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This study aims to illustrate the impacts of the motion of circular cylinders on the natural convection flow from variable heated partitions inside the X-shaped cavity filled with Al₂O₃-water nanofluid. A partial layer of a homogeneous/heterogeneous porous medium is located in the top area of the X-shaped cavity.

Three different cases of the porous media including homogeneous, horizontal heterogeneous and vertical heterogeneous porous media were considered. Three different thermal conditions of the embedded circular cylinders including hot, cold and adiabatic conditions are investigated. An incompressible scheme of smoothed particle hydrodynamics (ISPH) method is modified to compute the non-linear partial differential equations of the current problem. Two variable lengths of the left and right sides of the X-shaped cavity have a high-temperature T_h and a low-temperature T_c, respectively. The other wall parts are adiabatic. The numerical simulations are elucidating the dependence of the heat transfer and fluid flow characteristics on lengths of hot/cold source L_h, porous cases, Darcy parameter, thermal conditions of the embedded circular cylinders and solid volume fraction.

Overall, an increment in length of hot/cold source leads to augmentation on the temperature distributions and flow intensity inside the X-shaped cavity. The hot thermal condition of the circular cylinder augments the temperature distributions. The homogeneous porous medium slows down the flow speed in the top porous layer of the X-shaped cavity. The average Nusselt number decreases as L_h increases.

ISPH method simulated the motion of circular cylinders in the X-shaped cavity. The X-shaped cavity is saturated with a partial layer porous medium. It is found that an increase in hot source length augments the temperature and fluid flow. ISPH method can easily handle the motion of cylinders in the X-shaped cavity. Different thermal conditions of cylinders can change the temperature distributions in X-cavity.

This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles’ concentration, deposited nanoparticles’ concentration on the pore-walls and entrapped nanoparticles concentration in pore-throats.

A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated.

Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size.

The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters.

The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.

Posits that, by specifically examining price‐value relationship, buyers can avoid many of the problems inherent in comparing products/suppliers in terms of net delivered price. Provides background on economic value pricing, along with a detailed discussion of the steps and considerations for buyer‐side application to supplier price analysis and its managerial implications.

According to statistical reports, most of the national electorate is not sufficiently interested in politics to bother voting for candidates for public office. This indifference is not shared by many authors. More than 50 book titles in the 1981–82 Books in Print (New York, Bowker, 1981) have the words “Politics of …” followed by the subject of the book. Some are concerned with the politics of large issues such as war, peace, energy, human rights, justice, oil, technology, the media, Euroeconomics, or international air transportation. Other authors deal with more personal concerns such as the politics of alcoholism, drugs, Medicare, mental health, motherhood, language development, self‐sufficiency, or education. These titles indicate the control exercised by government in many different areas of life. Until a law, statute, ordinance, ruling, or regulation effects an individual, there is relatively little interest or concern with the actions of elected officials, or the agencies implementing these decisions.

Materiality is an ill‐defined yet important concept in auditing. However, lack of an auditing guideline exposes auditors to possible litigations due to failure to detect material misstatement in the financial statements. This paper assesses decisions by UK courts on materiality thresholds. The results from 28 selected cases failed to reveal any consistency in the adoption of materiality thresholds. A guideline is urgently needed by the Auditing Practices Board to increase consistency in decisions on material transactions/events.

The ideal top executive keeps his desk clear. Any letters or other material appearing on it are dealt with at once and removed by a secretary. Any special papers required are brought promptly on the push of a button or at a spoken request into a loud‐speaking telephone.