Search

This study examines MWCNTs-PG nanofluid with a uniform dispersion of MWCNTs in PG. It is assumed that both MWCNTs and PG exist thermally in equilibrium and no slip occurs between them. MWCNTs were suspended in PG uniformly and played a significant role. Firstly, the problem is formulated by utilizing empirical correlations, thermophysical attributes, and similarity equations. Then the model is treated numerically along with the coupling of a shooting algorithm. The results against the pertinent flow quantities were plotted and provide a basis for a comprehensive discussion, investigating whether MWCNTs-PG has high thermal storage characteristics under the effects of thermal radiation and combined convection effects. Due to their high energy storage capability, these fluids are reliable for industrial applications.

This analysis is concerned about the thermal performance of [(MgZn6Zr)/C8H18]nf by incorporating the essential concept of non-linear thermal radiations. The flow is configured over a 3D stretchable surface which is heated convectively and the surface boundaries updated with slip effects; uniform suction is applied. The proper mathematical modeling is performed by exercising the nanofluids’ empirical correlations and similarity equations. Thereafter, the RK scheme is utilized to execute the problem solution. The influences of imperative flow constraints are furnished and discussed deeply. The results revealed that [(MgZn6Zr)/C8H18]nf motion decays against suction (R1) and slip effects (γ1). The investigation of the results disclosed that the induction of non-linear thermal radiations in the model boosted the internal energy of the fluid, and hence, the nanofluid thermal efficiency improved. Moreover, convection provided from the surface (Bi number) was also of paramount interest regarding the heat transport in [(MgZn6Zr)/C8H18]nf. Furthermore, significant contribution of the temperature ratio parameter βw is examined in thermal enhancement. Optimum shear stress trends are investigated due to suction from the surface. Finally, we hoped that the problem would be beneficial in the field of applied thermal engineering, more specifically in the heat transport models.

In this work, we analyze the characteristics of periodic flows in non-isothermal viscous fluid over a heated block in the presence of thermal plates at Reynolds number (Re=100). The unsteady, incompressible Navier–Stokes (NS) equations with suitable initial and boundary data in 2D are executed by the finite element technique using a highly refined hybrid mesh. The temporal discretization is performed by an implicit stable backward differencing in time and a stable choice of finite elements from the finite element library for spatial discretization. The discrete nonlinear system arising from this discretization is linearized by Newton’s method and then solved through a direct linear solver PARDISO. For this forced convective study, the range of dimensionless parameters, namely, the Prandtl number (Pr) and power law index (n), are varied from 1 to 10 and 0.6 to 1.4 with a low Grashof number varying as (1≤Gr≤10) to produce a forced convection regime, respectively. For the authentication, we have compared our results with the literature at a similar configuration. After simulation, the results accomplished in the velocity profile, pressure, isotherm contours, drag and lift coefficients (trajectory motion), average Nusselt number (Nuavg), etc. are considered. For convergence of solution at low shear rate (n1), it converges to a single value. Furthermore, the drag (CD) and lift (CL) coefficients are more pronounced for shear-thinning cases (n1).

Abstract This article is devoted to studying Magnetohydrodynamic (MHD)'s combined effect and porosity on the entropy generation in two incompressible Newtonian fluids over a thin needle moving in a parallel stream. Two Newtonian fluids (air and water) are taken into consideration in this study. The viscous dissipation term is involved in the energy equation. The assumption is that the free stream velocity is in the direction of the positive x-axis—(axial direction). The thin needle moves in the same or opposite direction of free stream velocity. The reduced similar governing equations are solved numerically with the help of shooting and the fourth-order Runge–Kutta method. The expressions for dimensionless volumetric entropy generation rate and Bejan number are obtained through using similarity transformations. The effects of the magnetic parameter, porosity parameter, Eckert number, Bejan number, irreversibility parameter, Nusselt number, and skin friction are discussed graphically in detail for and taken as Newtonian fluids. The results are compared with published work and are found in excellent agreement.

Abstract Recently, novel coronavirus is a serious global issue and having a negative impact on the economy of the whole world. Like other countries, it also effected the economy and people of Pakistan. According to the publicly reported data, the first case of novel corona virus in Pakistan was reported on 27th February 2020. The aim of the present study is to describe the mathematical model and dynamics of COVID-19 in Pakistan. To investigate the spread of coronavirus in Pakistan, we develop the SEIR time fractional model with newly, developed fractional operator of Atangana–Baleanu. We present briefly the analysis of the given model and discuss its applications using world health organization (WHO) reported data for Pakistan. We consider the available infection cases from 19th March 2020, till 31st March 2020 and accordingly, various parameters are fitted or estimated. It is worth noting that we have calculated the basic reproduction number $${\mathfrak{R}}_{0} \approx 2.30748$$ R 0 ≈ 2.30748 which shows that virus is spreading rapidly. Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter $$\alpha$$ α on the model, various graphs are plotted. It is worth noting that the base of our investigation, we have predicted the spread of disease for next 200 days.

Modelling for many physical phenomena is greatly influenced by the usage of a fractional operator involving Mittag–Leffler function. The current investigation is concerned with an application of this modern fractional operator to analyze the Newtonian heating effects for the generalized Casson fluid flow. Magnetohydrodynamic (MHD) and porous effects for such fluids are also under consideration in this research. The main problem is modeled as partial differential equations. The “Velocity” and “Temperature” functions are attained by using the analytic tool namely Laplace transform. The analysis of the used modelling parameters has been made by using graphical representations. The numerical computations are performed to validate the data. The graphical results confirm that velocity diminishes obviously with an intensification of the magnetic parameter and grows with the rise of the porosity parameter (conjugate parameter). Fluid flow is controllable for all possible values of the Casson parameter. A special case of the main solution is discussed that reduces to Newtonian fluid.

