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This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure.

First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used.

The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh.

To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

To improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.

The mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.

The thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.

An extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

This paper proposed a bi-level mathematical model for location, routing and allocation of medical centers to distribution depots during the COVID-19 pandemic outbreak. The developed model has two players including interdictor (COVID-19) and fortifier (government). Accordingly, the aim of the first player (COVID-19) is to maximize system costs and causing further damage to the system. The goal of the second player (government) is to minimize the costs of location, routing and allocation due to budget limitations.

The approach of evolutionary games with environmental feedbacks was used to develop the proposed model. Moreover, the game continues until the desired demand is satisfied. The Lagrangian relaxation method was applied to solve the proposed model.

Empirical results illustrate that with increasing demand, the values of the objective functions of the interdictor and fortifier models have increased. Also, with the raising fixed cost of the established depot, the values of the objective functions of the interdictor and fortifier models have raised. In this regard, the number of established depots in the second scenario (COVID-19 wave) is more than the first scenario (normal COVID-19 conditions).

The results of the current research can be useful for hospitals, governments, Disaster Relief Organization, Red Crescent, the Ministry of Health, etc. One of the limitations of the research is the lack of access to accurate information about transportation costs. Moreover, in this study, only the information of drivers and experts about transportation costs has been considered. In order to implement the presented solution approach for the real case study, high RAM and CPU hardware facilities and software facilities are required, which are the limitations of the proposed paper.

The main contributions of the current research are considering evolutionary games with environmental feedbacks during the COVID-19 pandemic outbreak and location, routing and allocation of the medical centers to the distribution depots during the COVID-19 outbreak. A real case study is illustrated, where the Lagrangian relaxation method is employed to solve the problem.

The distinction between nominal and effective tariffs (or protection) is well established in the theoretical literature, albeit in the context of the traditional analysis of inter‐industry trade flows. This analysis is based upon assumptions such as product and production homogeneity, non‐increasing returns, armslength trade, and small open economy country conditions. Relaxation of some or all of these assumptions has direct implications for effective protection analysis under any type of trade flows. As is now widely recognised, however, relaxation of these assumptions is also likely to be associated with intra‐industry specialisation and exchange. It is to this wider issue of effective protection analysis in the context of “within‐industry” specialisation (vertical and/or horizontal) and of two‐way trade, that this paper is addressed.

Glass material is largely used for load-bearing components in buildings. For this reason, standardized calculation methods can be used in support of safe structural design in common loading and boundary conditions. Differing from earlier literature efforts, the present study elaborates on the load-bearing capacity, failure time and fire endurance of ordinary glass elements under fire exposure and sustained mechanical loads, with evidence of major trends in terms of loading condition and cross-sectional layout. Traditional verification approaches for glass in cold conditions (i.e. stress peak check) and fire endurance of load-bearing members (i.e. deflection and deflection rate limits) are assessed based on parametric numerical simulations.

The mechanical performance of structural glass elements in fire still represents an open challenge for design and vulnerability assessment. Often, special fire-resisting glass solutions are used for limited practical applications only, and ordinary soda-lime silica glass prevails in design applications for load-bearing members. Moreover, conventional recommendations and testing protocols in use for load-bearing members composed of traditional constructional materials are not already addressed for glass members. This paper elaborates on the fire endurance and failure detection methods for structural glass beams that are subjected to standard ISO time–temperature for fire exposure and in-plane bending mechanical loads. Fire endurance assessment methods are discussed with the support of Finite Element (FE) numerical analyses.

Based on extended parametric FE analyses, multiple loading, geometrical and thermo-mechanical configurations are taken into account for the analysis of simple glass elements under in-plane bending setup and fire exposure. The comparative results show that – in most of cases – thermal effects due to fire exposure have major effects on the actual load-bearing capacity of these members. Moreover, the conventional stress peak verification approach needs specific elaborations, compared to traditional calculations carried out in cold conditions.

