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This study aims to provide a solution of the power flow calculation for the low-voltage ditrect current power grid. The direct current (DC) power grid is becoming a reliable and economic alternative to millions of residential loads. The power flow (PF) in the DC network has some similarities with the alternative current case, but there are important differences that deserve to be further concerned. Moreover, the dispatchable distributed generators (DGs) in DC network can realize the flexible voltage control based on droop-control or virtual impedance-based methods. Thus, DC PF problems are still required to further study, such as hosting all load types and different DGs.

The DC power analysis was explored in this paper, and an improved Newton–Raphson based linear PF method has been proposed. Considering that constant impedance (CR), constant current (CI) and constant power (CP) (ZIP) loads can get close to the practical load level, ZIP load has been merged into the linear PF method. Moreover, DGs are much common and can be easily connected to the DC grid, so V nodes and the dispatchable DG units with droop control have been further taken into account in the proposed method.

The performance and advantages of the proposed method are investigated based on the results of the various test systems. The two existing linear models were used to compare with the proposed linear method. The numerical results demonstrate enough accuracy, strong robustness and high computational efficiency of the proposed linear method even in the heavily-loaded conditions and with 10 times the line resistances.

The conductance corresponding to each constant resistance load and the equivalent conductance for the dispatchable unit can be directly merged into the self-conductance (diagonal component) of the conductance matrix. The constant current loads and the injection powers from dispatchable DG units can be treated as the current sources in the proposed method. All of those make the PF model much clear and simple. It is capable of offering enough accuracy level, and it is suitable for applications in DC networks that require a large number of repeated PF calculations to optimize the energy flows under different scenarios.

The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

An integer multiple objective non‐linear mathematical programming formulation is developed for simultaneously forming part/machine cells. In the proposed model, generic capability units which are termed as resource elements are used to define the processing requirements of parts and processing capabilities of machine tools. Machine capabilities are not generally taken into account in the previous cell formation procedures. Explicit consideration of unique and overlapping machine capabilities can result in better manufacturing cell designs with higher utilisation levels and less machine duplication. The proposed cell formation model has distinguishing features. Several important cell formation objectives, such as minimisation of part dissimilarity (based on production requirements and processing sequences of parts) in formed cells, minimisation of cell load imbalance, and minimisation of extra capacity requirements for cell formation, are considered. In order to solve the mathematical programming model, a simulated annealing algorithm is developed. Cooperative game theoretic approach is applied for evaluating multiple objectives.

The gas assisted Iaser heating of engineering surfaces finds wide application in industry. Numerical simulation of the heating process may considerably reduce the cost spent on experimentation. In the present study, 2‐dimensional axisymmetric flow and energy equations are solved numerically using a control volume approach for the case of a gas assisted laser heating of steel surfaces. Various turbulence models including standard k‐ε, k‐ε YAP, low Reynolds number k‐ε and RSTM models are tested. The low Reynolds number k‐ε model is selected to account for the turbulence. Variable properties of both solid and gas are taken into account during the simulation. Air is considered as an assisting gas impinging the workpiece surface coaxially with the laser beam. In order to validate the presently considered methodology, the study is extended to include comparison of present predictions with analytical solution for the case available in the literature. It is found that the assisting gas jet has some influence on the temperature profiles. This effect is minimum at the irradiated spot center and it amplifies considerably in the gas side. In addition, account for the variable properties results in lower surface temperatures as compared to the constant properties case.

The purpose of this paper is to investigate the problem of entropy generation around a spinning/non‐spinning solid sphere subjected to uniform heat flux boundary condition in the forced‐convection regime.

The governing continuity, momentum, energy and entropy generation equations are numerically solved for a wide range of the controlling parameters; Reynolds number and the dimensionless spin number.

The dimensionless overall total entropy generation increases with the dimensionless spin number. The effect of increasing the spin number on the fluid‐friction component of entropy generation is more significant compared to its effect on heat transfer entropy generation.

