperature are different, it is wise not to neglect the convective boundary conditions. The application of convective conditions is useful for the fabrication of the final product in the manufacturing processes. Further, the renovation of the proposed model is obtained for the suitable assumption of the similarity transformation. Traditional numerical technique, i.e., fourth-order shooting-based Runge–Kutta is the best choice for the solution of the set of the transformed equation for the assumed parameters within their specified range. Velocity contour for different parameters vis-à-vis the parametric behavior is presented graphically. Numerical validation as well as the statistical testing for the rate coefficients are the novel approaches of this study. However, interesting outcomes are deployed as follows: The enhanced Brownian and thermophoresis both encourage the fluid temperature, whereas thermophoresis decelerates the fluid concentration. [ABSTRACT FROM AUTHOR]

This study warrants a broad analysis on the simultaneous effects of Brownian and thermophoresis on the chemically reacting Williamson nanofluid flow via a permeable expanding sheet. The analysis includes the properties of slip velocity and thermal radiation, providing a more representative picture of the physical phenomena. The differential equations governed by demonstrating the fluid flow phenomena are renewed to a set of nonlinear differential equations utilizing similarity rules. These transformed equations are subsequently handled numerically adopting the fourth-order Runge-Kutta method. The results reveal the significant control of Brownian motion together with thermophoresis and additionally, the inclusion of velocity slip and thermal radiation remarkably affect the velocity, temperature, and concentration distributions. Parametric studies show the validation of the present system to variations in the Williamson fluid parameter, slip parameter, radiative heat parameter, Brownian motion parameter, and thermophoresis parameter.

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature. [ABSTRACT FROM AUTHOR]

An acute bacterial infection called avian spirochetosis is spread by ticks to a variety of birds. Clinical symptoms can vary greatly and are frequently non-specific. To diagnose a condition, the infectious spirochete must be detected. Here, we structure an epidemic model for the transmission of avian spirochetosis to visualize the interaction between tick and bird populations. The recommended dynamics of avian spirochetosis is illustrated with the help of fractional framework. We inspected the steady-states of the system of the avian spirochetosis for the stability analysis. The next-generation technique is used to evaluate the model's reproduction parameter R 0. The infection-free and endemic steady-state of avian spirochetosis were shown to be locally asymptotically stable under the specified conditions. Through mathematical skills, the positivity of solutions is determined. Additionally, evidence supporting the existence and uniqueness of the avian spirochetosis framework solution has been shown. We conduct modified simulations of the suggested avian spirochetosis system with different input factors to study the complex phenomena of avian spirochetosis under the effect of numerous input parameters. Our outcomes illustrate the significance and plausibility of fractional parameter, and they also suggest that this input parameter may adequately account for these kinds of observations. [ABSTRACT FROM AUTHOR]

The paper is devoted to the comparative analysis of different CFD techniques used to solve the problem of high-pressure hydrogen release into the air. Three variations of a contemporary low-dissipation numerical technique (CABARET) are compared with each other and a conventional first-order numerical scheme. It is shown that low dissipation of the numerical scheme defines better resolution of the contact surface between released hydrogen and ambient air. As a result, the spatial structures of the jet and the reaction wave that arise during self-ignition are better resolved, which is useful for predicting the local effects of high-pressure hydrogen release. At the same time, the dissipation has little effect on the induction delay, so critical conditions of self-ignition can be reliably reproduced even via conventional numerical schemes. The test problem setups formulated in the paper can be used as benchmarks for compressible CFD solvers. [ABSTRACT FROM AUTHOR]

