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The electro-osmotic flow of Oldroyd-B fluids in a 90° curved tube with a rectangular section under a direct electric field is numerically studied. By introducing elastic forces into the force balance of viscous, electric, and centrifugal forces, another secondary flow pattern is found in addition to the stable state for Newtonian fluids, i.e., the periodic oscillation state. In this oscillating state, the position of the maximum velocity periodically moves from the center to the position near the wall. Meanwhile, a symmetric vortex can be periodically observed in the streamline figures. The secondary flow oscillates when the Deborah number De or the dimensionless wall potential ψ is sufficiently large, and the oscillating frequency increases with a larger Deborah number De or a larger dimensionless wall potential ψ. A phase diagram of the secondary flow as it depends on the Deborah number De and the dimensionless wall potential ψ is presented. There is a critical Deborah number De c r for a given wall potential ψ , and the secondary flow become periodically oscillating at De > De c r . The critical Deborah number De c r decreases as the value of the dimensionless wall potential ψ increases. Moreover, the critical Deborah number should be larger than 0.2 even though the wall potential ψ further increases, i.e., De c r > 0.2. At De ≤ 0.2 , the elastic forces are small, and the secondary flow is stable rather than oscillating similar to the phenomena of Newtonian fluids. [ABSTRACT FROM AUTHOR]

In this paper, the log-conformation representation method (LCR) is applied in an orthogonal curvilinear coordinate system to study the Giesekus fluid flow in a curved duct. Derivations for evolution equations of LCR in this curvilinear coordinate system are presented. Secondary flow patterns and oscillation solutions are computed by using the collocation spectral method. The influence of a wide range of Dean number, Weissenberg number, and dimensionless mobility parameter α on fluid behaviors is studied. A six-cell secondary flow pattern is found under very low Dean number and relatively high Weissenberg number and α. Moreover, both Weissenberg number and α are able to facilitate the development of the secondary flow. In addition, simulations under critical Reynolds number for oscillation imply that Giesekus fluid flow with W e ≥ 0.1 is not able to retain a four-cell secondary flow pattern in a steady state, which is different from Newtonian fluids. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a fractional diffusion model to simulate the movement of chloride in concrete. In such complex porous structure some of the free chlorides, which are affected by the surrounding heterogeneous physical environment, will be bounded physically and chemically. Furthermore, experiments reveal that the interesting heavy-tailed phenomena appear in diffusion process. The time and spatial fractional derivatives are introduced to explain the anomalous diffusion and the dependence of medium properties. The numerical research shows that present model could better fit the experimental data and the diffusion of chloride in concrete is time-dependent and space-dependent. [ABSTRACT FROM AUTHOR]

The convection heat transfer of a viscoelastic Giesekus fluid between a square cavity and a heated inner elliptical column is considered by the open source software OpenFOAM. When the Prandtl number is 7, physical parameters, such as Rayleigh number ( 10 3 ≤ R a ≤ 10 7 ), the long semiaxis of the inner elliptical column (0.2 H ≤ a ≤ 0.4 H), Weissenberg number (1 ≤ W i ≤ 100), mobility factor (0 ≤ α ≤ 0.5), and the polymer viscosity ratio (0.1 ≤ β ≤ 0.9), are investigated. These combined effects are discussed using streamlines, thermal field distributions, and average Nusselt numbers. The numerical results are validated by the comparison with other numerical and experimental ones. The high Rayleigh number destroys the symmetry of the streamlines of the Giesekus fluid, which is a phenomenon not present in Newtonian fluids. At the same time, the high Rayleigh number enhances the flow and heat transfer while exacerbating the instability, leading to periodic oscillations in both flow and heat transfer. The variations of multi-physics fields are analyzed for the cases such as strong elasticity without shear thinning, medium elasticity with medium shear thinning, and weak elasticity with strong shear thinning effects. Stronger elasticity favors the enhancement of flow and heat transfer in viscoelastic fluids, and this effect is more significant when the Weissenberg number is small. [ABSTRACT FROM AUTHOR]