An SIR-type (Susceptible-Infected-Recovered) model for the study of the spread of Ebola Virus Disease (EVD) is developed, by using conformable derivatives. Every possible way of transmission of the disease is incorporated (direct or indirect), such as funeral practices, consumption of contaminated bush meat and the environmental contamination etc. We have added an extremely important term to the model which have very high physical significance i.e., the possibility of the birth of an infected individual and the migration of an infected individual to the existing population. Well-posedness of the proposed problem has been shown by using a well-known theorem. The situations for the disease to be died out or sustain, have been discussed in the details. We found that the only disease-free situation is, the absence of flow of Ebola virus disease from the environment. We also have observed that by adopting a few strategies, such as isolation of infected individuals and careful burial of deceased bodies, the spread of EVD can be controlled. Memory effects for each case (disease-free and endemic states) are discovered (by using Khalil’s conformable transform) and plotted to make future predictions more accurately. Graphs are clearly elaborating that the problem is stable for both the equilibria states i.e., endemic state and disease-free state.

A new technique for modelling the fractional model of Casson fluid is used. More exactly, the Caputo fractional model has been developed using the generalized Fick’s and Fourier’s laws. The magnetohydrodynamics free convection flow of Casson fluid in a channel has been considered. A new transformation is applied to the energy and mass equations and then solved by using the Laplace and Fourier sine transformations jointly. The final solutions are presented in terms of special function, namely, the Mittag-Leffler function. The effects of various physical parameters have been portrayed in graphs and tables and discussed.

The purpose of this paper is to evaluate the exact solution of the unsteady flow of a generalized Brinkman type fluid under the effect of MHD in a channel. The classical Brinkman model reduced to non-dimensional form by using appropriate dimensionless variables. Furthermore, the non-dimensional Brinkman model is transformed to a generalize Brinkman model with Caputo-Fabrizio fractional derivative. The dimensionless Brinkman model has been solved with applicable conditions by integral transforms techniques that is Fourier and Laplace. The effect of different physical parameters and fractional order on fluid velocity and shear stress are illustrated graphically. Moreover, through this recent work, the recovery of classical Brinkman type fluid is possible through graphs.

Abstract In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-order phase transition, superconductivity, superfluidity, liquid crystals, and strings in field theory. A comparative approach is practised between the three suggested definitions of derivative viz. conformable, beta, and M-truncated. We have constructed the optical solitons of the considered model with a new extended direct algebraic scheme. By utilization of this technique, obtained solutions carry a variety of new families including dark-bright, dark, dark-singular, and singular solutions of Type 1 and 2, and sufficient conditions for the existence of these structures are given. Further, graphical representations of the obtained solutions are depicted. A detailed comparison of solutions to the considered problem, obtained by using different definitions of derivatives, is reported as well.

The present examination is centered around the transfer of heat for the flow of a boundary layer free convective incompressible fluid, past a stretching porous surface, assuming viscosity dependent on temperature linearly along with heat source and sink with imposed magnetic field. Lie group similarity transformation is used to obtain the symmetric graphs of the given problem. Solutions for velocity and heat profile are encountered numerically with fourth-order Runga-Kutta shooting technique and graphically presented and explained the impact on velocity profile and temperature profile of several physical parameters as temperature-dependent parameter of viscosity A, k1 as parameter of permeability, Prandtl number, λas parameter of heat generation and absorption and M as parameter of magnetic field. We observed that the thermal boundary layer thickness can be reduced by increasing viscosity parameter A and heat sink parameterλ. As we give increment in k1 we find a decrement in the horizontal velocity profile, which leads to the enhanced deceleration of the flow and, hence, the velocity decreases.

This theoretical study explores MHD convection flow confined to an unbounded vertical plate embedded in a permeable surface under the effect of heat generation and ramp temperature. Solutions of concentration, temperature, and velocity profiles are derived symmetrically by applying non-dimensional parameters along with Laplace transformation (LT) and numerical inversion algorithm. The graphical results for different physical constraints are produced for the velocity profiles. Our results suggest that an incremental value of the M is observed for a decrease in the velocity field, which reflects to control resistive force. Additionally, Atangana-Baleanu (ABC) model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.

Considering the higher flexibility in tuning process and finer control action of the fractional-order proportional integral derivative (FOPID) controller over the conventional proportional integral derivative (PID) controller, this paper explores its application in the automatic voltage regulator system. FOPID contains five tuning parameters as compared to three in the conventional PID controller. The additional tuning knobs in FOPID provide increased control flexibility and precise control action, however, their inclusion makes the tuning process more complex and tedious. Thus, the intelligence of an artificial intelligence (AI) technique called jaya optimization algorithm (JOA) is utilized in order to obtain an optimal combination of FOPID gains which further led to the optimal transient response and improved stability of the considered AVR system. To validate the performance superiority of the proposed approach its corresponding system’s dynamic response is compared with that of the other well-known AI-based approaches explored in recent literature. Furthermore, the stability study of the proposed AVR system is carried out by evaluating its pole/zero and bode maps. Finally, the robustness of the proposed optimized AVR system against the system’s parameter variation is evaluated by varying the time constants of all the four components of AVR (generator, exciter, amplifier and sensor) from −50% to +50% independently. The proposed algorithm based FOPID tuning technique provides 59.82%, 56.09%, 14.94%, 34.24%, 35.70%, 21.64%, 12.0%, 41.33%, 14.84% and 15.17% reduced overshoot than that of differential evolution (DE), particle swarm optimization (PSO), Artificial Bee Colony (ABC), Bibliography Based Optimization (BBO), Grasshopper Optimization Algorithm (GOA), Pattern Search Algorithm (PSA), Improved Kidney Inspired Algorithm (IKA), Whale Optimization Algorithm (WOA), Salp Swarm Algorithm (SSA) and Local Unimodal Sampling (LUS) algorithm respectively, thus validates its competence and effectiveness.