This paper studies the recent flow phenomena based upon the kerosene-based nanofluid through vertical parallel channel for the consideration of the variable thermal conductivity. The free convection of electrically conducting MHD fluid due to the interaction of inertial drag along with thermal radiation, heat source and the dissipative heat enriches the study as well. The structural behavior of the physical quantities is useful in recent applications like the cooling processes in refrigerators, semi-cryogenic rocket engine, etc. because of the practical application of the kerosene-based nanofluid. Also, the models associated with the thermophysical properties such as viscosity and thermal conductivity for the choice of volume concentration are favorable for the thermal enhancement. The designed model for the transport phenomena is transformed to its non-dimensional form for the suitable choice of similarity variables and the set of equations are handled by traditional numerical technique. Further, the involvement of the physical parameters and their physical significance is described briefly for the appropriate values within the specified range. Finally, the important outcomes of the study are that nanoparticle concentration has vital role in decelerating the fluid velocity and the fact is due to the heavier density and the inclusion of porous matrix is useful to retard the wall thickness at both the ends. Moreover, the increasing concentration favors in enhancing shear rate at the first wall whereas near the second wall, the impact is opposite. [ABSTRACT FROM AUTHOR]

The study focuses on the flow characteristics with geometrical considerations utilizing electrical-conduct Non-Newtonian Fluid. The tubular concentric annulus is the geometry selected for the investigation. The electric-conductive Non-Newtonian Fluid is a character-wise two-constant Bingham model used in this study. The study also utilized geometry, the magnetohydrodynamic (MHD) effect, and the hall current. The employed system had the inner tube spinning and the outer tube stationary. Prandtl's assumptions of boundary layer principles are applied to solve the governing equations using the finite difference method for various fluid flow parameters, the Gauss-Elimination method to compute the results, and the MHD field and geometrical factors with hall current. This paper discusses fluid flow properties such as axial, radial, tangential velocities, and pressure distribution. Further, the mentioned above flow properties impact the heat transfer effect. This research details how flow parameters in the concentric tube flow process affect the development of heat transfer effects in the MHD field and hall current. [Display omitted] • The development of MHD flow and heat transport have been studied computationally. • The impact of Hall current and Magnetic effect on the flow field has been considered. • This work refers to the non-Newtonian fluid as a two-constant yield stress fluid model. • The heat transfer impact has been calculated using the fluid flow properties. • This work has been done using a variety of fluid and geometric factors. [ABSTRACT FROM AUTHOR]

Ordinary Differential Equations (ODEs) play a crucial role in various scientific and professional domains for modeling dynamic systems and their behaviors. While traditional numerical methods are widely used for approximating ODE solutions, they often face challenges with complex or nonlinear systems, leading to high computational costs. This study aims to address these challenges by proposing an artificial neural network (ANN)-based approach for solving first-order ODEs. Through the introduction of the ANN technique and exploration of its practical applications, we conduct numerical experiments on diverse first-order ODEs to evaluate the convergence rate and computational efficiency of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the ANN-generated responses, confirming its reliability and potential for various applications in solving first-order ODEs with improved efficiency and accuracy.

The study of the stress-strain state and bearing capacity of compressed reinforced concrete elements of the annular section is of urgent importance, considering the ever-growing need to improve and optimise infrastructure facilities, such as bridges and supports, to ensure their reliability and safety. The purpose of this study is to investigate and analyse the stress-strain state of compressed reinforced concrete elements of annular section in order to determine their bearing capacity and improve the efficiency of design and construction of infrastructure facilities. The analytical method, classification, functional, statistical, synthesis, and other methods used in the paper should be highlighted. Compressed reinforced concrete elements of annular cross-section are widely used in various fields of engineering and construction. However, since the 90s of the 20th century, there has been a noticeable development of nonlinear deformation theory for the calculation of reinforced concrete structures, which complicates the analysis due to the specific features of round and annular sections and leads to the absence of simple analytical methods. This study presents an effective numerical technique for investigating the stress-strain state and bearing capacity of non-centrally compressed elements, using a linear fractional dependence for concrete under compression, approved in the Eurocode, and a symmetrical two-line diagram of reinforcement deformation. It is important to emphasise that this methodology avoids the need to classify elements as short or long, and to separately account for small and large eccentricities, as these aspects are automatically considered in the calculations. Confirmation of the effectiveness of this technique was obtained through the results of numerical experiments. The practical significance of this research lies in the development of more accurate and reliable methods for calculating and designing compressed reinforced concrete elements of annular section, which contributes to increasing the safety and durability of infrastructure facilities and reducing the risk of destruction