This paper presents a computational fluid dynamics study of the evaluation of wind-flow field characteristics around arch-supported structures. The effectiveness of numerical simulations is validated through a detailed comparison with wind tunnel experimental data from the literature. The mean, spatial variation, maximum and minimum wind pressure coefficient distributions on different roof shape arch-supported structures (cusp, flat, and vaulted structures) were examined, and the investigation was extended by discussing different wind directions and various rise-span ratio structures. Results indicate that the wind pressure coefficient and turbulence disturbance on the cusp structure decrease significantly in magnitude compared with other structures. Structures experience relatively larger mean wind pressure coefficient with lower terrain roughness index. Furthermore, for a cusp structure, an increase in the rise-span ratio leads to the growth of wind pressure on the structure surface. In comparison with other wind directions, the roof surface is loaded with stronger negative wind pressure with an oblique wind direction of 45°. In particular, investigations on the effects of oblique wind directions and cusp-shaped structures on wind pressure and field need to be performed because they can be used for optimal engineering design. [ABSTRACT FROM AUTHOR]

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions, the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud (Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228-1237 (2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution. [ABSTRACT FROM AUTHOR]

A mixed convection flow and heat transfer of pseudo-plastic power law nanofluid past a stretching vertical plate is investigated. Three types of nano-particles, such as copper (Cu), aluminum oxide (Al 2 O 3 ) and titanium oxide (TiO 2 ), are considered. The generalized Fourier law proposed by Zheng for varying thermal conductivity of nanofluids, which is dependent on the power law of velocity gradient as well as the nano-particles property, is taken into account. Dual solutions are obtained by Bvp4c with Matlab. The stability of the solution also is discussed by introducing the unsteady governing equations. Furthermore, a new interesting phenomenon is found: the local Nusselt number do not maintain the similar characteristics of Newtonian fluid near the point where the velocity ratio is equal to 0.5. [ABSTRACT FROM AUTHOR]

The unsteady, two-dimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. The governing equations are transformed into a coupled nonlinear two-points boundary value problem by a suitable similarity transformation. Unlike the classic Berman problem (Berman in J. Appl. Phys. 24:1232-1235, 1953), three new solutions (totally six solutions) and no-solution interval, which is one of important characteristics for the laminar flow through porous pipe with stationary wall (Terrill and Thomas in Appl. Sci. Res. 21:37-67, 1969), are found numerically for the first time. The multiplicity of the solutions is strictly dependent on the expansion ratio. Furthermore, the asymptotic solutions are constructed by the Lighthill method, which eliminates the singularity of the similarity solution, for large injection and by the matching theorem for the suction Reynolds number, respectively. The analytical solutions also are compared with the numerical ones and the results agree well. [ABSTRACT FROM AUTHOR]

The modified model of magneto-hydrodynamic (MHD) flow and heat transfer of power-law fluid over a stretching permeable surface with prescribed heat flux in the presence of heat generation or absorption is investigated. The thermal conductivity is assumed to be dependent on the power law of velocity gradient. The general boundary conditions are given and Lie-group method is used to determine the appropriate boundary conditions suitable for the similarity solution. By using the achieved similarity transformations, the similarity equations are obtained and solved numerically by Bvp4c with Matlab. Graphical solutions for the dimensionless velocity and temperature as well as skin-friction coefficient and Nusselt number for various parameters are presented and discussed. [ABSTRACT FROM AUTHOR]

The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink. [ABSTRACT FROM AUTHOR]

In this paper, Haar wavelet operational matrix(HWOM) is proposed to solve initial-boundary value problems for a class of time-space fractional partial differential equations of Caputo sense with variable coefficients in both time and space (1) ∑ i = 1 n θ i ∂ γ i u ( x , t ) ∂ t γ i = v ( x , t ) ∂ α u ( x , t ) ∂ x α + d ( x , t ) ∂ β u ( x , t ) ∂ x β + q ( x , t ) , 0 < x < 1 , 0 < t ≤ 1 , as an extension of Rehman and Khan's (2013) work. We obtain a matrix L instead of Q α in Rehman and Khan (2013). when dealing with boundary conditions. By utilizing the operational matrix of fractional integration and Hadamard product,we made an improvement of algorithm to deal with time-space coefficients and gave the error analysis of the HWOM for space-time dimensions. Some numerical results are paralleled with exact solutions to show the efficiency and precision of the presented technique. [ABSTRACT FROM AUTHOR]

