Search

In the present study, 3-dimensional squeezing movement in a circling conduit under the stimulus effective Prandtl number with the aid of thermal radiation is taken into account. Water and ethylene glycol are the base fluids along with gamma-alumina nanoparticles. The coupled nonlinear system of PDEs is transformed into a system of ODEs with the support of some appropriate resemblance alterations. Then, the explanation was obtained numerically by the Runge–Kutta–Fehlberg (RKF) method. The emerging parameters such as quotient of the electric magnetic field to viscous forces (M), Prandtl number (Pr), and Reynolds number (Re), along with physical parameters such as the Nusselt number and skin friction coefficient, will be integrated graphically. The Prandtl number is important for regulating the momentum and thermal boundary layers. As a result, the effect of the effective Prandtl number on the nanoboundary layer and laminar incompressible flow of γAl2O3−H2O and γAl2O3−C2H6O2 nanoparticles is considered. The impact of the radiation parameter (Rd) favors the temperature distribution. Furthermore, the thermal conductance enriches with the enhancement of solid volume fraction.

A brushless double-fed induction generator (BDFIG) has shown tremendous success in wind turbines due to its robust brushless design, smooth operation, and variable speed characteristics. However, the research regarding controlling of machine during low voltage ride through (LVRT) need greater attention as it may cause total disconnection of machine. In addition, the BDFIG based wind turbines must be capable of providing controlled amount of reactive power to the grid as per modern grid code requirements. Also, a suitable dynamic response of machine during both normal and fault conditions needs to be ensured. This paper, as such, attempts to provide reactive power to the grid by analytically calculating the decaying flux and developing a rotor side converter control scheme accordingly. Furthermore, the dynamic response and LVRT capability of the BDFIG is enhanced by using one of the very intelligent optimization algorithms called the Salp Swarm Algorithm (SSA). To prove the efficacy of the proposed control scheme, its performance is compared with that of the particle swan optimization (PSO) based controller in terms of limiting the fault current, regulating active and reactive power, and maintaining the stable operation of the power system under identical operating conditions. The simulation results show that the proposed control scheme significantly improves the dynamic response and LVRT capability of the developed BDFIG based wind energy conversion system; thus proves its essence and efficacy.

In this study, we intend to investigate the steady-state and laminar flow of a viscous fluid through a circular cylinder fixed between two parallel plates keeping the aspect ratio of 1 : 5 from cylinder radius to height of the channel. The two-dimensional, incompressible fluid flow problem has been simulated using COMSOL Multiphysics 5.4 which implements finite element’s procedure. The flow pattern will be investigated by using the Reynolds number from 100 to 1000. The reattachment length formed at the back of the cylinder and drag force when the fluid comes to strike with the front surface of the cylinder is expressed in terms of Reynolds numbers. We propose to calculate the velocity and the pressure before and after the cylinder. For this purpose, two-line graphs before and after the cylinder will be drawn to check the impact of cylinder on both velocity and pressure. It was found that the percentage change in the velocity as well as pressure before to after the cylinder is changing their behaviours at Re = 700. The study is important because the empirical equations between the vortex’s lengths formed along the cylinder using the linear regression process obtained in this study may be used for future implementation.

The goal of this paper is to study a new system of a class of variational inequalities termed as absolute value variational inequalities. Absolute value variational inequalities present a rational, pragmatic, and novel framework for investigating a wide range of equilibrium problems that arise in a variety of disciplines. We first develop a system of absolute value auxiliary variational inequalities to calculate the approximate solution of the system of absolute variational inequalities, and then by employing the projection technique, we prove the existence of solutions of the system of absolute value auxiliary variational inequalities. By utilizing an auxiliary principle and the existence result, we propose several new iterative algorithms for solving the system of absolute value auxiliary variational inequalities in the frame of four different operators. Furthermore, the convergence of the proposed algorithms is investigated in a thorough manner. The efficiency and supremacy of the proposed schemes is exhibited through some special cases of the system of absolute value variational inequalities and an illustrative example. The results presented in this paper are more general and rehash a number of some previously published findings in this field.

The historical analysis demonstrates that plasma scientists produced a variety of numerical methods for solving “kinetic” models, i.e., the Vlasov-Maxwell (VM) system. Still, on the other hand, a significant fact or drawback of most algorithms is that they do not preserve conservation philosophies. This is a crucial fact that cannot be disregarded since the Vlasov Maxwell system is associated with conservation rules and is capable of assessing after the accomplishment of certain helpful mathematical actions. To examine the fractional-order routine of charged particles, we constructed a fractional-order plasma model and proposed a higher-order conservative numerical approach based on operational matrices theory and Shifted Gegenbauer estimations. Numerical convergence is investigated to confirm its competence and compatibility. This concept may be used in problems involving variable order and multidimensionality, such as those involving Vlasov and Boltzmann systems.

COVID-19 is causing havoc to human health and the world economy right now. It is a single standard positive-sense RNA virus which is transferred by inhalation of a viral droplet. Its genome forms four structural proteins such as nucleocapsid protein, membrane protein, spike protein, and envelop protein. The capsid of coronavirus is a protein shell within which a positive strand of RNA is present which enables the virus to control the machinery of human cells. It has several variants, e.g., SARS, MERS, and now a new variant identified in 2019, which is a novel coronavirus that causes novel coronavirus disease (COVID-19). COVID-19 is a novel coronavirus disease that originally arose in Wuhan, China, and quickly spread around the world. Clinically, we identified the virus presence by a PCR-based test. Preventive measures and vaccination are the only treatment against coronavirus. Some of these include Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. A topological index (TI) is a mathematical function that assigns a numerical value to a (molecular) graph and predicts many physical, chemical, biological, thermodynamical, and structural features of that network. In this work, we will calculate a new topological index, namely, the first and second Gourava and Hyper-Gourava indices for the molecular graph of Remdesivir (GS-5734), Chloroquine, Hydroxychloroquine, and Theaflavin. We also plotted our computed results to examine how they were affected by the parameters involved. These findings could contribute in the development of new COVID-19 therapy options.