In various industrial vis-a-vis technological applications, the study of squeezing flow of carbon nanotube (CNT) nanofluid past along the Riga surface is vital. The present article aims in examining the role of velocity slip in two distinct cases considering the flow of CNT–water and CNT–kerosene nanofluid over a Riga-squeezing surface. The Riga surface generates Lorentz force and provides a platform for enhancing heat transfer characteristics. Additionally, the inclusion of dissipative heat along with radiant heat and irregular heat supplier energies the heat transport phenomenon. The mathematical model endorsed with dimensional features is transmuted into nondimensional form by the implementation of similarity rules, and the results of several flow profiles are manipulated by employing the traditional "Runge–Kutta fourth-order" along with shooting scheme. The parametric analysis is presented through graphs, and the validation with earlier investigation is depicted via tabular form representing the numerical results in the particular case. [ABSTRACT FROM AUTHOR]

Unsteady incompressible Sutterby fluid model is considered. The comparative results of stretching cylinder and sheet have been studied. The induced magnetic field is considered in the presence of thermal slip. Darcy resistance and viscos dissipation impacts have been studied. The thermal conductivity of liquid has considered as variable under the thermal radiation. The governing model of presence study have been developed under boundary layer approximation in term of partial differential equations. The differential equation become dimensionless by means of transformations. The dimensionless system have been solved through numerical procedure. Involving factor of physical influence presented in the form of tabular as well as graphical. Fluid temperature boosted up due to larger values of variable thermal conductivity. Physically, the thermal conductivity of liquid increased as well as variable thermal conductivity liquid enhanced as the temperature of fluid improved. The momentum layer thickness of stretching cylinder achieved mover than stretching sheet. The fluid velocity curves achieved higher thickness for boosting values of Darcy resistant factor. The velocity fluid curves revealed declining by increasing the Sponginess factor. Fluid temperature boosted up due to larger values of Eckert number.

The study uses Tiwari and Das’ nanofluid model to present a study on free convective flows in a right-angled trapezoidal cavity that is saturated with a porous bed and filled with Cu-water nanofluid material. This investigation aims to enhance the characteristics of hybrid fuel cells and energy depository devices by analysing the cavity's heat expansion and fluid flow properties. In trapezoidal enclosures, the inclined and right wall portions are maintained at different isothermal temperatures at all times. Finite difference-based stream function-vorticity numerical simulations are employed to carry out this analysis. The outcomes have been presented for isotherms, streamlines, and Nusselt numbers concerning nanoparticle volume fraction, Darcy number, and various Rayleigh numbers. It is found that the inverse relationship between the thermal Rayleigh number and the nanofluid’s volume has a significant impact on the average Nusselt number.

The consequence of thermal radiation vis-a-vis external heat generation/absorption on the inertial drag force of a hybrid nanoliquid flow in three-dimensional geometry is investigated. It is proposed that with the symmetric or non-symmetric particle shape, the velocity differs because of the direction of the drag. Furthermore, the conducting fluid for the interaction of the magnetic field through a permeable medium past an expanding surface influences the flow phenomenon. The present analysis is useful for the dialysis of blood in the artificial kidneys, the flow of blood in capillaries as well as the design of filters in engineering problems. However, the formulated problem is transformed into its non-dimensional form for the implementation of particular similarity rules. The set of nonlinear governing equations with specific contributing parameter values is subjected to handle by employing shooting-based Runge–Kutta fourth-order technique. Because of the system's irreversibility, the simulation of entropy and the Bejan value is the main draw. For each profile, the graphical results of specific parameters such as momentum, temperature, entropy, and the Bejan number are shown. Further, the important outcomes are the axial and the transverse velocity profiles are restricted by the inclusion of volume concentration in association with magnetic field and the enhanced Brinkman number augments the entropy generation significantly. However, the numerical validation shows a good correlation between the earlier investigations in particular cases. [ABSTRACT FROM AUTHOR]