In this paper, we examine the laminar film condensation of pseudo-plastic non-Newtonian fluids with variable thermal conductivity on an isothermal vertical plate. The thermal conductivity is assumed to be power-law-dependent on the velocity gradient. The dual similar solutions, which are influenced by the parameters of the power law number n and the thickness η δ of the condensation film, are obtained numerically by Runge–Kutta method coupled with shooting method. More attention is paid to discuss the first branch of the solutions with physical meaning. Especially the effects of above both parameters on the velocity and temperature distribution, condensation mass flow rate and the local Nusselt number are analyzed in detail. [ABSTRACT FROM AUTHOR]

In this paper, the flow of a micropolar fluid through a porous channel with deforming walls is investigated. The Lie group method is applied to determine symmetry reductions of partial differential equations. Compared with previous work, the similar variable for the microrotation velocity also is obtained, which is an extension of the case corresponding to the Newtonian fluids (Boutros et al., 2007). This problem we study here can be considered as an extension of the model discussed in Boutros et al. (2007). The effect of the permeation Reynolds number Re , the micropolar parameter K and the expansion ratio α are studied numerically and the results are plotted. Furthermore, the multiple solutions also can be found for some values of parameters. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of semilinear systems of reaction–diffusion on a bounded smooth domain with Dirichlet boundary condition. Applying the potential well method, we find invariant sets for the initial-boundary value problem and derive a threshold of blow up and global existence for its solution. [ABSTRACT FROM PUBLISHER]

Abstract: Considering the influence of the viscous dissipation in the energy equation, we investigate the flow and heat transfer of an incompressible micropolar fluid in a channel with expanding or contracting walls. By introducing suitable similarity transformations, the nonlinear partial differential equations are reduced to a system of ordinary differential equations. Homotopy analysis method (HAM) is employed to obtain the series solutions for the velocity, microrotation and temperature distribution. In order to analyze the influence of the micropolar parameter, the Reynolds number and the deformation of the wall, the graphs for velocity components, microrotation, temperature, couple stress and shear stress in the channel are presented and discussed in detail. [Copyright &y& Elsevier]

A time-distributed order fractional continuity model is proposed to simulate the rotating electro-osmotic slip flow of generalized Maxwell fluids in an alternating electric field. The model fully exhibits the wider memory characteristics of viscoelastic fluid. Complex momentum equation is discretized by L1 and L2 algorithms and verified by constructing analytical solutions method. Due to the stronger memory of generalized Maxwell fluids, reverse flow is restrained, and the time for oscillation reaching the steady state is postponed. Moreover, with the increase of Debye–Hückle coefficient the velocity will increase rapidly. • The time-distributed fractional order model is introduced to describe the characteristics of viscoelastic fluid. • The effects of alternating current frequency and Debye–Hückle coefficient are considered. • The reverse flow is restrained due to the existence of viscoelastic characteristics. • The time to reach constant amplitude oscillation is later compared with Newtonian fluid. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed. [Copyright &y& Elsevier]

This study numerically simulates the two-dimensional flow of Oldroyd-B fluid around an isosceles right-angled triangular cylinder with five orientations. The log-conformation reformulation is employed to stabilize the numerical simulations. By adjusting the triangular orientation angle (θ), three types of fluids development process can be observed: from steady to vortex shedding at θ = 0 and π , keeping the vortex shedding at θ = π 4 and 3 π 4 , and from vortex shedding to steady state at θ = π 2 . When the triangular cylinder faces the incoming stream with the inclined plane, the elastic effect acting on the cylinder is strong, otherwise it is weak. For θ = π 2 , the effects of the viscosity ratio (β), the Reynolds number (R e), and the Weissenberg number (W i) are further investigated. When the elasticity is reduced by changing the viscosity ratio (β) that ranged from 0 to 0.9, the final flow state will transition from stable to vortex shedding state, which indicates the restraining effect of elasticity on wake instability. In the high elastic Oldroyd-B fluid, the critical Reynolds number for vortex shedding is about 110 for W i = 1. Besides, the Weissenberg numbers (W i) ranged from 0.25 to 8 are discussed at R e = 100. With the increase of W i , four different flow states of the wake are observed: periodic vortex shedding at low Weissenberg number W i = 0. 25 , stabilizing for W i ranged from 0.5 to 1, semi-periodic strong vortex shedding for W i is about 2, and chaos when W i ≥ 4. The results indicate that excessively strong elastic effects may also lead to unstable flows. Finally, the flow states corresponding to each Reynolds number and Weissenberg number in a certain range (90 ≤ R e ≤ 120 and 0. 125 ≤ W i ≤ 4) are given in this study. • The strong elasticity mainly acts on the hypotenuse of the leading edge of the triangular cylinder. • The vortex shedding can be inhibited by the elasticity. • Inertial elastic instability is observed at high Weissenberg numbers. [ABSTRACT FROM AUTHOR]