Additive manufacturing (AM) technology has gained significant popularity, among which Fused Deposition Modeling (FDM) has emerged as the predominant technique for 3D printing. FDM offers the unique ability to achieve the desired and tailored engineering properties required for specific applications. This experimental study investigates the influence of varying FDM process parameters on the mechanical properties and highlights the optimal set of parameters for better tensile strength for a bi-layered composite of PLA-ABS (polylactic acid and acrylonitrile butadiene styrene). Also, it investigates the most-to-least influential printing parameters. Four process parameters were played out i.e., Infill density (50%, 75%, and 100%), number of layers (20,25 and 30), printing speed (20 mm sec ^−1 , 40 mm sec ^−1 , and 60 mm sec ^−1 ), and bed temperature (90 °C, 95 °C, and 100 °C), while keeping other parameters constant. Taguchi optimization technique was used for optimization and experiments were designed according to Taguchi orthogonal array L9 (3 4). After printing, the samples were evaluated for tensile properties and the results were analyzed. It is found that the infill density is the most influential parameter while bed temperature is the least influential. Infill density of 75%, 30 layers per part, a printing speed of 20 mm sec ^−1 , and a bed temperature of 100 °C are the optimal set of parameters for better tensile strength. Alongside, percent elongation, printing time, and strength-to-weight ratio were also analyzed and correlated.

Inspired by the widespread use of bioconvective nanofluids used in the formation of microbial fuel cells, microbial oil extraction processes, the food industry and more. Therefore, a two-dimensional flow of Eyring-Powell's nanofluid containing gyrotactic microorganisms has been developed by moving across a porous plate that is exposed to thermal radiation and surface suction. The Buongiorno nanofluid model is introduced to incorporate the energy and momentum equations, while the Rosseland nonlinear approximation was introduced to incorporate solar radiation properties into the energy equations. The MATLAB ‘bvp4c’ scheme was implemented to find a numerical solution to the problem. The influence of various physical parameters on the velocity, temperature and concentration distribution is analyzed. Suction lowers the temperature but increases the heat transfer rate. In addition, the suction velocity can be compensated by implanting a magnetic field in the flow field. With the enhancement of the Brownian movement and the thermophoretic movement, the temperature distribution of the brown movement increases faster than the temperature distribution of the thermophoretic movement, as does the volume fraction of the nanoparticles. The opposite trend can be observed as the Peclet number Pe increases. The suction reduces the concentration of the microorganisms and the magnetic field increases the concentration of the microorganisms. The higher the Lewis number, the lower the concentration of microorganisms. The Biot number Bi can increase the temperature and concentration of nanoparticles.

The studies of ordinary derivatives based nanofluids have limitations and some restrictions to solve and analyze the integer ordered leading partial differential equations and also have some memory effect complications. Fractional order in nanofluids can enhance and analyze more efficiently the memory effects on nanofluid behavior by different fractional derivatives techniques. In this study, the analytical solution of nanofluids containing water as a base fluid with copper oxide and silver as nanoparticles with heat and mass characteristics is investigated. The water-based nanofluid is flowing on an infinite sheet with constant temperature and thermal radiation. The dimensionless partial differential governing equations are solved in the sense of the most recent definition of fractional derivatives that is the Atangana-Baleanu fractional derivative. To dig out the mathematical solution of the developed fractional model of temperature and velocity field, the Laplace transformation technique and some of its inverse method i.e. Zakians method are utilized. To enhance the innovation of this article, the graphical and numerical representation of temperature and velocity fields are described and discussed by varying the values of different constraints such as fractional parameter and volume fraction. As a result, we concluded from the graphical illustration of the parameters, in comparison to copper oxide and silver nanofluid, CUo-water nanofluids has always slightly greater heat transfer rate as compared to Ag-water fractional nanofluid, which also depends on the enhancement of volume fraction. Furthermore, temperature and velocity profile shows decaying behavior with the enhancement in the fractional parameterβ.

An analysis for magnetohydrodynamic impacts on the rotational flow of nanofluids along with microorganisms, binary chemical reaction, and activation energy is considered. The equation of temperature is connected with Brownian motion, the theory of non-Fourier heat flux, and thermophoresis. The time-dependent 3D partially differentiate formulation is simplified in two independent coordinates (ξ, η). Glerikin discretization is used to employ finite element simulation in a MATLAB environment. It is noted that rising contributions of Hartmann number recede secondary as well as primary velocities; however, the primary skin friction attain negatively lower values and secondary skin friction exhibit an opposite trend. The growing input of thermophoresis and Brownian motion uplift the temperature, and the wall temperature gradient attains smaller values. The present solution of FEM has been affirmed with the available literature, indicating an incredible co-relation. The study has noteworthy applications in the industry of food and relevant to biomedical, energy systems, and current advances of aerospace technologies.