Drinking or recreating water that has been polluted with disease-causing organisms or pathogens is what causes waterborne infections. It should be noted that many water-borne infections can also transmit from person to person, by contact with animals or their surroundings, or by ingesting tainted food or beverages. Schistosomiasis is a water-borne infection found in different areas of the globe. Mostly people with this viral infection live in Africa with limited resources and medications. Therefore, investigation of this infection is significant to reduce its economic burden on the society. We formulated a novel epidemic model for schistosomiasis water-borne infection with the help of the Atangana–Baleanu derivative. The rudimentary theory of fractional-calculus has been presented for the analysis of our system. We start by looking at the model solution's non-negativity and uniqueness. The basic reproduction number and equilibria of the hypothesized water-borne infection model are next evaluated. Local stability of the infection-free steady-state has been established through Jacobian matrix method for R 0 < 1. In addition, the suggested model's solution is calculated using an iterative technique. Finally, we give numerical simulations for various input values to illustrate the impact of memory index and other input factors of the system. Our findings showed the influence of input parameters on the dynamical behaviour of the schistosomiasis infection. The results demonstrate the importance and persuasive behaviour of fractional order, and reveal that fractional memory effects in the model seem to be a good fit for this type of findings. [ABSTRACT FROM AUTHOR]

In this present work, we report the synthesis of RGO-PVDF nanopowder using the classical hydrothermal reaction process at 150°C in one pot followed by polymeric binding with PVA to create a highly elastic piezo-resistive sensing sheet. In this process, scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies were carried out to characterize the morphology of the resulting nanopowder. This sensing sheet is pasted on the upper layer of the glass fibre-reinforced composite (GFRP) produced by the hand lay-up method. The combined manufactured samples were tested on a universal testing machine (UTM) to characterize the mechanical properties of the composite in tension and flexural following ASTM standards. Simultaneously, the change in resistance of nanosensing sheets was also recorded and the data were correlated to determine the properties and response characteristics of the smart RGO-PVDF nanosensor, which has been encountered and verified by using the adequate numerical technique. [ABSTRACT FROM AUTHOR]

In this article, we investigate the controllability of damped dynamical system modelled by Hilfer derivative of fractional order [Formula: see text] and [Formula: see text]. The Mittag-Leffler matrix function of two parameters has been used to represent the solution of Hilfer fractional problem of damped dynamical system. With the use of the Schawder fixed point theorem and the contraction mapping theorem, the existence and uniqueness of the linear and non-linear system of Hilfer dynamical control system are determined. More specifically, fractional calculus are used to provide sufficient criteria for the controllability results. Finally, examples are given to show how the key results might be justified.

Based on the experimental-computational approach, a method for identifying deformation diagrams of elastoplastic materials by considering the inhomogeneity of the stress-strain state and large deformations was developed. Examples of the application of this method for various types of loading of the tested samples were presented: tension and torsion of cylindrical rods, kinetic indentation of a ball and a cylinder, dynamic compression of tablet samples, etc. A technique for interpolating the deformation diagram to take into account the type of stress state was proposed.

A family of three-step optimal eighth-order iterative algorithm is developed in this paper in order to find single roots of nonlinear equations using the weight function technique. The newly proposed iterative methods of eight order convergence need three function evaluations and one first derivative evaluation that satisfies the Kung–Traub optimality conjecture in terms of computational cost per iteration (i.e. $ {2^{n - 1}} $ ). Furthermore, using the primary theorem that establishes the convergence order, the theoretical convergence properties of our schemes are thoroughly investigated. On several engineering applications, the performance and efficiency of our optimal iteration algorithms are examined to those of existing competitors. The new iterative schemes are more efficient than the existing methods in the literature, as illustrated by the basins of attraction, dynamical planes, efficiency, log of residual, and numerical test examples.

