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Due to the extensive industrial applications of stagnation flow problems, the present work aims to investigate the magnetohydrodynamics (MHD) flow and heat transfer of a magnetite nanofluid (here Fe₃O₄–water nanofluid) impinging a flat porous plate under the effects of a non-uniform magnetic field and chemical reaction with variable reaction rate.

Similarity transformations are applied to reduce the governing partial differential equations with boundary conditions into a system of ordinary differential equations over a semi-infinite domain. The modified fourth-order Runge–Kutta method with the shooting technique which is developed for unbounded domains is conducted to give approximate solutions of the problem, which are then verified by results of other researchers, showing very good agreements.

The effects of the volume fraction of nanoparticles, permeability, magnetic field, chemical reaction and Schmidt number on velocity, temperature and concentration fields are examined and graphically illustrated. It was found that fluid velocity and temperature fields are affected strongly by the types of nanoparticles. Moreover, magnetic field and radiation have strong effects on velocity and temperature fields, fluid velocity increases and thickness of the velocity boundary layer decreases as magnetic parameter M increases. The results also showed that the thickness of the concentration boundary layer decreases with an increase in the Schmidt number, as well as an increase in the chemical reaction coefficient.

The thermophysical properties of the magnetite nanofluid (Fe₃O₄–water nanofluid) in different conditions should be checked.

Stagnation flow of viscous fluid is important due to its vast industrial applications, such as the flows over the tips of rockets, aircrafts, submarines and oil ships. Moreover, nanofluid, a liquid containing a dispersion of sub-micronic solid particles (nanoparticles) with typical length of the order of 1-50 nm, showed abnormal convective heat transfer enhancement, which is remarkable.

The major novelty of the present work corresponds to utilization of a magnetite nanofluid (Fe₃O₄–water nanofluid) in a stagnation flow influenced by chemical reaction and magnetic field. It should be noted that in addition to a variable chemical reaction, the permeability is non-uniform, while the imposed magnetic field also varies along the sheet. These, all, make the present work rather original.

This study aims to introduce a new modified method for estimating steam turbine high pressure (HP)-intermediate pressure (IP) leakage flow based on the experimental data extracted from a 250 MW re-heat steam turbine.

Effects of measurement uncertainties on the test results are investigated and key parameters are specified via a new modified method to diminish the test uncertainties. The recommended method is based on a constant IP turbine pressure ratio at the same loads. Considering this assumption, it was found that the turbine pressure ratio can be achieved in the second and the third tests with a much longer duration.

The results showed that the cross-over temperature is a major parameter in the leakage flow estimation tests, whereas hot reheat and cross-over pressures are the next priorities. It was also observed that as the cross-over temperature varies by 1°C, the estimated leakage flow error significantly differs by up to 72.6 per cent.

It is concluded that the present modified HP-IP leakage flow estimation method seems to be more accurate in comparison with previously proposed methods in literature.

The purpose of this paper is to study various combination forms of the three basic sharing elements (i.e. orders sharing, manufacturers capacity sharing and suppliers capacity sharing) in the cluster supply chain (CSC), formulate a distributed model to protect enterprises’ decision privacy and seek to develop an effective method for solving the distributed complex model.

A distributed assembly cluster supply chain configuration (ACSCC) model is formulated. An improved augmented Lagrangian coordination (ALC) is proposed and used to solve the ACSCC model. A series of experiments are conducted to validate the improved ALC and the model.

Two major findings are obtained. First, the market order’s quantity change and the sales price of the product have a great impact on both the optimal results of the ACSCC and the cooperative strategy, especially, when the market order increases sharply, enterprises have to adopt multiple cooperative strategies to complete the order; meanwhile, the lower sales price of the product helps independent suppliers to get more orders. Second, the efficiency and computational accuracy of the improved ALC method are validated as compared to the centralized ALC and Lingo11.

This paper formulated the single-period ACSCC model under certain assumptions, yet a multi-period ACSCC model is to be developed, a more comprehensive investigation of the relationships among combination forms is to be extended further and a rigid proof of the improved ALC is necessary.

Enterprises in the industrial cluster should adopt different cooperative strategies in terms of the market order’s quantity change and the sales price of the product.

The proposed various combination forms of sharing elements and the formulated ACSCC model provide guidance to managers in the industrial cluster to choose the proper policy.

This research studies various combination forms of the three basic sharing elements in the CSC. A distributed ACSCC model has been established considering simultaneously multiple sharing elements. An improved ALC is presented and applied to the ACSCC problem.