Abstract The aim of this present investigation is establishing Minkowski fractional integral inequalities and certain other fractional integral inequalities by employing the Marichev–Saigo–Maeda (MSM) fractional integral operator. The inequalities presented in this paper are more general than the existing classical inequalities cited.

Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments. A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation. Slip boundary conditions are used for velocity, temperature and concentration of the nanoparticles. Brownian diffusion and thermophoresis is attended. An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid. The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity. A fourth order Runge-Kutta (RK) scheme is enforced to solve the system numerically. Graphs are prepared for various progressive values of non-dimensionalized parameters whereas; variation in wall drag factor, heat and mass transfer rates is analyzed through numerical data. Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow. Temperature is found as a progressive function for the Brownian motion factor and thermophoresis. The magnitude of wall drag factor, heat transfer and mass transfer rates shows reduction for progressive values of slip parameters.

The intention of the current study is analyzing the significance of nonlinear radiation on magnetic field involving hybrid AA7075 and AA7072 alloys nanomaterials through thin needle. The scenario has been modeled mathematically by captivating the binary chemical reaction and activation energy. Similarity variables are deployed to change the system of PDE’s into nonlinear ODE’s and subsequently solved these equations through bvp4c solver. Influence of distinct material parameters on the velocity, concentration and temperature along with the correlated engineering features quantities such as drag force, heat and mass transfer rate are obtained and demonstrated via plots. The velocity of the liquid is declining function of magnetic field, while the temperature augments. In addition, obtained numerical results are contrasted through the available literature and appeared to be in admirable harmony. The current investigation shows the important features in solar hybrid alloy nanomaterials systems and aircraft technology.

Current effort is devoted to investigate the thermophysical aspects of viscous material in a triangular enclosure interacting with a heated square cylinder placed at central position. To view thermal aspects in explicit manner laminar, steady, incompressible viscous material for two different thermal situations are considered bottom wall is (a) uniformly heated (b) non-uniformly heated. Mathematical modelling of phenomenon is attained in the form of dimensional partial differential expressions. To handle manipulated partial differential system an efficient finite element method is implemented. Discretization of domain at multiple levels is generated in the form hybrid grid containing triangular and quadrilateral elements. Velocity, pressure and temperature are approximated by LBB-stable element. Impact of flow controlling parameters on velocity and thermal profiles for spacious range of Rayleigh number (Ra) and Prandtl number (Pr) are considered. Impact of the sundry parameters on coefficient of convective heat transfer, vortex centres and kinetic energy is also computed and shown in tabular format. It is deduced from heat is more efficiently and effectively supplied for non-uniform heating base wall than the uniformly heated wall. It is worthwhile to mention that discontinuity appears in case of uniform heat supply whereas this singularity is removed in the situation where non-uniform heat is provided. Positive trends in Nusselt number and kinetic energy are disclosed for uplifting magnitude of Rayleigh number. It is also found that velocity magnitude at all locations in cavity increments for intensifying values of Rayleigh number.

Current communication is manifested to investigate flowing features of power law material in a newly proposed physical configuration namely the channel driven cavity. Since power law fluid discloses the dynamical features of shear thinning, shear thickening and Newtonian materials so in present communication it is considered for depiction of flow attributes. To achieve the desired outcomes from the work, a unit length cavity is placed below the channel. The flow is induced with parabolic inlet velocity and a Neumann condition is applied at the outlet, while no slip condition is set at all other boundaries. A square cylinder is placed in the channel with varying positions giving rise to three computational grids named as G1, G2 and G3. Mathematical modelling is constructed by obliging fundamental conservation and rheological laws for power law fluid. Since the representative equations are complex in nature so an efficient computational procedure based on finite element method (FEM) is executed. A hybrid computational grid is generated at coarse level and then further refinement is done to improve the accuracy of the solution. The solution is approximated by adopting P2−P1 element based on second and first order polynomial shape functions. Graphical trends against involved parametric variables are adorned. In addition for more physical insight of problem velocity and pressure plots and line graphs are added. Furthermore, the hydrodynamical benchmark quantities like pressure drop, drag and lift coefficients are evaluated in tabular form around the outer surface of obstacle.

In this exploration, transportation of heat along with homogeneous–heterogeneous reactions for the peristaltic transport phenomenon by considering Ellis fluid model is reported in a symmetric channel comprising compliant walls. Using low Reynolds number and long wavelength assumptions, the governing system of equations of fluid transport problem is abridged and solved using the perturbation technique. The skin friction coefficient and Nusselt number are also incorporated in this contemplation. Particular attention is given to elastic parameters and Brinkman number and plotted their graphs for temperature, concentration, and velocity distribution. Results are deliberated in detail for the various non-Newtonian and Newtonian models. It is initiated that velocity distribution is enhanced for higher values of elastic parameters, which is because less resistance occurs at the channel walls. Relatively reverse comportment is portrayed in the case of concentration profile. The impact of heterogeneous and homogeneous reactions shows reverse bearing on the concentration field. It is comprehended that Brinkman number is an increasing function of viscous dissipation effects, which contribute to enhancing the temperature field for Newtonian and non-Newtonian cases. Moreover, augmentation in skin friction is noticed by escalating the parametric values of damping and rigidity. It is worth mentioning that, fluid velocity grows fastly for the Newtonian model case as compared with the non-Newtonian case by mounting the values of the elastic parameter. Moreover, the temperature field upsurges fastly in a non-Newtonian case as compared with the Newtonian case. The current investigation has an extensive range of use in biomedical science i.e. electromagnetic peristaltic micropumps.