Modern technologies of thermal power engineering make it possible to design and build systems using renewable energy sources. Often, energy accumulation and storage require the development and adaptation of appropriate systems, the simplest of which are passive systems based on phase-change materials. In this study, a numerical analysis of heat transfer in a brick wall containing several materials with different melting temperatures is carried out. The unsteady two-dimensional conjugate problem of phase transitions is considered, taking into account natural convection in the melt, which has been solved using the developed in-house finite difference technique. A numerical experiment has been carried out for a brick block with several rectangular inserts filled with PCMs under various external thermal conditions. As a result of the numerical analysis, it has been shown that the relative arrangement of materials with different melting points has a significant impact on the heat transfer and heat exchange between the environment and the room. [ABSTRACT FROM AUTHOR]

Unsteady incompressible Sutterby fluid model is considered. The comparative results of stretching cylinder and sheet have been studied. The induced magnetic field is considered in the presence of thermal slip. Darcy resistance and viscos dissipation impacts have been studied. The thermal conductivity of liquid has considered as variable under the thermal radiation. The governing model of presence study have been developed under boundary layer approximation in term of partial differential equations. The differential equation become dimensionless by means of transformations. The dimensionless system have been solved through numerical procedure. Involving factor of physical influence presented in the form of tabular as well as graphical. Fluid temperature boosted up due to larger values of variable thermal conductivity. Physically, the thermal conductivity of liquid increased as well as variable thermal conductivity liquid enhanced as the temperature of fluid improved. The momentum layer thickness of stretching cylinder achieved mover than stretching sheet. The fluid velocity curves achieved higher thickness for boosting values of Darcy resistant factor. The velocity fluid curves revealed declining by increasing the Sponginess factor. Fluid temperature boosted up due to larger values of Eckert number. [ABSTRACT FROM AUTHOR]

The paper is devoted to the comparative analysis of different CFD techniques used to solve the problem of high-pressure hydrogen release into the air. Three variations of a contemporary low-dissipation numerical technique (CABARET) are compared with each other and a conventional first-order numerical scheme. It is shown that low dissipation of the numerical scheme defines better resolution of the contact surface between released hydrogen and ambient air. As a result, the spatial structures of the jet and the reaction wave that arise during self-ignition are better resolved, which is useful for predicting the local effects of high-pressure hydrogen release. At the same time, the dissipation has little effect on the induction delay, so critical conditions of self-ignition can be reliably reproduced even via conventional numerical schemes. The test problem setups formulated in the paper can be used as benchmarks for compressible CFD solvers.

Development of numerical code for evaluating the solidification of water has been scrutinized in this work. The container has two circular and sinusoidal cold walls at bottom and top surfaces. Galerkin-based code has been employed to model this phenomenon. To elevate the conductivity of phase change material (PCM), alumina particles with nanosized were utilized with incorporating different shapes. The conductivity of nanoencapsulated phase change material (NEPCM) is a function of concentration and shapes of nanoparticles. The freezing process is mainly dominated by conduction and selecting curved shaped and adding nanoparticles can affect this mechanism. Verification test reveals the good accommodation and applying adaptive grids leads to higher accuracy. As shape coefficient increases, the period of process declines around 10.65% owing to stronger conduction. Also, mixing water with alumina nanopowders with blade shape causes decrement in needed time around 32.51%. Besides, outputs reveal that utilizing blade shape of powders has more effect on required time than that of cylindrical shape. [ABSTRACT FROM AUTHOR]

