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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.

Laser sintering kinetics and part reliability are critically dependent on the melt viscosity of materials, including polyamide 12 (PA‐12). The purpose of this paper is to characterise the viscosity of PA‐12 powders using alternative scientific methods: constrained boundary flows (capillary rheometry) and rotational rheometry.

Various PA‐12 powders were selected and characterised by both techniques. Measurement of molecular weight was also carried out to interpret the viscosity data.

Results demonstrate conventional pseudoplastic flow in all PA‐12 materials. Zero‐shear viscosity has been quantified by rotational rheometry; a notable observation is the striking difference between virgin/used PA‐12. This is interpreted in terms of molecular weight and chain structure modifications, arising from polycondensation of PA‐12 held at the bed temperature during laser sintering.

Accurate zero‐shear viscosity data provide scope for use in predictive computational models for laser sintering processes. Careful sample preparation and equipment operation are critical prerequisites for accurate rheological characterisation of PA‐12 powders.

Differences in flow behaviour and molecular structure allow prediction and deeper understanding of process‐property relationships in laser sintering, giving potential for further optimisation of material specification and in‐process machine parameter control.

This is believed to be the first time that techniques other than melt flow rate (MFR) have been reported to measure the viscosity of PA‐12 in a laser sintering context, noting the effects of pre‐drying and molecular weight, then predicting differences between virgin/used powders in practical sintering behaviour.

Oil film thickness measurements made in the front main bearing of an operating 3.8 L, V‐6 engine were compared with rheological measurements made on a series of commercial and experimental oil blends. High‐temperature, high‐shear‐rate viscosity measurements correlated with the film thickness of all single‐grade and many multigrade oils. However, the film thickness provided by some multigrade oils were larger than could be accounted for by their high‐temperature, high‐shear‐rate viscosities alone. Although the pressure/viscosity coefficients of some of the oils were significantly different from those of the majority of oils tested, they were not oils which produced unusual film thicknesses. As a consequence, correcting oil viscosities for the esimated pressures acting within the bearing was unsuccessful in improving the correlations. The correlations were improved, however, by accounting for the elastic properties of the multigrade oils. Measurements of oil relaxation times at high temperatures and shear rates showed large differences in elastic properties among the test oils. A good correlation (R2 = 0.73) was obtained from a multiple linear regression of film thickness as a function of both high‐temperature, high‐shear‐rate viscosities and relaxation times.

The purpose of this paper is to investigate how the formulation of a solder paste (with regards to the flux and particle size distribution (PSD)), can influence its creep and recovery performance.

New lead‐free paste formulations were characterised utilising viscometry and oscillatory methods, after which creep/recovery investigations were conducted to determine the recovery performance. Measurements were recorded using a rheometer with a parallel plate geometry of 40 mm and a sample height of 1 mm.

Results from the study highlighted that the formulation of a solder paste can have a significant impact on the creep/recovery measurements. Variations in flux and PSD highlighted a considerable difference in the recoverability of the solder pastes, in one instance demonstrating more than a 20 per cent increase in structural recovery.

More extensive research is needed relating to reduced PSDs, such as type 6 and 7 solder pastes, to fully understand their influence on the creep/recovery performance.

The results presented in this paper emphasise important information and investigational methods for research and development, and quality control.

The paper highlights how the composition of new paste formulations can influence the creep/recovery behaviour. It was found that the recoverability can be increased by careful selection of the flux and PSD, which in turn could reduce slumping influences in the print process. If used as a quality control tool, this paper may allow for the reduction in print defect occurrence.

THIS year's exhibition, held last month, attracted an even greater number of visitors than last year, and there were a number of stands showing products which could be of value in connection with lubrication.

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 is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

• It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

• It guarantees the convergence of series solutions for nonlinear problems.

• It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, u_o(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

By defining a vector u → = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , … , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

where:

Applying L⁻¹ on both sides of Equation (6), we get:

In this way, we obtain u_m for m ⩾ 1, at mth-order, we have:

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P₁) and (P₂), respectively. Moreover, temperature Θ(Ω₁) enhances for greater values of Brownian motion parameter (N_b), non-uniform heat source/sink parameter (B₁) and thermophoresis factor (N_t). Reverse behavior of concentration ϒ(Ω₁) field is remarked in view of (N_b) and (N_t). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.

A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.

Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.

A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.

The purpose of this study is to investigate viscoelastic properties for the constitutive equation in terms of distributed-order derivatives.

The authors considered the steady oscillatory shear flow between two parallel plates (one is fixed and another oscillates in its own plane), and then examined the effects of different forms of the order-weight functions.

The constitutive equation in terms of distributed-order derivatives can characterize viscoelastic properties. The order-weight functions can effectively describe viscoelasticity.

Model the viscoelastic constitutive equation in terms of distributed-order derivatives, where order-weight functions can select to respond viscoelastic properties.

The purpose of this paper is to present a semi-analytical solution to one-dimensional (1D) consolidation induced by a constant inner point sink in viscoelastic saturated soils.

Based on the Kelvin–Voigt constitutive law and 1D consolidation equation of saturated soils subject to an inner sink, the analytical solutions of the effective stress, the pore pressure and the surface settlement in Laplace domain were derived by using Laplace transform. Then, the semi-analytical solutions of the pore pressure and the surface settlement in physical domain were obtained by implementing Laplace numerical inversion via Crump method.

As for the case of linear elasticity, it is shown that the simplified form of the presented solution in this study is the same as the available analytical solution in the literature. This to some degree depicts that the proposed solution in this paper is reliable. Finally, parameter studies were conducted to investigate the effects of the relevant parameters on the consolidation settlement of saturated soils. The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils.

The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils. Consolidation behavior of viscoelastic saturated soils could be reasonably predicted by using the proposed solution with considering variations of both flux and depth because of inner point sink.