Non-Newtonian fluid rheology representing the properties of pseudoplastic and dilatant materials has received overwhelming attention due to extensive applications in industrial and technological sectors like in metallurgical processes, shock absorbing materials, smart structures, and devices with adaptive stiffness, damping, emulsions, suspensions and so forth. Thus, in current communication characteristics of power law fluid elucidating attributes of pseudoplastic and dilatant materials in channel driven cavity is addressed. Finite element method (FEM) is implemented to interpret rheological features of power law fluid by varying flow controlling parameters. Discretization of domain at coarse level is performed by using stable first and second order polynomial (P2−P1) shape functions. Square shaped cylinder is placed at (1, 1.5) above the cavity. Hydrodynamics forces like pressure difference drag and lift variations are measured at outer surface of cylinder. The impact of primitive parameters like power law index (n) and Reynold number on velocity, pressure and viscosity for shear thinning and thickening cases is adorned. It is deduced that pressure difference increased against the variation in power law index. In similar way the impact of drag and lift forces mounts by increasing power law index. Reynold number has delineating impact on drag and lift forces near the obstacle. It is also seen that pressure shows optimized non-linear behavior near the obstacle and becomes linear along the downstream as expected in channel flow. It is divulged that pressure drops more rapidly for increasing magnitude of Reynold number. Velocity of fluid increases when power law fluid flow is behaving as shear thinning fluid in comparison to shear thickening case.

Abstract A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.

Unsteady free convection slip flow of second grade fluid over an infinite heated inclined plate is discussed. The effects of mass diffusions in the flow are also eligible. Caputo-Fabrizio fractional derivative is used in the constitutive equations of heat and mass transfer respectively. Laplace transform is utilized to operate the set of fractional governing equations for both ramped and stepped wall temperature. Expression for Sherwood number and Nusselt number with non-integer order are found by differentiating the analytical solutions of fluid concentration and temperature. Numerical results of Sherwood number, Nusselt number and skin friction are demonstrated in tables. Solutions are plotted graphically to analyze the impact of distinct parameters i.e. Caputo-Fabrizio fractional parameter, second grade parameter, slip parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number to observe the physical behavior of the flow.

In recent years, material analysis of fluids has generated prodigious interest of researchers due to their effective role in interdisciplinary sciences. In view of its importance, the present communication is devoted to analyze the flow of power law fluid representing the features of shear thinning, shear thickening and Newtonian materials. Constitutive equations expressed in the form of tensorial representations depicting power law relation between viscosity and shear rate. The whole mathematical model is solved computationally via of finite element method by using stable P2−P1 finite element pair. A highly refined hybrid mesh is obliged for the accurate computation of results. Material properties of power law fluid are disclosed in physical configuration renowned as channel driven cavity combining various benchmark problems like cavity flow, forward and backward facing steps and channel flow. Impact of material parameters on pertinent profiles is disclosed through graphs. Verification of computed results is done by comparing the velocity, viscosity, pressure fields for power law fluid with the Newtonian case. Keywords: Finite element method, Power-law fluid, Channel driven cavity, Shear thinning and shear thickening

In current pagination the flow problems involving shear rate dependent nonlinear viscosity have been treated successfully in the sense of space discretization and solvers. The stable finite element pair Q2/P1disc is employed to approximate the velocity and pressure spaces independently. Discretized form of non-linear expressions is linearized by implementing Newton’s procedure and the resulting systems are solved using a geometric multigrid approach. The flow generated by way of driven cavity and by an obstacle are very important benchmarks of computational fluid dynamics. In current pagination shear rate reliant viscosity model renowned as Carreau Yasuda fluid is capitalized. The obtained results are demonstrated and analyzed with the help of velocity and viscosity plots. In addition, we have produced new reference data for kinetic energy (K.E) for driven cavity problem and drag and lift coefficients for circular obstacle problem. The obtained results for driven cavity problem reveal the fact that K.E is an increasing function of the relaxation parameter (λ) and power law exponent (n) whereas a decreasing function of the model parameter (a). For the case of flow around obstacle the drag coefficient (CD) and the lift coefficient (CL) show strong dependence on (λ) and (n), however a weak dependence on the parameter (a). Keywords: Carreau yasuda fluid, Driven-cavity problem, Flow around obstacle, Multigrid method, Finite element method

The present article applies the newly developed concept of Atangana-Baleanu time-fractional derivatives to the electro-osmotic magnetohydrodynamic (MHD) free convectional flow of Walters’-B fluid along with heat and mass distribution. The motion generates in the fluid is due to the oscillations of the vertical plate which is embedded in a porous medium. Employing the idea of Atangana-Baleanu time-fractional order derivatives the conventional model of the Walters’-B liquid is transfigured to the fractional model. With the help of the imposed initial and boundary conditions and by making use of the Laplace transform technique (LTT), analytical solutions are procured for concentration, velocity, and temperature. The impact of various physical parameters on the fluid flow is plotted graphically. It is worth seeing from the graphs of the velocity distribution that the greater values of Walters’-B fluid parameter Γ, cause a decrease in the velocity. Furthermore, it is likewise noted from the graphs that higher values of an electro-osmotic parameter Es cause a decline in velocity profile. This behavior of electro-osmotic on the velocity profile may also work in the process of separation of the fluids at the atomic level and can play a very important job for medication dischargers. Keywords: Walters’-B fluid, Electro-osmotic flow, Mass transfer analysis, Atangana-Baleanu approach, Laplace transform technique

Abstract In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases.