In this study, we have addressed the flow of hybrid nanofluid (Cu−Al2O3-Sodium Alginate), nanofluid (Cu-Sodium Alginate), and nanofluid (Al2O3-Sodium Alginate). Flow is because of the heated boundary of the channel and its different movements. The flow is modelled using Casson fluid's momentum equation, and the heat equation is generalized using the generalized Fourier’s law based on Caputo-time fractional derivatives. The non-dimensional fractional partial differential equations are solved using the Laplace and Fourier transforms. The velocity and temperature show variations for different values of the fractional parameter; also, the plots are drawn for the classical model. The temperature distribution increases for the volume fractions of the nanoparticles and has maximum vales for hybrid nanoparticles with the highest chosen volume fractions values. Furthermore, intensification in heat transfer rate is increased due to hybrid nanoparticles.

In this study, a new computing model by developing the strength of feed-forward neural networks with Levenberg-Marquardt Method (NN-BLMM) based backpropagation is used to find the solution of nonlinear system obtained from the governing equations of unsteady squeezing flow of Heat and Mass transfer behaviour between parallel plates. The governing partial differential equations (PDEs) for unsteady squeezing flow of Heat and Mass transfer of viscous fluid are converting into ordinary differential equations (ODEs) with the help of a similarity transformation. A dataset for the proposed NN-BLMM is generated for different scenarios of the proposed model by variation of various embedding parameters squeeze Sq, Prandtl number Pr, Eckert number Ec, Schmidt number Sc and chemical-reaction-parameter γ . Physical interpretation to various embedding parameters is assigned through graphs for squeeze Sq, Prandtl Pr, Eckert Ec, Schmidt Sc and chemical-reaction-parameter γ . The processing of NN-BLMM training (T.R), Testing (T.S) and validation (V.L) is employed for various scenarios to compare the solutions with the reference results. For the fluidic system convergence analysis based on mean square error (MSE), error histogram (E.H) and regression (R.G) plots is considered for the proposed computing infrastructures performance in term of NN-BLMM. The results based on proposed and reference results match in term of convergence up to 10-02 to 10-08 proves the validity of NN-BLMS. The Optimal Homotopy Asymptotic Method (OHAM) is also used for comparison and to validate the results of NN-BLMM.

Background: Huntington’s disease is an inherited autosomal dominant trait neuro-degenerative disorder caused by changes (mutations) of a gene called huntingtin (htt) that is located on the short arm (p) of chromosome 4, CAG expansion mutation. It is characterized by unusual movements, cognitive and psychiatric disorders. Objective: This review was undertaken to apprehend biological pathways of Huntington’s disease (HD) pathogenesis and its management by nature-derived products. Natural products can be lucrative for the management of HD as it shows protection against HD in pre-clinical trials. Advanced research is still required to assess the therapeutic effectiveness of the known organic products and their isolated compounds in HD experimental models. Summary: Degeneration of neurons in Huntington’s disease is distinguished by progressive loss of motor coordination and muscle function. This is due to the expansion of CAG trinucleotide in the first exon of the htt gene responsible for neuronal death and neuronal network degeneration in the brain. It is believed that the factors such as molecular genetics, oxidative stress, excitotoxicity, mitochondrial dysfunction, neuroglia dysfunction, protein aggregation, and altered UPS leads to HD. The defensive effect of the natural product provides therapeutic efficacy against HD. Recent reports on natural drugs have enlightened the protective role against HD via antioxidant, anti-inflammatory, antiapoptotic, and neurofunctional regulation.

The novel Coronavirus Disease 2019 (COVID-19) is a highly infectious disease caused by a new strain of severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2). In this work, we proposed a mathematical model of COVID-19. We carried out the qualitative analysis along with an epidemic indicator which is the basic reproduction number (R0) of this model, stability analysis of COVID-19 free equilibrium (CFE) and Endemic equilibrium (EE) using Lyaponuv function are considered. We extended the basic model into optimal control system by incorporating three control strategies. These are; use of face-mask and hand sanitizer along with social distancing; treatment of COVID-19 patients and active screening with testing and the third control is prevention against recurrence and reinfection of humans who have recovered from COVID-19. Daily data given by Nigeria Center for Disease Control (NCDC) in Nigeria is used for simulation of the proposed COVID-19 model to see the effects of the control measures. The biological interpretation of this findings is that, COVID-19 can be effectively managed or eliminated in Nigeria if the control measures implemented are capable of taking or sustaining the basic reproductive number R0 to a value below unity. If the three control strategies are well managed by the government namely; NCDC, Presidential Task Force (PTF) and Federal Ministry of Health (FMOH) or policymakers, then COVID-19 in Nigeria will be eradicated.

The present study investigates the rate of heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface subject to the heat generation/absorption and mass suction. The analysis has been carried out for the two different conditions of heat transfer stated as prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). Moreover, an exterior magnetic field is applied with an inclined angle along the stretched surface. Mathematically, the existing flow problem has been configured in accordance with the fundamental laws of motion and heat transfer. The similarity transformations have been used to transform the governing equations into the nonlinear ordinary differential equations (ODEs). The numerical solution to the resulting nonlinear ODEs with the associated boundary conditions have been obtained with the utilization of bvp4c package in MATLAB. The behavior of the resulting equations of the problem is checked graphically under the influence of various flow parameters which ensures that the rate of heat transfer decreases with the increase of Brownian motion parameter as well as it increases with the increase of thermophoresis parameter. Moreover, the Sherwood number increases with the rising values of the Prandtl number and Lewis number.