In this paper, a delayed fractional-order epidemic model with general incidence rate and incubation period is proposed for the Corona Virus Disease 2019 (COVID-19) pandemic. The corresponding sufficient conditions are established to analyze the existence and stability of disease-free equilibrium and endemic equilibrium of the proposed model. The conditions for the existence of Hopf bifurcation are obtained by selecting the time delay as the bifurcation parameter. The control strategies for the COVID-19 pandemic are designed, and the corresponding delay fractional order optimal control problem (DFOCP) is analyzed based on the generalized Euler–Lagrange equation. The parameters of the model are identified based on the data of multiple types of the COVID-19 pandemic. Further, the effectiveness of the model in describing the trend of the COVID-19 pandemic is verified. Based on the results of parameter identification, the influence of incubation period on the COVID-19 pandemic is discussed. The forward–backward sweep method (FBSM) is adopted to numerically solve DFOCP, and the control effects under different control measures are analyzed. [ABSTRACT FROM AUTHOR]

The finite difference schemes for equations depicting the fluid flow, heat and mass transfer of viscoelastic fluid in porous media based on fractional constitutive model are analyzed, when Soret and Dufour effects are taken into account. Different from the conventional fractional partial differential equations, the governing momentum equation of this system not only contains convection terms, but also a term: D t β 0 (∂ 2 u / ∂ y 2) , which are great challenges when we do the stability analysis. In addition, the temperature equation and concentration equation are coupled with each other, which increases the difficulty of numerical analysis. By using the energy method, the stability and convergence of the finite difference schemes employed for the governing equations are obtained. The accuracy of the scheme for momentum equation is O (τ + h x 2 + h y 2) , while the one for temperature and concentration equations is O (τ 2 + h x 2 + h y). Finally, numerical examples are presented to verify methods and demonstrate the analysis effectiveness. [ABSTRACT FROM AUTHOR]

Steady forced convection of non-Newtonian nanofluids around a confined semi-circular cylinder subjected to a uniform magnetic field is carried out using ANSYS FLUENT. The numerical solution is obtained using the finite volume method. The user-defined scalar (UDS) is used for the first time to calculate the second order velocity slip boundary condition in semi-circular curved surface and the calculated results are compared with those of the first order velocity slip boundary condition. Besides, the effects of volume fraction, size, type of nanoparticles and magnetic field strength on heat transfer are studied. The present study displays that adding nanoparticles in non-Newtonian fluids significantly enhances heat transfer. In addition, it is observed that the heat transfer rate decreases first and then increases with the increase of Hartmann number. The effects of blocking rate on Nusselt number, wake length and heat transfer effect are shown in the form of graphs or tables. [ABSTRACT FROM AUTHOR]

This work investigates unsteady electro-osmotic flow of a fractional second-order viscoelastic fluid in a micro-rectangle channel with considering depletion effects. Due to the existence of depletion, there are depletion layer near the plate and bulk flow adjacent to depletion layer for the flow in the whole domain. In order to express the boundary conditions at the interface, we introduce Maxwell stress to describe the interaction between Newtonian fluid and viscoelastic fluid with fractional derivative. To ensure the validity of the semi-analytical solution obtained by Laplace transform, the numerical solutions are acquired by finite difference method and Grünwald-Letnikov approximation and both of them have a better agreement. The increasing viscosity of viscoelastic fluid leads to the increasing driving difficulty of fluid in non-depleted layer and the decreasing velocity amplitude at steady state. Moreover, the increasing interfacial zeta potential difference can promote the fluid flow, and the change of interface charge density makes the velocity at the interface change dramatically. [ABSTRACT FROM AUTHOR]