The aim of the present work is to calculate the closed form solutions of the unsteady couple stress nanofluids flow in a channel. Couple stress nanofluids (CSNF) is allowed to pass through the parallel plates separated by a distance h. In this study, we choose blood as base fluid with gold nanoparticles suspension. The lower plate is at rest and the upper plate is suddenly moved with constant velocity U0. Recently, Atangana-Baleanu (AB) introduced a new definition of fractional derivatives. This AB definition of fractional derivative has been applied to the present couple stress nanofluid (CSNF) model. The closed form solutions of present CSNF model via AB approach are obtained by using the Laplace and finite Fourier sine transforms. Exact results of velocity and temperature are displayed and discussed for different parameters of interest. Solutions obtained here are reduced to three different cases in limiting sense i.e. (i) fractional couple stress nanofluid without external pressure gradient. (ii) ordinary couple stress nanofluid. (iii) regular couple stress fluid. Finally, skin friction and Nusselt number are evaluated at lower and upper plates and listed in tabular forms. The results show that increasing external pressure gradient, CSNF velocity increases whereas decreases by increasing Reynolds number. Increasing volume fraction slow down the CSNF velocity. The velocity of Newtonian viscous fluid is higher than CSNF velocity.

The main focus of this theoretical inspection is to explore the control of Newtonian heating on heat transfer for an unsteady natural convection flow of Oldroyd-B fluid confined to an infinitely long, vertically static plate. Partial differential equations are constructed effectively to describe the fluid flow and heat transfer. Some appropriate dimensionless quantities and Laplace transformation are employed as basic tools to evaluate the solutions of these differential equations. However, due to the complex nature of velocity field, solution is approximated by using Durbin's numerical Laplace inverse algorithm. This solution is further validated by obtaining the velocity solution through algorithms proposed by Stehfest and Zakian. The temperature and velocity gradient are also determined to anticipate the heat transfer rate and skin friction at wall. Some well known results in literature are also deduced from the considered model. Conclusively, to have a deep understanding of the physical mechanism of considered model, and influence of implanted parameters, some outcomes are elucidated with the assistance of tables and graphs. As a result, it is found that under the effect of Newtonian heating, freely convective viscous fluid has greater velocity than Oldroyd-B fluid, Maxwell fluid and second grade fluid.

In diabetes mellitus, the efficient alleviation of hyperglycemia, an elevated glycemic concentration, is quite crucial to avoid persistent complications. Thus, it is of prime importance to have an automated closed-loop insulin delivery system, often termed as an artificial pancreas, in the patient's body. The requisite amount of exogenous insulin bolus must be determined by a control algorithm, which is the primary constituent of the closed-loop system. In this article, a finite-time synergistic control approach, based on a gain-scheduled Luenberger observer (GSLO), is introduced. The proposed control strategy establishes a closed-loop insulin delivery system, which confirms the glycemic regulation that is quite obligatory in type-1 diabetic (T1D) patients. The control law is synthesized by using a recursive backstepping with a sliding mode control (SMC) approach. Besides, the nonlinear terms are incorporated, in the pseudo control inputs, which provide the finite-time convergence of the system's trajectories. Since the proposed control law relies on the system's information, thus, a virtual patient simulator, presented by Bergman minimal model (BMM), is transformed into an equivalent dynamic structure, which facilitates the design of GSLO. The observer's gains, which modify in each iteration, are based on the updated values of the system's states. Also, it endorses the separation principle, thus proving the closed-loop system's stability. The proposed closed-loop insulin delivery system confirms the suppression of postprandial hyperglycemia and hypoglycemic events in T1D patients. The efficacy is demonstrated via in-silico testing, which is executed in MATLAB/Simulink environment.

To find the solutions to the equations containing non-linear terms is a very tough task for the researchers. Even it becomes more challenging when someone wants to find the exact solutions. The exact solutions play a vital role which can be used as a benchmark for numerical and empirical solutions. Therefore, the present article aims to investigate the amalgamated effect of viscous dissipation and joule heating on the electro-osmotic flow of generalized Maxwell nanofluid along with heat transfer in a channel. Nanofluid is formed by the uniform dispersion of ultra-fine nano-sized solid particles of clay in concrete which is considered as a base fluid. The classical model of the Maxwell nanofluid is generalized by using the new definition of the Atangana-Baleanu time-fractional derivative. Fourier sine transform and the Laplace transform techniques are used to evaluate the exact expressions for the velocity and temperature distributions. The impact of various embedded parameters such as fractional parameter, Maxwell fluid parameter, volume fraction parameter, zeta potential parameters, electro-kinetic parameter, Brinkman number, joule heating parameter and Prandtl number on velocity and temperature profiles are drawn and illustrated graphically. It is interesting to see that by using nano-clay in concrete the rate of heat transfer increases with 25.5%.