The sublimation process, which directly transforms solid materials into gaseous water vapor, is typically utilized with items of great value, particularly in the food and pharmaceutical industries, where it is feasible to have both significant investment in capital and operating expenses. In light of this, modeling of convection within the sublimated region as well as at the interface is carried out. The model accounts for temperature-dependent heat conductivity and mass diffusivity. In addition, a linear profile of the volumetric internal heat is assumed to improve the operating time with least energy consumption. The condition for limitation of sublimation is derived for full nonlinear model. It is shown that sublimation can only take place in the region under the sublimation limit curve. The current model is solved by Legendre wavelet collocation technique. The correctness of the obtained results is verified with the results of finite-difference technique in the case of full nonlinear problem and found good acceptance. Moreover, results obtained from the current numerical approach show excellent acceptance with the analytical results of the linear model. It is found that temperature-dependent mass diffusivity enhances the concentration profile more than fixed mass diffusivity. With temperature-dependent heat conductivity, materials sublimate faster than usual. [ABSTRACT FROM AUTHOR]

Present study highlights the behavior of the weir crest head and width parameter on the discharge coefficient of a compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations. In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in the transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs. The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using the volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing. The comparative analysis of the numerical simulations and experimental observations confirm the performance of the CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharge coefficients for various heads over the weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%. HIGHLIGHTS The Head-Discharge relation is established for discharge measurement using a compound broad crested weir, experimentally and numerically.; Assessment of head over the weir crest for different step widths of the proposed weir on the discharge coefficient is executed.; Experimental and CFD results of weir performance demonstrate good agreement between the theoretical discharges by traditional rectangular weir formulae keeping Cd constant.;

Applications: Thermal conductivity of nanomaterials potentially contributes in heat transport applications. Due to heat absorbing and cooling characteristics, nanoparticles broadly use in environmental engineering, solar plates, computational chemistry, chemical engineering and thermal engineering etc. Thus, it is substantial to identify the nanomaterials with effective heat generating or absorbing properties which have variety of applications in mechanical engineering. Purpose: and Methodology: The main focus of this study are to introduce a nanofluid model using ZnO-SAE50 nanolubricant under additional effects of solar thermal radiations, magnetic field and resistive heating. This parametric study will help to maintain the temperature under various ranges of physical parameters which has broad applications in many engineering disciplines. The achieved model analyzed through numerical approach and comprehensive analysis provided in the view of furnished results. Major findings: Investigation of the results provided that the heat transport is maximize using ZnO-SAE50 nanolubricant while; conventional SAE50 is not good to achieve desired heat transfer rate. Solar thermal radiations and dissipation effects positively act on the temperature role of ZnO-SAE50.

It is renowned that the immune reaction in the tumour micro environment is a complex cellular process that requires additional research. Therefore, it is important to interrogate the tracking path behaviour of tumor-immune dynamics to alert policy makers about critical factors of the system. Here, we use fractional derivative to structure tumor-immune interactions. Furthermore, in our research, we concentrated on the qualitative investigation and time series analysis of tumor-immune cell interactions. The solution routes are examined using a new numerical technique to emphasis the impact of the factors on tumor-immune system. We focused on the behaviour of the system with fluctuation of different values. The most crucial components of the proposed system are identified and policymakers are advised. The outcomes of the present study are the strong predictor of clinical success and the in-out of immune cells in a tumour is also critical to treatment efficacy. As a result, studying the behaviour of tumor-immune cell interactions is important to predict crucial factors for the prevention and management to the health officials. [ABSTRACT FROM AUTHOR]

The study uses Tiwari and Das' nanofluid model to present a study on free convective flows in a right-angled trapezoidal cavity that is saturated with a porous bed and filled with Cu-water nanofluid material. This investigation aims to enhance the characteristics of hybrid fuel cells and energy depository devices by analysing the cavity's heat expansion and fluid flow properties. In trapezoidal enclosures, the inclined and right wall portions are maintained at different isothermal temperatures at all times. Finite difference-based stream function-vorticity numerical simulations are employed to carry out this analysis. The outcomes have been presented for isotherms, streamlines, and Nusselt numbers concerning nanoparticle volume fraction, Darcy number, and various Rayleigh numbers. It is found that the inverse relationship between the thermal Rayleigh number and the nanofluid's volume has a significant impact on the average Nusselt number. [ABSTRACT FROM AUTHOR]