The electro-osmotic flow and heat transfer of a Maxwell fluid with distributed-order time-fractional characteristics in a microchannel under an alternating field is investigated, while considering viscous dissipation and Joule heating. The unsteady momentum and energy equations are computed numerically directly using the finite volume method. The accuracy of the numerical method is validated by comparison the constructed velocity distribution with the velocity distribution in previous references. With the time going on, oscillation of alternating current with a constant amplitude will afford periodic velocity distribution. The temperature will periodically increase. Furthermore, the velocity and temperature distributions characteristics of a Newtonian fluid, fractional Maxwell fluid, and generalized Maxwell fluid with time distribution are compared. Finally, the effects of different physical parameters K, S, Br, Ha, λ, Ω, ψ1, ψ2, Pr , and δ on the velocity and heat distributions under an alternating field are discussed. [ABSTRACT FROM AUTHOR]

Abdominal aortic aneurysm (AAA) is a serious dilated vascular disease. The risk factors of aneurysm rupture and postoperative blood pressure are the major clinical concerns. The purpose of this work is to analyze the hemodynamic difference between preoperative and postoperative AAA using patient-specific boundary conditions and explore the rupture risk of AAA with different torsion and to simulate the blood flow of different degrees of hypertension. A three-element Windkessel model is utilized as the outlet boundary condition. 20-sim software and self-developed user-defined functions are used to calibrate the parameters. To analyze the influence of aortic tortuosity on hemodynamics, five AAA geometries with different torsion degrees are modified and obtained. We also grade the hypertension and explore the effect of hypertension after operation. The analysis results are consistent with the patient-specific situation. The results show that stent implantation for aneurysms reduces the pressure at the lesion site and increase the speed and wall shear stress. Vessels with high torsion have lower time-averaged wall shear stress (TAWSS), higher oscillatory shear stress index (OSI) and relative retention time, and more disordered blood flow. After stent implantation, with the increase in blood pressure, TAWSS and OSI continue to increase, and the blood flow speed is also faster. AAA with high torsion is more likely to rupture. In clinical practice, attention should be paid to the degree of torsion of the lesion site. Furthermore, blood pressure should be monitored and controlled in time to prevent postoperative complications. [ABSTRACT FROM AUTHOR]

In order to avoid insufficient sterilization caused by uneven heating and nutrition loss generated by excessive heating, researchers and scientists have focused on the topics of controllable heat transfer and predictable temperature fields in food processing. In this paper, the temperature distribution of power-law liquid food under the combination impacts of the thermal radiation and natural convection is studied by the numerical technique. Three kinds of open symmetrical heating containers commonly used are paid attention to, and the height and cross-sectional area of containers are set to equal for the convenience of comparing the effect of the container geometry on the temperature fields. The governing equations are treated in a dimensionless way as well as the boundary conditions. The finite element method is used to obtain the solutions, which has been proved robust and accurate. It has been displayed that the temperatures in the cylindrical container (i.e., the noodle bowl) are the highest, which proves its best heating effect. The liquids of egg yolk and egg white are adopted as special cases of non-Newtonian power-law fluids. The temperature fields of egg yolk and egg white are less affected by the generalized Grashof number than the thermal radiation number NR. The technique of adjusting the generalized Grashof number and the thermal radiation to control the heat transfer behavior applied in the present research could be extended to related food engineering applications. [ABSTRACT FROM AUTHOR]

The boundary layer of a pseudoplastic fluid on a semi-infinite plate for a high generalized Reynolds number is analyzed. Based on the Prandtl mixing length theory, the turbulent region is divided into two regions. The coupled momentum and temperature equations, with a generalized thermal conductivity model, have made the process of finding the analytical solutions much difficult. By using the similarity transformation, the equations are converted to four ordinary differential equations constrained by ten boundary conditions. An interesting technique of scaling and translation of the calculation domain of one region into another is used to make the system of equations easier to solve. It is found that the fluid with a smaller power-law index, associated with a thinner velocity boundary layer thickness, processes a lower friction coefficient. Furthermore, the increase in the Reynolds number causes a thinner velocity boundary layer and a decreasing friction coefficient on the wall. Changes in temperature occur more slowly near the plate surface with a rise in the power-law index and a decrease in the Reynolds number. [ABSTRACT FROM AUTHOR]