The Lagrangian approach for the two-dimensional incompressible fluid flows has been studied with the help of dynamical systems techniques: Kolmogorov-Arnold-Moser (KAM) theory, stable, unstable manifold structures, and Lagrangian coherent structures (LCSs). For the time-dependent perturbation problems, we analyze in detail the development of transport barriers that play an important role in the transport process. Firstly, the analytical study of KAM theory is adopted to explain the transport and mixing phenomenon in measured and simulated airfoil flow. Then, the flow topology of unsteady flow behind an airfoil is investigated for the low Reynolds number problem. Simulations are carried out based on a particular Finite-Time Lyapunov Exponent (FTLE) technique for the detection of invariant manifolds of the hyperbolic trajectories. Besides, the Characteristic Base Split (CBS) scheme combined with a dual time stepping technique is utilized to simulate such transient flow problems. Thus, in the course of the current research, the role of the velocity phase plot during vortex formation is explored that is highly periodic and resulted in the formation of a stable pattern of manifolds and invariant tori. Hence, the proposed study encouraged the new picture of the vortex shedding and flow separation process. As a conclusion, our results give a better understanding of invariant tori control transport phenomena that will lead to a new heuristic for unsteady flows.

The aim of this study is to obtain the closed form solutions for the laminar and unsteady couple stress fluid flow. The fluid is allowed to flow between two infinite parallel plates separated by distance ℓ. Moreover, we have considered that the lower plate is moving with uniform velocity U0 and upper plate is stationary. For this purpose, engine oil is taken as a base fluid and to enhance the efficiency of lubricating oil, Molybdenum disulphide nanoparticles are dispersed uniformly in the engine oil. The flow is formulated mathematically in terms of partial differential equations of order four. Furthermore, the derived system of partial differential equations are fractionalized by using the mostly used definition of Caputo-Fabrizio time fractional derivative. The more general exact solutions for velocity, temperature and concentration distributions are obtained by using the joint applications of Fourier and the Laplace transforms. The effect of different parameters of interest of the obtained general solutions are discussed by sketching graphs. Furthermore, substituting favorable limits of different parameters, four different limiting cases are recovered from our obtained general solutions i.e. (a) Couette flow (b) Classical couple stress fluid (c) Newtonian viscous fluid and (d) in the absence of thermal and concentration. Moreover, the effect of different physical parameters on the velocity, temperature and concentration distributions are discussed graphically. It is worth noting that couple stress parameter corresponds to a decrease in the velocity profile. In order to observe the differences clearly, all the figures are compared for integer order and fractional order which provide a more realistic approach as compared to the classical model. Additionally, skin friction is calculated at lower as well as upper plate. Nusselt number and Sherwood number are also tabulated. It is noticed that the rate of heat transfer of engine oil can be enhanced up to 12.38% and decrease in mass transfer up to 2.14% by adding Molybdenum disulphide nanoparticles in regular engine oil.

The development and improvements in wind energy conversion systems (WECSs) are intensively focused these days because of its environment friendly nature. One of the attractive development is the maximum power extraction (MPE) subject to variations in wind speed. This paper has addressed the MPE in the presence of wind speed and parametric variation. This objective is met by designing a generalized global sliding mode control (GGSMC) for the tracking of wind turbine speed. The nonlinear drift terms and input channels, which generally evolves under uncertainties, are estimated using feed forward neural networks (FFNNs). The designed GGSMC algorithm enforced sliding mode from initial time with suppressed chattering. Therefore, the overall maximum power point tracking (MPPT) control is very robust from the start of the process which is always demanded in every practical scenario. The closed loop stability analysis, of the proposed design is rigorously presented and the simulations are carried out to authenticate the robust MPE.

In this work, efforts are made to scrutinize the influence of MHD on nonlinear radiative flow comprising Ti6Al4V nanoparticle through streamwise direction along with a crossflow. Activation energy with binary chemical reaction is also explored through cross-flow comprising Ti6Al4V nanoparticle which has not been discussed yet. Similarity variables are employed to transform PDEs into nonlinear ODEs system. Then, it executed numerically through bvp4c from Matlab. Multiple solutions analysis is used to obtain first and second solutions. Influences of controlling non-dimensional parameters on liquid velocity and fluid temperature are scrutinized through the assist of diagrams. Results disclose that the drag surface force and rate of heat transfer increase for greater values of suction, while the rate of mass transfer decreases. Besides, multiple results are noticed for certain values of the moving parameter. Keywords: Titanium alloy nanoparticle, activation energy, binary chemical reaction, cross-flow, non-linear radiation

Researchers are using different types of nanomaterials for the enhancement of the thermal performance of regular fluids such as water, kerosene oil, etc. However, these days, the researchers are more interested in hybrid nanomaterials. The purpose of this communication is to examine the stability analysis of Cu–Al2O3/water hybrid nanofluid over a non-linear shrinking sheet. The hybrid nanomaterials are composed of Cu and Al2O3. These hybridized nanomaterials are then dissolved in water taken as base fluid to form Cu–Al2O3//water hybrid nanofluid. Mathematical analysis and modeling have been attended in the presence of viscous dissipation and suction/injection effects. The governing equations of mathematical models are transformed into self-similar solutions in the form of ODEs by using similarity transformation. Solutions of the non-linear ODEs are created by employing of three-stage Lobatto IIIa formula which is built-in BVP4C function in the MATLAB software. A comparison of the current study has been done with the preceding published literature. The distributions of velocity, temperature profiles, coefficient of skin friction and heat transfer rate are presented graphically and conferred for numerous significant parameters entering into the problem. Results revealed the existence of dual solutions for a certain range of the suction/blowing parameter. Stability analysis is also done in order to obtain dual solutions stability. The smallest eigenvalues suggest that the first solution is stable from the second solution. Hybrid nanomaterials have a high scope toward nurturing our day-to-day life. Keywords: Hybrid nanomaterials, Nanofluid, Dual solutions, Stability analysis, Viscous dissipation, Shrinking surface