This article communicates the heat transfer improvement with bioconvective-flow of generalized second-grade nanofluid under melting mechanisms through a stretched surface in the occurrence of microorganisms. The impacts of activation action and nonlinear thermal radiation are considered. Heat dependent thermal conductivity and thermal diffusivity with the impacts of thermal and solutal Robin's conditions are adopted. The set of PDE's is reducing into coupled ordinary differential equations by introducing appropriate similarity transformation. The numerical solution of the dimensionless ordinary ones is attained by implementing a numerical scheme specifically the bvp4c tool in MATLAB. Aspects of distinguishing vital parameters against velocity field, heat profile, the concentration of nanoparticles, microorganisms' field are revealed graphically. The numerical estimation of skin friction coefficient, temperature transfer rate, mass transfer rate, and microorganisms mass transfer rate are also acquired in tabular data. This scrutiny reported that the flow of fluid is improved with increment in the magnitudes of modifies second-grade fluid parameter while reducing for buoyancy ratio parameter. Furthermore, the heat field reduces for a larger melting number. The microorganism's field is riches for greater microorganisms Biot number.

A successful ignition is the consequence of corresponding conditions of fuel mass flow rates, mixture ratio, as well as initiation energy in time and space. If ignition does not take place accurately, serious damages can take place within or outside the engine. The dynamical behavior of the combustion chamber was investigated during ignition. Single shear coaxial injector combustion chamber test case is used in the present study. At the time of propellant injection, mostly the pressure and temperature remain subcritical. When injected these increases promptly and convert into supercritical conditions. The thermodynamic state usually changes from subcritical to supercritical during ignition. Navier Stokes equations along with Soave Redlich Kwong equation model has been applied during steady-state, while transient simulations with ideal gas assumptions are performed to analyze the dynamical behavior of the combustor. All the simulations were performed in the present study using the ANSYS Fluent 16.2 code. The computational findings have strong analytical consistency with the experimental data. Due to inappropriate modeling of the equation of state and limited information about initial and boundary conditions for ignition transient results have some differences with experimental data. The difference between the observed chamber pressure during the experiment and numerical computation using 0.4 RFL value is only 2 bar (approximately 7% difference).

Conservation laws, non-classical heat and mass flux models, and correlations for thermos-physical properties of hybrid nanostructures and fluid are used for the formulation of problems. The numerical solutions for modeled flow problems (PDEs with suitable boundary conditions) are computed using the finite element method (FEM). These numerical solutions are used in simulations under variation of various types of parameters obtained as a result of dimensional analysis. The role of simultaneous dispersion of MoS2 and SiO2 as hybrid nanoparticles on the thermal performance of Williamson fluid and transport of species in Williamson fluid are investigated. A significant rise in the effectiveness of thermal conductivity of Williamson is observed due to the dispersion of hybrid nanostructures. It is also noted that the effectiveness of thermal conductivity due to hybrid nano-structures is higher than the effectiveness of thermal conductivity due to nano-structures. A remarkable drag on the flow of fluid due to the presence of porous medium is observed. Further, Forchheirmer porous medium offers more resistance to flow than the resistance by Darcy's porous medium. A significant decrease in temperature and concentration fields against relaxation parameters is observed. Consequently, a decline in thermal and concentration thickness is noted.

In this article, we investigated entropy generation analysis for viscous fluid over a thin needle. Two types of viscous fluids namely air and water are considered as counter examples. The energy dissipating term is included in the axial direction. The Newtonian heating condition is considered on the needle boundary. The governing equations for the flow under consideration are modeled in terms of partial differential equations (PDEs) which are then transformed into ordinary differential equations (ODEs) by using appropriate similarity variables. The transformed ODE's are then solved numerically using a numerical technique known as the Quasi-linearization method. The effects of embedded flow parameters on velocity, skin-friction, temperature, Nusselt number, Bejan number, and the irreversibility distribution ratio are determined graphically in several plots for both air and water. It is noticed that the total entropy generation Nst rate decreases with the increasing size of the thin needle. It is also found that the velocity ratio parameter ε reduced the skin friction. It is worth noting that the needle size a and the Newtonian heating parameter γ reduced the irreversibility distribution ratio Φ.

The main objective of the recent article is to investigate the flow of Sutterby nanofluid with applied magnetic field and convective boundary aspects referred to as two coaxially rotating stretching disks. Nanofluids are a combination of simple fluids and small particles, the particles are evenly distributed in the base fluid and have impressive uses in thermal transport sources. Nanofluids play a significant role in enhancing the heat transfer coefficient in fluids via the suspension of nanomaterials in the base fluids. This study is specific to involve non-Newtonian base fluid namely the Sutterby model. In addition, non-uniform thermal conductivity, non-linear thermal radiation, and bioconvection of motile microorganism's characteristics are taken into consideration. Bioconvection is a process in which the motion of motile microorganisms is addressed which may be helpful to avoid the probable settling of nano entities. PDEs such as momentum, boundary conditions, temperature, volume fraction, and motile microorganism density are upgraded into a model of non-linear ordinary differential equations employing appropriate similarity transformation. Transmuted dimensionless ODEs are tackled with shooting techniques and outcomes of prominent physical parameters are attained with a built-in bvp4c solver via MATLAB (Lobatto-IIIa) computational software. Inspirations of interesting physical parameters against the velocity field, temperature field, the solutal field of species, and microorganisms' profile are elaborated and briefly investigated numerically and graphically. The flow speed becomes faster directly with mixed convection parameter but it retards against magnetic field parameter and bioconvection Rayleigh number. The fluid temperature enhances in direct response to the parameters of thermal conductivity, thermophoresis, temperature ratio, and Biot number.