This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]

Atherosclerosis of lower extremity is often accompanied by thrombosis and plaque injury. Currently, there is a lack of comprehensive hemodynamics study that combines platelet activation related to thrombosis and plaque injury in atherosclerosis. Thus, we first analyze the mechanism of platelet activation and plaque injury and further investigate the effects of stenosis and hematocrit through hemodynamic results. An Euler–Euler method is used for the mixed fluid containing red blood cells (RBCs) coupled with a Lagrangian approach for the transport of plasma particles. To more realistically implement this mathematical model, we employ user-defined functions to incorporate platelet level of activation (LOA), vessel specific Windkessel model, RBCs form factor, and platelet form factor into the simulation calculation framework. Our results suggest that in a narrow larynx, high wall shear stress activates platelets. Subsequently, platelets accumulate downstream of the stenosis due to the reflux caused by the stenosis or hyperviscous blood stasis on account of increased hematocrit. The stenosis rises from 0.00% to 70.01%, or the hematocrit from 0.55 to 0.65, and increases LOA by 5.00% or 34.41%, respectively, in conclusion high stenosis and high hematocrit predispose to thrombosis and plaque injury. Therefore, it is necessary to regularly check the degree of stenosis in patients with atherosclerosis, especially in those with high hematocrit caused by related disease. The results obtained could provide a theoretical basis for the diagnosis and treatment of lower limb atherosclerosis. [ABSTRACT FROM AUTHOR]

Viscoelastic fluids have many applications in engineering, and studying the complex fluidity of viscoelastic fluids can improve their applicability. Based on the flow caused by the pressure or the moving plate with various velocities, the aim of this paper is to deeply study the significance of absorbing boundary condition for the flow mechanism analysis of the fractional Maxwell fluid, of which the constitutive relation is formulated by introducing the relaxation parameter and the fractional parameter with considering the memory characteristics. For treating the model in a semi-infinite boundary domain, the artificial boundary method is applied to transfer it to a problem in a bounded domain with absorbing boundary condition, which is solved numerically by the finite difference method combined with the L1 formula and verified by numerical examples. The difference of the flow characteristics is subject to the direct truncation boundary condition and the absorbing boundary condition is compared and the effectiveness and rationality are analyzed graphically, and the influences of the dynamic parameters on the velocity and the flow mechanism are also discussed. The main findings of this research are that the larger relaxation parameter plays a role in a stronger delay effect, a larger fractional parameter refers to the stronger memory characteristics of the delay effect, and the smaller Reynolds number leads to the larger viscous force, all of which lead to a slower flow process. [ABSTRACT FROM AUTHOR]

Based on the linearized Poisson–Boltzmann equation, the electro-osmotic flow of a generalized Maxwell fluid under an alternating field in an isosceles right triangle microchannel is studied. The finite volume method and L2 interpolation method are used to obtain the numerical solution. An analytical solution is constructed to verify the accuracy of the numerical solution. Under the alternating current, the velocity will oscillate periodically. The velocity amplitude of the Maxwell fluid with the distributed order time fractional derivative is larger than that of Newtonian fluids and fractional Maxwell fluids, which indicates that its elastic characteristics further promote fluid flow. However, oscillation of the velocity does not achieve synchronization with the oscillation of the electric fields. Furthermore, due to the existence of the angle effect, the velocity will develop at acute angles and form a larger value of velocity first. The numerical results show that the relaxation time, electrokinetic width, zeta potential, and angular Reynolds number play important roles in determining the velocity and amplitude of electro-osmosis. [ABSTRACT FROM AUTHOR]

This paper is concerned with multiple solutions of a singular nonlinear boundary value problem (BVP) on the interval [ 0 , 1 ] , which arises in a study of the laminar flow in a porous pipe with an expanding or contracting wall. For the singular nonlinear BVP, the correct boundary conditions are derived to guarantee that its linearization has a unique smooth solution. Then a numerical technique is proposed to find all possible multiple solutions. For the suction driven pipe flow with the expanding wall (e.g. α = 2 ), we find a new solution numerically and classify it as a type VI solution. The computed results agree well with what can be obtained by the bifurcation package AUTO. In addition, we also construct asymptotic solutions for a few cases of parameters, which agree well with numerical solutions. These serve as validations of our numerical results. Thus we believe that the numerical technique designed in the paper is reliable, and may be further applied to solve a variety of nonlinear equations that arise from other flow problems. [ABSTRACT FROM AUTHOR]