In this paper, we discussed the effect of nanoparticles shape on bioconvection nanofluid flow over the vertical cone in a permeable medium. The nanofluid contains water, Al2O3 nanoparticles with sphere (spherical) and lamina (non-spherical) shapes and motile microorganisms. The phenomena of heat absorption/generation, Joule heating and thermal radiation with chemical reactions have been incorporated. The similarity transformations technique is used to transform a governing system of partial differential equations into ordinary differential equations. The numerical bvp4c MATLAB program is used to find the solution of ordinary differential equations. The interesting aspects of pertinent parameters on mass transfer, energy, concentration, and density of themotilemicroorganisms' profiles are computed and discussed. Our analysis depicts that the performance of sphere shape nanoparticles in the form of velocity distribution, temperature distribution, skin friction, Sherwood number and Motile density number is better than lamina (non-spherical) shapes nanoparticles. [ABSTRACT FROM AUTHOR]

Applications: The interaction of nanoparticles and base solvents of different nature attained much interest of the researchers in the recent time. These use in medication, detection of cancer cells, applied thermal engineering, and electrical and mechanical engineering. Among the broad range of applications, investigation of nanofluid through converging/diverging channel is important which is of much interest in the field of medical sciences. Purpose and methodology: The core purpose of this study is to introduce a new heat transfer model for two natures of nanofluids with bi host solvents. The model in hand achieved through nanofluid expressions, similarity equations and induction of novel dissipation effects. At later stage, numerical treatment is performed to explore the actual behaviour of nanofluids inside the oblique walls which is very important. Core findings: From the drawn results, it is found that the motion could be controlled by expanding the channel walls (α = 5 o ) and high Re and in Al2O3-H2O it is optimum. The nanofluids based on Al2O3 and C2H6O2 have much ability to transmit heat than the other nanofluids. Moreover, dissipation effects (E c = 0. 1 , 0. 2 , 0. 3 , 0. 4) played significant role and boosted the temperature while keeping R e = 70 , α = 5 o and α = − 5 o , respectively. Also, the study is validated and achieved good agreement between existing and the current study. [ABSTRACT FROM AUTHOR]

This research presents a computational investigation of the thermal convection of a heat-generating liquid having variable viscosity in a semi-cylindrical cavity. The analysis is carried out to obtain the time patterns of the average Nusselt number at the lower border of the chamber and understand the impact of the variable viscosity, the Prandtl number, and the Rayleigh number on this parameter. The natural convection in the cavity is defined by the set of non-dimensional equations based on the Boussinesq approach employing the non-primitive parameters such as vorticity and stream function. These governing equations are worked out numerically based on the finite difference technique. The time dependencies have been obtained at the Rayleigh number equal to 104, 105, and 106 and the Prandtl number taking values of 7.0, 70, and 700. The results obtained for variable and constant viscosity have been compared. Additionally, the paper represents maps of isotherms and streamlines for the mentioned values of the Rayleigh number. The influence of variable viscosity on the parameters of natural convection is poorly studied in closed systems; therefore, this research gives necessary data to understand the general time nature of the average Nusselt number at cooling surface of various parameters. Additionally in this research, the model for simulating the natural convection in non-primitive variables is presented in polar coordinates when the dynamic viscosity varies with temperature. The computational model designed could be used to simulate the free convection in systems with inner heat production such as chemical reactors, inductive metal melting facilities, or corium in-vessel retention to analyze the impact of various factors on the parameters of the natural convection in such systems. [ABSTRACT FROM AUTHOR]