In this research article, we establish a fractional-order mathematical model to explore the infections of the coronavirus disease (COVID-19) caused by the novel SARS-CoV-2 virus. We introduce a set of fractional differential equations taking uninfected epithelial cells, infected epithelial cells, SARS-CoV-2 virus, and CTL response cell accounting for the lytic and non-lytic effects of immune responses. We also include the effect of a commonly used antiviral drug in COVID-19 treatment in an optimal control-theoretic approach. The stability of the equilibria of the fractional ordered system using qualitative theory. Numerical simulations are presented using an iterative scheme in Matlab in support of the analytical results.

In this article, a dynamical model with advection-diffusion, elucidating the transmission process of disease infection type computer virus, is studied. Such kind of systems help to alleviate the effects of virus by prior predictions described in the model. The existence and uniqueness of the solutions of the system is investigated. A solution space (Banach space) is considered to make the possibility of existence of the solutions of proposed system. A closed and convex subset is defined in the Banach space, in which the solutions of the coupled system are optimized. The essential explicit estimates for the solutions are also calculated for the corresponding auxiliary data. Moreover, a non-standard finite difference scheme is applied to find the approximate solution of the prescribed problem. For the validity of the proposed scheme, the possession of some important structural properties by the applied numerical technique are presented. These structural properties are consistency and stability. To prove the numerical stability, Von-Neumann criteria is adopted. In the study of such population dynamics type models, positivity is one of the most important physical properties of the numerical scheme that must be preserved. To prove the positivity of the numerical method, a reliable result is established. The validation of the present study is shown by illustrating an example. The behaviors of the state variables are described by plotting the graphs of the associated example.

De-Levie’s model has become an indispensable model for knowing a porous electrode because electrochemical supercapacitors provide electrical energy storage and they use nanoporous electrodes to store large amounts of charge. This manuscript proposes the fractional analysis of De-Levie’s model via three types of modern fractional differentiations namely Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional operators. The system of ordinary coupled differential equations of De-Levie’s model have been fractionalized and coupled into equivalent form of diffusion equation. The analytic solutions of voltage are traced out by means of Fourier sine and Laplace transforms subject to the satisfaction of sinusoidal and exponential conditions. The general solutions of De-Levie’s model have been investigated in term of special and elementary functions. The graphs of comparative analysis have been depicted for voltage through three approaches of fractional derivative based on singular, non- singular and non-local kernels. Finally, our results suggest that construction of the electrodes with optimal utilization can be controlled by fractional approaches. Keywords: Analytic solutions, De-Levie’s model, Modern fractional approaches, Fourier sine and Laplace transforms

This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. The results are derived by using the Burkholder-Davis-Gundy (in short BDG), Hölder's, Doobs martingale's and Gronwall's inequalities. Subject to non-linear growth condition, it is revealed that the Euler-Maruyama approximate solutions are bounded in $ M_G^2([t_0,T];\mathbb {R}^n) $ . In view of non-linear growth and non-uniform Lipschitz conditions, we give estimates for the difference between the exact solution $ Z(t) $ and approximate solutions $ Z^q(t) $ of SDEs in the framework of G-Brownian motion.

The significance of solar energy has recently diverted the attention of researchers; this is due to the experimental or the numerical analyises of solar energy and lack of fractional analytic approaches. This manuscript is communicated to model the problem of the enhancement of heat transfer rate of solar energy devices, using single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) and to investigate the analytic solutions of the modeled problem. The nano-sized particles are added to the heat transfer fluid such as single and multi-walled carbon nanotubes (SWCNTs and MWCNTs). The governing partial differential equations are modeled by the newly defined Caputo–Fabrizio fractional derivatives. The analytic solutions have been investigated for heat transfer and velocity field by employing Laplace transforms. The heat transfer and profile of nanofluids are presented by the variations of different nanoparticles and their different volume fractions. The similarities and differences between single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) improve the thermo-physical properties of the nanofluid. Theoretical results assure that the efficiency of solar collectors is enhanced by adding single and multi-walled carbon nanotubes (SWCNTs and MWCNTs). Finally, the graphical results indicated that performance of solar collector is significant via Caputo–Fabrizio fractional derivatives and the incoming sunlight can be absorbed more effectively. Keywords: Solar collectors, SWCNTs and MWCNTs, Laplace transforms, Caputo–Fabrizio fractional operator and graphical depictions

Abstract The present article investigates the effects of diffusion-thermo, thermal radiation, and magnetic field of strength B0 $B_{0}$ on the time dependent MHD flow of Jeffrey nanofluid past over a porous medium in a rotating frame. The plate is assumed vertically upward along the x-axis under the effect of cosine oscillation. Silver nanoparticles are uniformly dispersed into engine oil, which is taken as a base fluid. The equations which govern the flow are transformed into a time fractional model using Atangana–Baleanu time fractional derivative. To obtain exact expressions for velocity, temperature, and concentration profiles, the Laplace transform technique, along with physical initial and boundary conditions, is used. The behaviors of the fluid flow under the impact of corresponding dimensionless parameters are shown graphically. The variations in Nusselt number and Sherwood number of relative parameters are found numerically and shown in tabular form. It is worth noting that the rate of heat transfer of engine oil is enhanced by 15.04% when the values of volume fraction of silver nanoparticles vary from 0.00 to 0.04, as a result the lubricant properties are improved.