This work explores the effect of second order slip on magnetohydrodynamic (MHD) flow of a fractional Maxwell fluid on a moving plate and a comparison between two numerical algorithms (Tzou and Stehfest’s algorithm). The problem is formulated for Maxwell fluid with Caputo-time fractional derivatives. Semi analytical solutions are derived using Laplace transform. The solution is obtained using numerical technique of Laplace transform Stehfest’s algorithm. To insight the physical behavior of the fluid, a graphical illustration is made. The influence of fractional parameter, the magnetic force, the porosity parameter, the slip parameters are analyzed and discussed. A tabular and graphical comparisons with Tzou’s algorithm are made for the sake of validation of the present results. Keywords: Fractional Maxwell fluid, Porous medium, Second order slip, Numerical Laplace inverse

Hybrid nanofluid is an emerging field due to the rapid enhancement of heat transfer and stable nanoparticles in base fluid properties. A three dimensional hybrid nanofluid flow model is constructed over biaxial porous stretching/shrinking sheet with heat transfer, Radiative heat and mass flux (3D-HNF-RHF). Bayesian Regularization technique based on Backpropagated neural networks (BRT-BNNs) is employed to estimate the solution of proposed model. It is the mathematical process which converts nonlinear regression fitting into a well-posed statistical process in the form of ridge regression. This method diminishes length cross validation need and more robust then Backpropagation technique. The proposed flow system 3D-HNF-RHF is transferred to ordinary differential equations (ODEs) possessing physical variations through self-similar transformations. The effect of derived variations such as thermal relaxation parameter, mass flux parameter, Stretching/shrinking parameter, Prandtl number, Skin friction and Nusselt number observed over the velocity and temperature fields. Numerical results of these physical parameters have been presented in tabulated form obtained from a dataset constructed through Homotopy Analysis Method imposed on 3D-HNF-RHF model. Statistical tests through mean square error, histogram curve and regression fitting curves are employed to check the accuracy and convergences of the solution obtained through BRT-BNNs. It is observed that Stretching/shrinking quantity and mass flux parameter slow down the flow rate whereas, increase radiative heat flux upsurges the temperature gradient. The impacts of surface drag force and heat transfer are illustrated through the different graphical illustrations.

This numerical study is about the steady incompressible non-Newtonian fluid flow in a channel with static obstacles. The flow field is governed by the Generalized Navier-Stokes equations incorporating the constitutive relation of power-law fluids. Three cases are considered: 1) circular obstacle (C1), 2) semicircular obstacle (C2), and 3) both circular and semicircular obstacles. A range of values of the power-law index 0.3≤n≤1.7 are considered at Re=20 to check the impact of shear-thinning and shear-thickening viscosity on the drag and lift coefficients. The correlation between drag and lift coefficients is calculated against the power-law index. The simulated results of velocity and pressure are investigated at different sections of the channel. Benchmark results of drag and lift for the Newtonian fluid are reproduced as a special case. A strong positive correlation is observed between drag and lift coefficients in the case of a single obstacle, while in the case of dual obstacles and inverse correlation, drag and lift coefficients have been found.

This research presents the stagnation point flow with heat transfer of water-based hybrid nanofluid over a stretching/shrinking wedge. Magnetic field is applied normal to the wedge with melting heat transfer effect. The wall of the boundary with slip effect on the surface. Water as base fluid with two different nanoparticles (Al2O3 and Cu) is considered. The Navier-Stokes and heat equation are first simplified through similarity variables to convert the partial differential equations (PDEs) into non-dimensional ordinary differential equations (ODEs). The numerical solutions are obtained with the help of bvp4c technique in MATLAB programming. This study is focused on the impacts of different dimensionless parameters on the velocity field, temperature distribution, skin friction coefficient and Nusselt number. It is seen that the solution of governing ODEs has two branches, first and second branch solutions in some specific range of supervising parameters. It is found that heat transfer rate enhances against melting parameter in the first branch solution and converse behavior can be observed for second branch solution. It is also uncovered that in hybrid nanofluid, the momentum and thermal boundary layer thickness enhances in first solution while reduces in the second solution with the advancement of angle of wedge parameter.

Conversion of fructose to furan aldehydes is a rapidly developing concept considering the emergent scenario of the replacement of fossil-derived components to biomass-derived green precursors. 5-hydroxymethyl furfural (HMF) and levulinic acid (LA) are the two most important bio-precursors with expanded downstream utilization in modern industries. Their production from biomass-derived sugars is a complex reaction due to competitive side reactions with a variety of byproducts. Therefore, their simulated optimization is an important tool that can help for process optimization in an economical way. In this article, we have developed a mathematical solution for fructose conversion, HMF production, and levulinic acid (LA) formation in a reactive environment. The accuracy of the developed model is further verified through experiments and found satisfactory with high accuracy. Therefore, the developed model can be used to simulate the reaction environment and product optimization under a given set of conditions.

The quantum (or q-) calculus is widely applied in various operators which include the q-difference (q-derivative) operator, and this operator plays an important role in geometric function theory (GFT) as well as in the theory of hypergeometric series. In our present investigation, we introduce and study q-differential operator associated with q-Mittag–Leffler function which is an extension of the Salagean q-differential operator. By using this newly defined operator, we define a new subclass of analytic function and studied certain subclass of analytic function in generalized conic domain Ωk,q,γ. For this class, we investigate structural formula, coefficient estimates, sufficient condition, Fekete–Szegö problem, and also some subordination results.

