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The purpose of this study is to investigate the unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time power-law-dependent stretching plate. Based on the characteristics of pressure in the boundary layer, the momentum equation with the fractional Maxwell model is firstly formulated to analyze unsteady stagnation-point flow. Furthermore, generalized Fourier’s law is considered in the energy equation and boundary condition of convective heat transfer.

The nonlinear fractional differential equations are solved by the newly developed finite difference scheme combined with L1-algorithm, whose convergence is verified by constructing a numerical example.

Some interesting results can be revealed. The larger fractional derivative parameter of velocity promotes the flow, while the smaller fractional derivative parameter of temperature accelerates the heat transfer. The temperature boundary layer is thicker than the velocity boundary layer, and the velocity enlarges as the stagnation parameter raises. This is because when Prandtl number < 1, the capacity of heat diffusion is greater than that of momentum diffusion. It is to be observed that all the temperature profiles first enhance a little and then reduce rapidly, which indicates the thermal retardation of Maxwell fluid.

The unsteady stagnation-point flow model of Maxwell fluid is extended from integral derivative to fractional derivative, which has more flexibility to describe viscoelastic fluid’s complex dynamic process and provide a theoretical basis for industrial processing.

This study aims to investigate the two-dimensional magnetohydrodynamic flow and heat transfer of a fractional Maxwell nanofluid between inclined cylinders with variable thickness. Considering the cylindrical coordinate system, the constitutive relation of the fractional viscoelastic fluid and the fractional dual-phase-lag (DPL) heat conduction model, the boundary layer governing equations are first formulated and derived.

The newly developed finite difference scheme combined with the L1 algorithm is used to numerically solve nonlinear fractional differential equations. Furthermore, the effectiveness of the algorithm is verified by a numerical example.

Based on numerical analysis, the effects of parameters on velocity and temperature are revealed. Specifically, the velocity decreases with the increase of the fractional derivative parameter α owing to memory characteristics. The temperature increase with the increase of fractional derivative parameter ß due to a decrease in thermal resistance. From a physical perspective, the phase lag of the heat flux vector and temperature gradients τ_q and τ_T exhibit opposite trends to the temperature. The ratio τ_T/τ_q plays an important role in controlling different heat conduction behaviors. Increasing the inclination angle θ, the types and volume fractions of nanoparticles Φ can increase velocity and temperature, respectively.

Fractional Maxwell nanofluid flows from a fixed-thickness pipe to an inclined variable-thickness pipe, and the fractional DPL heat conduction model based on materials is considered, which provides a basis for the safe and efficient transportation of high-viscosity and condensable fluids in industrial production.

The purpose of this paper was to verify the possibility of applying differential calculus of incomplete order to describe relaxation of the material obtained using selective laser sintering (SLS) technology.

The samples were made using the incremental technology for three print directions. Relaxation tests were conducted. The theoretical curves, which are the solution of the equation describing the five-parameter Maxwell-Wiechert model for derivatives in relation to the total time of complete order and fractional order, were adjusted to the obtained experimental curves.

The SLS technology creates new possibilities regarding modelling polymeric elements which might be applied as functional models (products). Therefore, it is necessary to conduct an in-depth study of their properties, including relaxation properties, which is associated with the necessity to use proper mathematical tools to describe those properties. The differential calculus of incomplete order was applied herein to describe the anisotropy of relaxation properties because of the print direction in relation to the relaxation curves adjusted with the five-parameter Maxwell-Wiechert model.

As a result of the conducted considerations, the authors obtained the dependencies describing the anisotropy of relaxation properties with the use of coefficients alpha and beta, which stand for the derivative order of the differential equation, whereas coefficient kappa stands for the translation coefficient which is an innovative application of this type of mathematical apparatus.

The developed method might be applied to describe the anisotropy of a broader group of materials manufactured with the use of incremental technologies.

The application of the differential calculus of incomplete order to describe the anisotropy of the materials manufactured from polyamide powder using the SLS technology is a distinctive feature of this paper. A crucial cognitive element of the conducted research is the fact which confirms that the dynamic viscosity coefficients have the greatest impact on the anisotropy of material properties depending on the print directions.

The purpose of this paper is to undertake an unsteady flow problem of an anomalous Maxwell fluid. The flow takes place between two side walls over a plate perpendicular to them and is driven by a sudden pressure force with constant gradient.

A finite element method is invoked and is blended with a finite difference method for left Caputo fractional time derivatives in order to study the anomalous dynamics of the fluid.

A numerical scheme for the constitutive equations of the prescribed flow in order to approximate the velocity field is designed. The graphical results to draw different physical conclusions on the flow problem are also presented.

A rigorous mathematical exposition of the numerical scheme is provided and the results are valid for large values of the parameters.

Creep behavior of concrete at high temperature has become a major concern in building structures, such as factories, bridges, tunnels, airports and nuclear buildings. Therefore, a simple and accurate prediction model for the high-temperature creep behavior of concrete is crucial in engineering applications.

In this paper, the variable-order fractional operator is introduced to capture the high-temperature creep behavior of concrete. By assuming that the variable-order function is a linear function with time, the proposed model benefits from the advantages of both formal simplicity and the physical significance for macroscopic intermediate materials. The effectiveness of the model is demonstrated by data fitting with existing experimental results of high-temperature creep of two representative concretes.