• A Caputo fractional-order COVID-19 model with generalized incidence rate is established, and some dynamic behaviors are analyzed. • Identify the parameters of the model according to relevant statistical data, which verifies the effectiveness of the model for depicting the COVID-19 pandemic. • Based on the relevant statistical data, the corresponding fractional optimal control problem is proposed and analyzed. • The numerical format of Riemann–Liouville adjoint system with transversality condition is given, and the fractional optimal control problem of the COVID-19 model is solved numerically. In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R 0 , the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann–Liouville (R–L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed. [ABSTRACT FROM AUTHOR]

The diffusion in comb structure is an important kind of anomalous diffusion with widespread applications. The special structure corresponds to a novel characteristic of anomalous diffusion, which is characterised by the Dirac delta function in the governing equation. By considering the memory characteristic, the fractional derivative is introduced into the constitutive relation, and a new fractional governing equation in the infinite regions is constructed. Instead of simply truncating for the infinite regions, the exact absorbing boundary conditions are deduced by using the (inverse) Laplace transform technique and the stability is analysed. To deal with the governing equation containing the Dirac function, the finite difference method is proposed and the term with the Dirac function is handled using an integration method. The stability and convergence of the numerical scheme are discussed in detail. A fast algorithm is presented that the normal L 1-scheme is approximated via a sum-of-exponentials approximation. Three examples are conducted, in which the particle distributions and the mean square displacement for the anomalous diffusion in comb structure are discussed. The computational time between the normal numerical scheme and the fast numerical scheme is compared and the rationality and validity of absorbing boundary conditions are analysed. An important finding is that the distribution of the mean square displacement with the absorbing boundary conditions can match the exact one accurately, which demonstrates the effectiveness of the method. • The absorbing boundary conditions are originally proposed to analyse the anomalous diffusion in the comb model. • An integration technique is used to eliminate the influence of the singular Dirac function. • A fast algorithm is presented and the superiority compared with the traditional L1-scheme is analysed. • The mean square displacement with the absorbing boundary conditions can match the exact expression accurately. [ABSTRACT FROM AUTHOR]

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid (blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model. The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function (UDF). Numerical solutions are obtained by the finite volume method based on a nonuniform grid structure. The accuracy and efficiency of the solver are verified through a comparison with the literature. The results are presented graphically for different parameter values, and the effects of the magnetic number, the magnetic source position, the vascular obstruction ratio, the slip parameter, and the power-law index on the flow and temperature fields are illustrated. [ABSTRACT FROM AUTHOR]

This paper is concerned with asymptotic solutions of a nonlinear boundary value problem (BVP), which arises in a study of laminar flow in a uniformly porous channel with retractable walls and an applied transverse magnetic field. For different ranges of the control parameters (i.e. α , Re and M ) arising in the BVP, four cases are considered using different singular perturbation methods. For the first case, unlike those in the existing literature, we make use of the Lighthill method and successfully construct an asymptotic solution with high-order derivatives at the center of the channel. For the second case, under large suction we consider M 2 = O (1) and M 2 = O ( Re ), respectively, which will further extend the applying range of asymptotic solutions. In other cases, asymptotic solutions with a boundary layer are successfully constructed. In addition, numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed in this paper are more reliable. Finally, the influences of some parameters on flow field are discussed to develop a better understanding of the flow problem. [ABSTRACT FROM AUTHOR]

In order to study the mass separation or mixture of EOF for biological or chemical fluids with viscoelastic characteristics, the EOF of two layers consisting of Newtonian fluid and fractional second-order fluid in a rotating frame in parallel microchannel is investigated. The numerical solutions are obtained by finite difference method. Two interesting phenomena can be found. One of them is that reverse flow can be found near the interface as the rotation velocity is big enough. Another is that the streamwise velocity will increase firstly and decrease subsequently before the steady flow reaches on account of the existence of angular velocity. [ABSTRACT FROM AUTHOR]