Since the boundary‐layer analysis is used, the flow is presented up to only the point of external flow separation.

Entropy generation analysis can be used to evaluate the design of many heat transfer systems and suggest design improvements.

A review in the open literature indicated that no study is available for the entropy generation in the unconfined flow case about a spinning sphere.

The global energy industry transports supplies and personnel via helicopter to offshore locations and is increasingly focusing on optimizing upstream logistics. This paper aims to and achieves a mutually beneficial balance between research and practice by providing generalizable methods to a problem routinely encountered in practice. Overall, the development and execution of the heterogeneous capacitated helicopter routing problem with split deliveries and multiple depots is validated by the networks’ results.

Using a unique sample of deepwater and ultra-deepwater permanent offshore locations in the Gulf of Mexico, transportation networks consisting of 57 locations operated by 19 firms are optimized via a randomized greedy algorithm. The study’s randomized greedy algorithm yields depot assignment, vehicle assignment, passenger assignment and routing. All data processing techniques and iterative algorithm processes are defined and explained.

Results show that the model effectively solves the complex transportation networks consisting of subject firms’ offshore nodes and eligible depots. Specifically, average load factors related to seat capacity and effective vehicle capacity of 87.7 and 95.7% are realized, respectively. The study’s model is a unique contribution to the extant literature and provides researchers and practitioners a practical approach to model development and solution deliverance.

The extant literature encompasses works that inadequately observe the complexity associated with the transportation of personnel. Specifically, this research, unlike many works in the extant literature, uses a heterogeneous versus homogeneous fleet, includes multiple depots versus a single depot and allows split deliveries. Also, the current research ensures all relevant aircraft capabilities and limitations are observed. In particular, the paper takes into account vehicles’ seat capacities, effective capacities via maximum gross takeoff weights and reserve fuel requirements. The current model, which is built upon a heterogeneous capacitated helicopter routing problem with split deliveries and multiple depots (HCHRPSDMD), sufficiently provides a practical approach to model development and solution deliverance while promoting future research endeavors. Future research may use these findings for other geographical regions and similar transportation networks and could adopt firm-specific actual cost parameters instead of the estimated average hourly costs of operating different helicopters. Furthermore, future endeavors may employ other techniques for the derivation of solutions. Future works may be enhanced with actual cost data in lieu of estimations. In the current study, cost data were not available; however, estimations do not inherently proscribe sound interpretations of the models’ outputs. Also, future research endeavors including manual method results may enable comparative results to establish cost variance analysis. Although the current study is, to some extent, limited, the practicality for practitioners and contribution to researchers is comprehensible. Due to the idiosyncrasies and complexity prevalent in modern transportation networks, optimization is and will continue to be a rich opportunity for implementation and research.

As described by previous researchers, energy firms may more efficiently use their contracted aircraft via implementation of a decision-making mechanism for passenger assignment, aircraft selection, depot selection and aircraft routing. Most energy firms possess numerous and spatially segregated offshore facilities and, therefore, are unable to efficiently and effectively make such decisions. Ultimately, the efficient use of firms’ contracted helicopters can enhance profitability via reduced costs without compromising operational performance. Reduced costs are likely to be realized by a potential workforce or workload reduction, reduced flight hours and enhanced bargaining power with commercial helicopter operators. Specifically, enhanced bargaining power may be realized as a result of minimized depots from which the aircraft are operated and an overall reduction of aircraft via increased asset utilization. In essence, the efficient use of commercial helicopters may yield systemic efficiencies that can be shared among all stakeholders, contracting energy firms and commercial helicopter operators. The achievement of operational efficiencies, ultimately, may determine the realization of target performance or solvency of a plethora of firms in the future (Krishnan et al., 2019).