The results show that the proposed model fits well with the experimental data, and the value of order is increasing with the increase of the applied stress levels, which meets the fact that higher stress can accelerate the rate of creep. Furthermore, the relationship between the model parameters and loading conditions is deeply analyzed. It is found that the material coefficients are constant at a constant temperature, while the order function parameters are determined by the applied stress levels. Finally, the variable-order fractional model can be further written into a general equation of time and applied stress.

This paper provides a simple and practical variable-order fractional model for predicting the creep behavior of concrete at high temperature.

A direct integration method for the dynamic analysis of structures equipped with viscoelastic dampers (VED) is presented in this paper. The constitutive model of the damper is set using a system of Maxwell elements composed in parallel (MPS); the evolutive behavior of the VE material is accounted for by introducing temperature‐dependent mechanical properties. The solution procedure follows an incremental approach of implicit type that, by means of a discrete‐time formulation of the problem, allows expression of the damping force discretization in a form suitable to be included in a standard integration scheme. The resulting algorithm is proved to be very effective and robust; the distinctive features of the proposed numerical method suggest the possibility of a successful implementation of an MPS procedure in the frame of a standard finite element code.

The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues.

The resulting non-linear system is solved through the homotopy analysis method.

An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ.

To the best of author’s knowledge, no such consideration has been given in the literature yet.

The purpose of this paper is to highlight the studies of momentum and transmission of heat on mixed convection boundary layer Darcy‒Forchheimer flow of Casson liquid over a linear extending surface in a porous medium. The belongings of homogeneous‒heterogeneous retorts are also affianced. The mechanism of heat transmission is braced out in the form of Cattaneo‒Christov heat flux. Appropriate restorations are smeared to revolutionize coupled nonlinear partial differential equations conforming to momentum, energy and concentration of homogeneous‒heterogeneous reaction equations into coupled nonlinear ordinary differential equations (ODEs).

Numerical elucidations of the transmogrified ODEs are accomplished via a dexterous and trustworthy scheme, namely optimal homotopy analysis method. The convergence of planned scheme is exposed with the support of error table.

The exploration of mixed convection Darcy‒Forchheimer MHD boundary layer flow of incompressible Casson fluid by the linear stretched surface with Cattaneo‒Christov heat flux model and homogeneous‒heterogeneous reactions is checked in this research. Imitations of the core subsidized flow parameters on velocity, temperature and concentration of homogeneous‒heterogeneous reactions solutions are conscripted. From the recent deliberation, remarkable annotations are as follows: non-dimensional velocities in x_a− and x_b− directions shrink, whereas the non-dimensional temperature upsurges when the Casson fluid parameter ameliorates. Similar impact of Casson fluid parameter, magnetic parameter, mixed convection parameter, inertia parameter, and porosity parameter is observed for both the components of velocity field. An escalation in magnetic parameter shows the opposite attitude of temperature field as compared with velocity profile. Similar bearing of Casson fluid parameter is observed for both temperature and velocity fields. Enhancement in concentration rate is observed for growing values of (N_s) and (Sc), and it reduces for (k₁). Both temperature and concentration of homogeneous‒heterogeneous upturn by mounting the magnetic parameter. Demeanor of magnetic parameter, Casson fluid parameter, heat generation parameter is opposite to that of Prandtl number and thermal relaxation parameter on temperature profile.

In many industrial and engineering applications, the current exploration is utilized for the transport of heat and mass in any system.

As far as novelty of this work is concerned this is an innovative study and such analysis has not been considered so far.

Admittance control is a typical complaint control methodology. Traditionally, admittance control systems are based on a dynamical relationship described by Voigt model. By contrast, after changing connection of spring and damper, Maxwell model produces different dynamics and has shown better impact absorption performance. This paper aims to design a novel compliant control method based on Maxwell model and implement it in a robot catching scenario.

To achieve this goal, this paper proposed a Maxwell model based admittance control scheme. Considering several motion stages involved in one catching attempt, the following approaches are adopted. First, Kalman filter is used to process the position data stream acquired from motion capture system and predict the subsequent object flying trajectory. Then, a linear segments with parabolic blends reaching motion is generated to achieve time-optimal movement under kinematic and joint inherent constraints. After robot reached the desired catching point, the proposed Maxwell model based admittance controller performs such as a cushion to moderate the impact between robot end-effector and flying object.

This paper has experimentally demonstrated the feasibility and effectiveness of the proposed method. Compared with typical Voigt model based compliant catching, less object bounding away from end-effector happens and the success rate of catching has been improved.

The authors proposed a novel Maxwell model based admittance control method and demonstrated its effectiveness in a robot catching scenario. The author’s approach may inspire other related researchers and has great potential of practical usage in a widespread of robot applications.

The main purpose of this paper is to study the effect of heat transfer on the peristaltic flow of a magnetohydrodynamic Walters B fluid through a porous medium in an inclined asymmetric channel.

The approximate analytical solutions of the governing partial differential equations are obtained using the regular perturbation method by taking wave number as a small parameter. The solutions for the pressure difference and friction forces are evaluated using numerical integration.

It is noticed that the pressure gradient and pressure difference are increasing functions of inclination angle and Grashof number. The temperature and heat transfer coefficients both increase with increase in inclination angle, Darcy number, Grashof number and Prandtl number. Increase in Hartmann number and phase difference decreases the size of trapped bolus.

The problem is original, as no work has been reported on the effect of magnetohydrodynamics on the peristaltic flow of a Walters B fluid through a porous medium in an inclined asymmetric channel with heat transfer.