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The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

This paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC).

The magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes.

It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique.

The main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions.

In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke.

It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique.

The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.

This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.

The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.

The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.

Refers to the history of the maritime sale of goods which resulted in a bill of lading, representing goods at sea in a ship. Attempts to determine whether or not a bill of lading is a negotiable instrument if it is characterized by such words as to order or to bearer. Compares US, Greek and English law and finds that English law is not in line with US and Greek law. Refers to the English Carriage of Goods by Sea Act (COGSA) 1992. Claims that differences in law may cause some problems for international trade and mentions the European Commission’s project to examine the feasibility of electronic bills of lading.

The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it.

At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed.

The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach.

The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.

This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

ISM technique is one of the tools of interest in soft operations research. The soft nature of this technique has made inevitable use of indeterminacy theories. The present research attempts to develop ISM technique and MICMAC analysis in a neutrosophic space due to the complexity and uncertainty of the decision-making environment.

In this study, single-valued triangular neutrosophic numbers is used to develop Neutrosophic ISM (NISM) and Neutrosophic MICMAC (NMICMAC). First, the general algorithm of NISM and NMICMAC is provided. In the following, the complete description of NISM steps including level value determination, Factor Leveling Algorithm and NISM digraph algorithm are presented. Finally, a description of the NMICMAC steps is described.

An illustrative example – supplier selection problem – is given to verify the effectiveness of the proposed method and in the discussion section; the comparison and analysis of different aspects of the NISM with the previous methods are discussed.

In this study, NISM and NMICMAC are presented for the first time, so that each pairwise comparison judgment is provided as single valued triangular neutrosophic numbers. The development of the model is continued until the final stages of calculations with neutrosophic numbers, and only in the final stage the results are crispy presented. In addition, not only the factors of process are leveled, but at each level the factors are lined up and their importance is determined.

The purpose of this study is to analyze the entropy generation in magnetohydrodynamics stagnation point mixed convection flow of Carreau nanofluid through porous medium.

The system is solved using the homotopy scheme.

Minimizing radiation, magnetic, permeability and temperature difference parameters responds to minimizing entropy production.

To the best of the authors’ knowledge, no such analysis has yet been reported.

We are growing accustomed to shock tactics of the US Administration in dealing with toxic residues in food or additives which are a hazard to man, as well as the daily press infusing sensation, even melodrama, into them, but the recent action of the FDA in calling in from the food market several million cans of tuna and other deep sea fish because of the presence of mercury has had the worthwhile effect of drawing world attention to the growing menace of environmental pollution. The level of mercury in the fish is immaterial; it should never have been there at all, but it stresses the importance of the food chain in the danger to man and animal life generally, including fish beneath the sea. Without underestimating risks of pollution in the atmosphere from nuclear fission products, from particulate matter carried in the air by inhalation or even skin absorption, food and drink, which includes aqua naturale would seem to be the greatest danger to life. What these recent events illustrate in a dramatic manner, however, is the extent of pollution.