Abstract This article deals with the generalization of natural convection flow of Cu−Al2O3−H2O $Cu - Al_{2}O_{3} - H_{2}O$ hybrid nanofluid in two infinite vertical parallel plates. To demonstrate the flow phenomena in two parallel plates of hybrid nanofluids, the Brinkman type fluid model together with the energy equation is considered. The Caputo–Fabrizio fractional derivative and the Laplace transform technique are used to developed exact analytical solutions for velocity and temperature profiles. The general solutions for velocity and temperature profiles are brought into light through numerical computation and graphical representation. The obtained results show that the velocity and temperature profiles show dual behaviors for 0

Due to employing electric field, nanofluid heat transfer enhances. This phenomenon in a porous geometry has been simulated in this paper. To augment heat transfer, the radiation term is included in the model. Ethylene glycol nanofluid is considered as the homogenous model. Electric field and shape of nanoparticles can affect the properties of ferrofluid. CVFEM is proposed for simulating the treatment of EHD flow. Voltage, permeability, radiation parameters, and nanoparticles' shape are important variables. The results prove that the platelet shape leads to the highest convective flow. As electric force enhances, temperature gradient augments. Greater permeability leads to more convective flow.

Thermal radiations and effective characteristics of the nanoparticles play a vibrant role in the heat transfer enhancement. This work aims to investigate the influence of thermophysical characteristics of nano-diamond (ND) and silver (Ag) nanoparticles on the heat transfer intensifications in the nonlinear radiative and dissipative flow over an arched geometry. A self-similar coupled nature of the nanofluid model is acquired via similarity transformations. Furthermore, the mathematical treatment of the model is carried out by the RK scheme. Moreover, stimuli of various pertinent flow parameters on the velocity, heat transfer, streamlines, and isotherms are examined graphically.

Different from a Newtonian fluid, couple stress fluid (CSF) includes a new material constant, which is responsible for couple stress and the lubricant viscosity. This material constant comes with the fourth-order spatial derivative term, and due to this higher-order derivative term in the momentum equation, this fluid (CSF) is comparatively less investigated even for the classical fluid problems. This paper aims to study the fractional model of CSF, based on the Atangana-Baleanu (AB) fractional derivatives definition. Since this AB definition is new, therefore, for the sake of comparison and correctness, this problem is also solved using the Caputo-Fabrizio (CF) fractional derivative definition. The CSF is considered to flow between two parallel plates, one of which is at rest and the other is moving with constant velocity. The external pressure gradient is also applied. This type of flow situations is usually called generalized Couette flow. The problem is first written in dimensionless form and then solved for the exact solution using the Laplace transform and the finite Fourier sine transform. The CSF velocity obtained via an AB fractional derivative is compared with the CSF velocity obtained via a CF fractional derivative approach, and the results obtained are shown graphically. The CSF results for interesting fluid parameters are displayed in various graphs for both the AB and CF fractional derivatives. It is observed that the CSF velocities obtained with the AB and CF fractional derivatives are the same for unit time. For time less than one and greater than one, variation in CSF velocities is observed. In limiting sense, the present CSF solutions are reduced to a similar Newtonian fluid problem solution in the absence of external pressure gradient.

In this work, the buoyancy-driven unsteady flow of Casson nanofluid is analyzed. The effects of Brownian motion and thermophoresis on the flow fields are studied in the presence of magnetic field. Moreover, the convective boundary conditions on temperature and concentration walls are also considered. The similarity solutions are obtained numerically through Keller-box scheme. The accuracy of numerical results is verified via comparison with the results of accessible literature. Investigations perceived that the dimensionless temperature is not much affected with Brownian motion and thermophoretic parameters, whereas the impact of both parameters is noted stronger on nanoparticles concentration. The velocity field is observed more pronounced with the strength of magnetic parameter. Also, the influence of Casson fluid parameter on velocity and nanoparticle concentration is noticed opposite. The influence of magnetic parameter on velocity and temperature is seen more pronounced as compared to nanoparticle concentration. Further, the impact of Biot number on dimensionless temperature and nanoparticles concentration is found identical for both steady and unsteady flows. A reduction in velocity field is also observed with increment in slip parameter.

The objective of this article is to investigate the combined effects of the magnetic field and heat transfer on electrically conducting viscoelastic incompressible dusty fluid, flowing between two non-conducting rigid plates. The flow generation in the aforementioned fluid is caused by the oscillating pressure gradient and heat transfer. It is also assumed that all the dust particles having spherical shapes are homogeneously distributed in the fluid. In order to investigate analytical solutions, Light Hill method has been used. Furthermore, the effects of different parameters like an elastic parameter, radiation parameter, Reynolds number and Grashof number on velocity and applied shear stress have been discussed. A noteworthy relation of applied magnetic field with velocity and applied shear stresses is noticed, from the present study it is depicted that in boundary layer flow velocity increases and shear stress decreases with increase in applied magnetic field, while in ordinary course of nature, by increasing applied magnetic field decrease occurs in fluid velocity and shear stress increases.

The finite element method (FEM) is applied to study the impacts of prominent parameters on microrotation, velocity, and temperature to know the characteristics of the flow of incompressible water-ethylene glycol base fluids (60% water + 40% ethylene glycol) with single-wall and multiwall carbon nanotube nanoparticles micropolar ferromagnetic fluid due to porous stretching surface. A magnetic dipole of significant strength together the applied magnetic field contributes to better saturation of magnetic nanoparticles. Appropriate similarity transforms are applied to acquire the ordinary differential form of the governing non-linear partial differential equations and resulting equations are discretized in the prospectus of FEM. The detailed parametric study has been carried out, the results are presented in graphical and tabular form. The increment in the ferromagnetic interaction parameter slows down the fluid velocity but it upsurges the microrotation and thermal distribution. The multiwall carbon nanotube (MWCNT) in comparison to the single-wall carbon nanotube (SWCNT) has a greater impact on velocity and microrotation profiles also single-wall carbon nanotube (SWCNT) is compared to the multiwall carbon nanotube (MWCNT) has a greater impact on the temperature profile. The validation of the MATLAB code and the numerical scheme has been verified with an excellent comparison of present results with previous ones in the existing literature.