Fractional fluid models are usually difficult to solve analytically due to complicated mathematical calculations. This difficulty in considering fractional model further increases when one considers nth order chemical reaction. Therefore, in this work an incompressible nanofluid flow as well as the benefits of free convection across an isothermal vertical sheet is examined numerically. An nth order chemical reaction is considered in the chemical species model. The specified velocity (wall's) is time-based, and its motion is translational into mathematical form. The fractional differential equations are used to express the governing flow equations (FDEs). The non-dimensional controlling system is given appropriate transformations. A Crank Nicholson method is used to find solutions for temperature, solute concentration, and velocity. Variation in concentration, velocity, and temperature profiles is produced as a result of changes in discussed parameters for both Ag-based and Cu-based nanofluid values. Water is taken as base fluid. The fractional-order time evaluation has opened the new gateways to study the problem into a new direction and it also increased the choices due to the extended version. It records the hidden figures of the problem between the defined domain of the time evaluation. The suggested technique has good accuracy, dependability, effectiveness and it also cover the better physics of the problem specially with concepts of fractional calculus.

In this article, two-phase compressible six equation flow model is numerically investigated. The six-equation model consists of velocity, pressure equations, and also relaxation terms. An extra seventh equation is included describing the total energy of the mixture to ensure the correct treatment of the sharp discontinuities. The model is hyperbolic and poses numerous difficulties for numerical schemes. An efficient and well-balanced scheme can handle the numerical difficulties related to this model. The second order space-time CE/SE scheme is extended to solve the model. This scheme offers an effective numerical method for several continuum mechanics problems. The suggested scheme suppresses the numerical oscillations and dissipation effects. Several numerical test cases have been carried out to reveal the efficiency and performance of the proposed approach. The results are compared with the exact solution and also with Runge-Kutta Discontinuous Galerkin (RKDG) and central (NT) schemes.

This study presents a modified simplest equation method (MSEM) to investigate some real and exact solutions of conformable time fractional Benjamin-Bona-Mahony (BBM) equation and Chan-Hilliard (CH) equation. We use traveling wave transformation to obtain the results in the form of series solution. Some calculations are performed through Mathematica software to analyze the accuracy of this approach. Graphical representations are reported for more significant results at different fractional-order which demonstrates that this approach is very simple, adequate, and legitimate.

This article has concentrated on heat transfer analysis in the unsteady MHD natural convection flow of viscous fluid under radiation and uniform heat flux over an infinite vertical plate embedded in a porous medium. Overall solutions are found for temperature as well as velocity by the Laplace transform techniques. In the literature, the solutions that have been achieved are rare, meet with all the initial and boundary conditions imposed, and can make general solutions for any problem with motion with this form’s methodological relevance. Also, few different cases of engineering applications are discussed. Solutions are plotted graphically through the use of the Mathcad software to analyze how the variation is taking place in the physical behavior of the viscous fluid flow with respect to the change in a distinct physical parameter.

This article aims to investigate the combined effects of the heat transfer and magnetic field on the electrically conducting magnetohydrodynamic two-phase free convective flow of dusty Casson fluid between parallel plates. The flow is caused by buoyancy force with heat transfer due to free convection. Moreover, the left plate moves at uniform velocity while the right plate is stationary, and all dust particles with spherical forms are scattered evenly throughout the fluid. Mathematically, the flow is described as partial differential equations. A newly introduced fractional derivative, namely Caputo-Fabrizio fractional derivative, is used to generalize the given derived system of PDEs. The problem is solved using joint applications of finite sine Fourier and Laplace transforms. Exact solutions of velocity and temperature profile are obtained. Moreover, the impact of different parameters like a magnetic parameter, Grashof number, Dusty fluid parameter, Casson parameter, Peclet number, Reynold number, and particle's mass parameter on temperature, and dust particle and Casson fluid velocity have been discussed. The graphical results for Casson fluid, dusty fluid, and temperature profiles are plotted through Mathcad-15. The behavior of Casson fluid and dusty fluid is matching for different embedded parameters. Moreover, the Nusselt number and skin friction are also determined. It is shown in Table 1 that by increasing the value of the peclet number, the rate of heat transfer decreases. Furthermore, Table 2 shows that by increasing the magnetic parameter, the skin friction decreases. Graphical results conclude that fractional Casson fluid model described a more realistic aspect of the both (Fliud and dust particle) velocities profile, temperature profile, rate of heat transfer and skin friction than the classical Casson fluid model.

Quantum correlations at higher-order were measured in lead–lead collisions at the world largest collider, and a substantial suppression was reported while measuring the three and four pions interferences. The fraction of coherence owing to pion generation in collisions of heavy ions at extreme energies can be investigated along with this suppression. We show and examine pions excretion from a dispersion grouping of droplets using Bose–Einstein condensation which influences the multi-pion correlations to study the structure of the sources as well as the peculiarities of the coherence fraction in collisions at higher energy. We surmised that pions appear to be the preeminent contender for coherence fractions in the following sequence and the correlation functions resulted in the creation of a composite phase of partons–hadronic matter. The main contribution of this research is that we explore the sequences of three and four particles correlations as well as the genuine correlations carried out to probe the fraction of pions condensation during the collisions of heavy nuclei employing a granular structured source. We perceived the considerable difference in the normalized correlations functions between two sources at various droplets number and coherence fractions with this unique technique. We also compared our model results to the scientific results and obtained the coherent fraction which is consistent with the experimental data.

The major motivation behind this work is to utilize p,q-calculus and inspected the generalized p,q-Ruscheweyh differential operator. At the present time, we utilized p,q-Ruscheweyh differential operator and examined some new subfamilies of S and study some essential properties, for example, inclusion and subordination properties.

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.