For economies, communities and industries depending on crude oil and natural gas production, people’s livelihoods are significantly impacted due to price fluctuations (Rostan and Rostan, 2020; Solaymani, 2019). Based on a unique set of inputs and outputs, the International Energy Agency region (IEA), which includes the current study’s sample set, was found to achieve greater overall production efficiency relative to the Organization of the Petroleum Exporting Countries (OPEC) and the Organization of Arab Petroleum Exporting Countries (OAPEC) (Ohene-Asare et al., 2018). Therefore, enhanced logistics efficiency within the energy industry’s transportation sector across the globe is reasonably likely. For countries relying on these commodities’ exportation, production efficiency is and will continue to be a priority. With limited resources available in industry and society, efficiency is prone to yield advantageous results for all stakeholders. Furthermore, in the context of this study, a reduction of carbon dioxide and noise pollution in air, above water and on land will contribute to society’s drive to protect the environment and preserve our natural resources for future generations.

The current study represents the lone or one of few research endeavors to evaluate the heterogeneous capacitated helicopter routing problem with split deliveries and multiple depots. Furthermore, research pertaining to transportation via helicopter in the Gulf of Mexico’s offshore basin is unprecedented. Lastly, this work yields actionable knowledge for practitioners while enhancing current and promoting future research endeavors.

The hybrid nanofluid flow due to a rotating disk has numerous applications, including centrifugal pumps, paper production, polymers dying, air filtration systems, automobile cooling and solar collectors. This study aims to investigate the convective heat transport and magnetohydrodynamics (MHD) hybrid nanofluid flow past a stretchable rotating surface using the Yamada-Ota and Xue models with the impacts of heat generation and thermal radiation.

The carbon nanotubes such as single-wall carbon nanotubes and multi-wall carbon nanotubes are suspended in a base fluid like water to make the hybrid nanofluid. The problem’s governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. Then, the numerical solutions are found with a bvp4c function in MATLAB software. The impacts of pertinent parameters on the flow and temperature fields are depicted in tables and graphs.

Two solution branches are discovered in a certain range of unsteadiness parameters. The fluid temperature and the rate of heat transport are enhanced when the thermal radiation and heat generation effects are increased. The Yamada-Ota model has a higher temperature than the Xue model. Furthermore, it is observed that only the first solution remains stable when the stability analysis is implemented.

To the best of the authors’ knowledge, the results stated are original and new with the investigation of MHD hybrid nanofluid flow with convective heat transfer using the extended version of Yamada-Ota and Xue models. Moreover, the novelty of the present study is improved by taking the impacts of heat generation and thermal radiation.

Presents a quasi three‐dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no‐slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air‐filled (empty) surfaces. The formulation was developed to analyse the sections which lie in the xy‐plane or may be oriented arbitrarily in three‐dimensional space. Solves the discretized thickness‐integrated finite element flow equations by using the implicit mixed velocity‐pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three‐dimensional thin section cavities of irregular shape.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

The purpose of this paper is to present a new eddy‐viscosity formulation designed to exhibit a correct response to streamline curvature and flow rotation. The formulation is implemented into a linear k‐ ε turbulence model with a two‐layer near‐wall treatment in a commercial computational fluid dynamics (CFD) solver.

A simple, robust formula is developed for the eddy‐viscosity that is curvature/rotation sensitive and also satisfies realizability and invariance principles. The new model is tested on several two‐ and three‐dimensional problems, including rotating channel flow, U‐bend flow and internally cooled turbine airfoil conjugate heat transfer. Predictions are compared to those with popular eddy‐viscosity models.

Converged solutions to a variety of turbulent flow problems are obtained with no additional computational expense over existing two‐equation models. In all cases, results with the new model are superior to two other popular k‐ ε model variants, especially for regions in which rapid rotation or strong streamline curvature exists.

The approach adopted here for linear eddy‐viscosity models may be extended in a straightforward manner to non‐linear eddy‐viscosity or explicit algebraic stress models.

The new model is a simple “plug‐in” formula that contains important physics not included in most linear eddy‐viscosity models and is easy to implement in most flow solvers.

The present model for curved and rotating flows is developed without the need for second derivatives of velocity in the formulation, which are known to present difficulties with unstructured meshes.