The purpose of this research is to scrutinize thermally charged heated bi-phase nanofluid flow in elongated parallel slippery walls governed by an external pressure gradient. The couple stress flow of nanofluid is subject to suspension with nano-sized metallic particles. The interaction effects of a transverse magnetic field have been taken into account. The lubrication effects at the walls are considered to avoid the roughness of the walls. Governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations via similarity transformations, and then the bvph2 algorithm is employed for its solution. The impacts of non-dimensional governing parameters, such as magnetic field, particle density, stress, and slip, on the velocity profile and thermal field curves are exposed graphically. Numerical results were compared with another homotopic approach, and excellent agreement was perceived.

In this article, a predictor-corrector type non-standard finite difference scheme has been formulated to avoid unnatural chaos, and numerical instabilities depend on a long time step, lead to a better strategy for overcoming the transmission of infectious diseases. The construction, development, and analysis of our proposed numerical scheme is done for the SEIR epidemiological model regarding the transmission dynamics of measles. Based on the mathematical study of the proposed scheme, the stability analyses are performed in detail. Further, the behavior of the scheme is accessed by the evaluation of the Eigenvalues of the Jacobian at a steady state. MATLAB algorithm is used for numerical simulations, and results demonstrated that the NSFD-PC scheme double refines the solution and gives physically realistic solutions even for large step sizes. The effectiveness of the scheme has been investigated by comparison with renowned numerical methods in literature like the RK4 and Euler method of a predictor-corrector type. It has been found that the presented scheme is dynamically compatible with the continuous system, unconditionally convergent, and satisfies the positivity of the state variables involved in the system of the SEIR model. Conclusively, the proposed numerical scheme preserves all essential control measuring features of the corresponding dynamical system and reduces additional cost when examined over long periods. Therefore, it is highly recommended.

Mathematical modeling with nonlinear delay differential equations (DDES) impart a significant role in the different disciplines such as epidemiology, computer modeling, immunology, physiology, neural networks, social sciences, bio-medical engineering, and many more. In this manuscript, a nonlinear delayed model is investigated to study the dynamics of a virus in a computer network. Many important results are established for the stability of equilibria of the model using the Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. Also, a nonstandard finite difference method is presented for the computational analysis of the model. The delay tactics like, be cautious while opening the email attachments, disable image previews in your email client, use an anti-malware solution, monitor all devices proactively, utilize administrator rights, pay attention to virus-related warnings and notifications, are precautionary measures which can help us in removing the virus from network. The impact of delay tactics on the threshold number is also analyzed. In the end, numerical results are presented to strengthen the theoretical analysis of the model.

Sediment loss is an indispensable geological phenomenon that determines the reduction of mass in time interval with the differential influence of controlling factors. In this study, the competence of rocks is considered as a controlling factor while weathering and erosion are termed as the decaying parameter. Attributed to the reduction of the total mass in unit time. A mathematical model is [proposed for the above-mentioned phenomenon and generalized using the Caputo fractional derivatives approach to better understand and predict the sediment loss. The model is solved for exact solutions using the Laplace transform technique. The results obtained for β and -β are in strong agreement with the field images of selected outcrop sections. The memory effect is also shown with different values of αThe results revealed that the mathematical model better explains the geological processes.

The primarily object of this article is to derive the solutions of modified fractional kinetic equations (MFKEs) containing the incomplete Aleph functions by using the application of Elzaki and inverse Elzaki transforms and hereto we also established some novel results such as the Elzaki transform of well-known the Riemann–Liouville operator and the incomplete Aleph functions (IAFs). The solutions of modified FKEs discusses in this article can be utilized to figures out the variation of the chemical composition in our solar system. In this article, we also see that the character of thermonuclear function is presented in terms of the incomplete ℵ-functions and many more special functions through some interesting corollaries. Finally, we established here a compact and easily figure out solutions in form of incomplete special functions and display the graphs of the obtained results in the end of this article to show the behavior of integral operator of fractional order on reaction rate of the particle. Furthermore, results holds here are also associated to the recent investigation of feasible astrophysical solutions of solar system problems. The derived results notify the known results more precisely.

The increasing global demand for energy necessitates devoted attention to the formulation and exploration of mechanisms of thermal heat exchangers to explore and save heat energy. Thus, innovative thermal transport fluids require to boost thermal conductivity and heat flow features to upsurge convection heat rate, and nanofluids have been effectively employed as standard heat transfer fluids. With such intention, herein, we formulated and developed the constitutive flow laws by utilizing the Rossland diffusion approximation and Stephen’s law along with the MHD effect. The mathematical formulation is based on boundary layer theory pioneered by Prandtl. Governing nonlinear partial differential flow equations are changed to ODEs via the implementation of the similarity variables. A well-known computational algorithm BVPh2 has been utilized for the solution of the nonlinear system of ODEs. The consequence of innumerable physical parameters on flow field, thermal distribution, and solutal field, such as magnetic field, Lewis number, velocity parameter, Prandtl number, drag force, Nusselt number, and Sherwood number, is plotted via graphs. Finally, numerical consequences are compared with the homotopic solution as a limiting case, and an exceptional agreement is found.