The presented numerical results confirm that the fire endurance analysis of ordinary structural glass elements is a rather complex issue, due to combination of multiple aspects and influencing parameters. Besides, FE simulations can provide useful support for a local and global analysis of major degradation and damage phenomena, and thus support the definition of simple and realistic verification procedures for fire exposed glass members.

Mindfulness, a kind of mental perception, has a long history in Buddhist spiritual traditions, but has also a well-developed use in clinical psychology as a mental health intervention. Meditative mindfulness provides therapeutic benefits in the treatment of mental trauma. Recently, an interest in the outcomes derived from meditative mindful experience has emerged in tourism studies. Tourists experiencing a mindful-like event may get a sense of peacefulness and a harmonic relationship between the self and the environment. This chapter discusses how meditative mindfulness can be integrated into tourism experiences and create subtle therapeutic-like effects. Theoretically, this study bridges the relationship between a meditative mindful tourist experience and its perceived consequences. Practically, it explains how to generate mental health outcomes from tourism experiences.

Integrating project scheduling and material ordering problems is vital in realistically estimating project cost and duration. Also, the quality level of materials is important as one of the key project success factors.

In this paper, a three-objective mathematical model is presented for green project scheduling with materials ordering problems considering rental resources. The first objective is to minimize the total cost of the project site and logistics. The second objective is to minimize the environmental impacts of producing materials and the third objective is to maximize the total quality of materials. Since costs trigger several challenges in projects, cost constraints are considered in this model for the first time and also the cost of delay in supplying of materials by the suppliers has been deducted from the project costs. Subsequently, the model was implemented in a real case and solved by the Lagrangian Relaxation algorithm as an exact method on GAMS software for model validation.

Based on sensitivity analysis of some parameters, the findings indicate that the cost constraint and lead time have considerable effects on the project duration. Also, integrating project scheduling and material ordering improves the robustness of the project schedule.

The primary contributions of the present research can be stated as follows: considering the cost constraints in the project scheduling with material ordering problem, incorporating the rental resources and taking the quality levels of materials as well as the environmental impacts into account.

This paper aims to investigate the suitability of additive manufacturing to produce O-ring seals.

The O-rings were made by the PolyJet-Matrix technology using four different digital materials and then tested for relaxation properties under static and dynamic (sliding) conditions. The approximation of the relaxation curves involved modelling with a Prony series.

The PolyJet-Matrix technology offers new opportunities to model elastomeric elements, with examples being the O-rings produced and tested for their relaxation properties. Describing the behaviour of the particular materials fabricated with this technology by using relaxation functions will extend the knowledge base on digital materials.

The four types of photopolymers used in the experiment differed in viscoelastic properties. The analysis of the stress relaxation of the O-ring models was performed at four different step displacements of the loading element.

The test results may be useful for the design of O-ring seals made of new elastomeric materials. The relaxation properties of the O-rings made of such materials can be applied to analyse the dynamics of seals, for instance, face seals.

The originality of the work lies in the use of digital materials to design and produce elastomeric elements with different relaxation properties, which was confirmed by the test results. This paper presents results of a relaxation analysis for a ring model and the material that the ring is made of. It also discusses how 3D printing and digital materials can be applied in practice.

Optimisation of the discretising steps in the space and time domains has been studied for the evaluation of corresponding optimum value of over‐relaxation parameter in the numerical solution of transient heat flow equation using successive‐over‐relaxation method in the finite difference code. No closed form solutions are available for the optimisation of a complete set of involved parameters in such problems. The present work deals quantitatively with the need for a more generalised closed form relation involving discretising steps in the space and the time domains for an optimal over‐relaxation parameter. The maximum finite difference error and the number of iterations required to achieve a reasonable error tolerance in the functional value are the two criteria used to obtain an optimised set of parameters. The effect of deviation from the optimised values of any of the involved parameters has been shown over a model problem of one‐dimensional diamond‐IIa medium of 100 micrometer length and for a time duration of 1.24 micro‐seconds.