In the current article, we investigate the boundedness of commutators of the bilinear fractional p-adic Hardy operator on p-adic Herz spaces and p-adic Morrey-Herz spaces by considering the symbol function from central bounded mean oscillations and Lipschitz spaces.

This paper provides numerical estimation of Newtonian fluid flow past through rectangular channel fixed with screen movable from 10° to 45° by increasing the Reynolds number from 1000 to 10,000. The two-dimensional incompressible Navier Stokes equations are worked out making use of the popular software COMSOL MultiPhysics version 5.4 which implements the Galerkin’s least square scheme to discretize the governing set of equations into algebraic form. In addition, the screen boundary condition with resistance coefficient (2.2) along with resistance coefficient 0.78 is implemented along with slip boundary conditions applied on the wall. We engaged to find and observe the relationship between the optimum velocity, drag force applied by the screen, and pressure occurred in the channel with increasing Reynolds number. Because of the linear relationship between the optimum velocities and the Reynolds number, applying the linear regression method, we will estimate the linear equation so that future prediction and judgment can be done. The validity of results is doing with the asymptomatic solution for stream-wise velocity at the outlet of the channel with screens available in the literature. A nondimensional quantity, i.e., ratio from local to global Reynolds number Rex/Re, is introduced which found stable and varies from -0.5 to 0.5 for the whole problem. Thus, we are in the position to express the general pattern of the velocity of the particles as well as the pressure on the line passing through the middle of the channel and depart some final conclusion at the end.

An oscillatory mixed-convection fluid flow mechanism across a nonconducting horizontal circular cylinder embedded in a porous medium has been computed. For this purpose, a model in the form of partial differential equations is formulated, and then, the governing equations of the dimensionless model are transformed into the primitive form for integration by using primitive variable formulation. The impact of emerging parameters such as porous medium parameter Ω, Richardson number λ, magnetic force parameter ξ, and Prandtl number Pr on skin friction, heat transfer, and current density is interpreted graphically. It is demonstrated that accurate numerical results can be obtained by the present method by treating nonoscillating and oscillating parts of coupled partial differential equations simultaneously. In this study, it is well established that the transient convective heat transfer, skin friction, and current density depend on amplitude and phase angle. One of the objects of the present study is to predict the mechanism of heat and fluid flow around different angles of a nonconducting horizontal circular cylinder embedded in a porous medium.

The aim of this paper is to propose the generalized version of the multipolar neutrosophic soft set with operations and basic properties. Here, we define the AND, OR, Truth-Favorite, and False-Favorite operators along with their properties. Also, we define the necessity and possibility of operations for them. Later on, to extend it to solve the decision-making problems, we define some information measures such as distance, similarity, and correlation coefficient for the generalized multipolar neutrosophic soft set. Several desirable properties and their relationship between them are derived. Finally, based on these information measures, a decision-making algorithm is stated under the neutrosophic environment to tackle the uncertain and vague information. The applicability of the proposed algorithm is demonstrated through a case study of the medical-diagnosis and the decision-making problems. A comparative analysis with several existing studies reveals the effectiveness of the approach.

As of late quantum calculus is broadly utilized in different parts of mathematics. Uniquely, the hypothesis of univalent functions can be newly portrayed by utilizing q-calculus. In this paper, we utilize our recently presented symmetric p,q-number m˜ p,q to characterize new symmetric p,q-derivative D p,q of analytic function f in the open unit disk U. Utilizing D p,q, we introduce new class of analytic star-like functions and examine some fascinating results.

Nonisothermal flow through the rectangular channel on a circular surface under the influence of a screen embedded at the middle of a channel at angles θ is considered. Simulations are carried out via COMSOL Multiphysics 5.4 which implements the finite element method with an emerging technique of the least square procedure of Galerkin’s method. Air as working fluid depends upon the Reynolds number with initial temperature allowed to enter from the inlet of the channel. The nonisothermal flow has been checked with the help of parameters such as Reynolds number, angle of the screen, and variations in resistance coefficient. The consequence and the pattern of the velocity field, pressure, temperature, heat transfer coefficient, and local Nusselt number are described on the front surface of the circular obstacle. The rise in the temperature and the flow rate on the surface of the obstacle has been determined against increasing Reynolds number. Results show that the velocity magnitudes are decreasing down the surface and the pressure is increasing down the surface of the obstacle. The pressure on the surface of the circular obstacle was found to be the function of the y-axis and does not show any impact due to the change of the resistance coefficient. Also, it was indicated that the temperature on the front circular surface does not depend upon the orientation of the screen and resistance factor. The heat transfer coefficient is decreasing which indicates that the conduction process is dominating over the convection process.

The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non-Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second-order in dimensionless Weissenberg number We. The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number We. The obtained results demonstrate that for shear-thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We. Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies.

The Plateau-Bézier problem with shifted knots is to find the surface of minimal area amongst all the Bézier surfaces with shifted knots spanned by the admitted boundary. Instead of variational minimization of usual area functional, the quasi-minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points. The coefficients of these control points bear symmetry for the pair of summation indices as well as for the pair of free indices. These linear constraints are then solved for unknown interior control points in terms of given boundary control points to get quasi-minimal Bézier surface with shifted knots. The functional gradient of the surface gives possible candidate functions as the minimizers of the aforementioned Dirichlet functional; when solved for unknown interior control points, it results in a surface of minimal area called quasi-minimal Bézier surface. In particular, it is implemented on a biquadratic Bézier surface by expressing the unknown control point P11 as the linear combination of the known control points in this case. This can be implemented to Bézier surfaces with shifted knots of higher degree, as well if desired.