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In this innovative study, a unique approach was engaged to simulate the flow characteristics of nanofluid inside a tank featuring a surface subjected to uniform flux. The testing fluid for this investigation was fabricated by incorporating alumina powders with varying shapes into water. The derivation of the final equations involved the application of Darcy’s law and the formulation of the stream function. The container experienced the combined efficacy of both the Lorentz force and gravity forces. The incorporation of additives resulted in a significant enhancement of the Nusselt number (Nu), demonstrating an increase of 19.8% and 40.28%, contingent on the magnitude of the Hartmann number (Ha). Moreover, an elevation in the shape factor led to a notable rise in Nu by 14%. Remarkably, as the Ha increased, there was a substantial reduction in the cooling rate by 51.33%. Furthermore, in the absence of the Ha, an escalation in the Rayleigh number (Ra) caused Nu to surge by 65.8%. This study holds paramount importance as it introduces a novel technique for simulating nanofluid flow with a sinusoidal surface, providing valuable insights into the complex interplay of forces within the container. The utilization of varying shapes of alumina powders adds a layer of sophistication to the experimentation, making this investigation a noteworthy contribution to the existing body of knowledge. The findings not only enhance our understanding of heat transfer dynamics but also offer practical implications for applications involving nanofluids in containers with nonuniform surfaces subjected to heat flux.

The numerical approach to a large class of one- and two-dimensional Fokker–Planck equations (FPE) often encountered in modeling Brownian Motors is presented. The method is based on Finite Element scheme with additional modifications for specific problems. We compare results from discretization of FPE with those obtained from Monte Carlo (MC) simulation of the corresponding Langevin equations. Accuracy, efficiency and applicability are also discussed.

We compute general-relativistic polytropic models of differentially rotating neutron stars. A brief description of our numerical treatment is given as follows. First, the relativistic Oppenheimer–Volkoff equations of hydrostatic equilibrium are solved for nonrotating models obeying the well-known polytropic equation of state. Then, uniform rotation assumed for such models is treated in the framework of Hartle's perturbation method; thus, corrections to mass and radius, owing to spherical and quadrupole deformations, are calculated. Next, a perturbative approach to the stellar structure up to terms of third order in the angular velocity is carried out; angular momentum, J, moment of inertia, I, rotational kinetic energy, T, and gravitational potential energy, W, are quantities drastically corrected by the third-order approach. Finally, assuming that our polytropic models satisfy a particular differential rotation law, we compute the increase in mass and in some other significant physical characteristics owing to the differential rotation.

In this study, the flow pattern and scouring around the submerged sharp edge weir, with different slope angles, have been numerically simulated using the Flow-3D model. After validating the results of the numerical model in simulating the flow pattern and scour around the weir with a 90^∘ angle, the effect of the weir angles relative to the upstream and downstream on the flow and scour field had been investigated. The results showed upstream and downstream of the weir, vortex flows were formed and by taking an angle of 90^∘, the vortex flows were weakened. In addition, the downstream slope of the weir had little effect on the upstream water level and most changes occurred in the downstream flow depth with a 90^∘ angle. The downstream scour depth was independent of the upstream slope angle and the upstream scour depth was independent of the downstream slope. When the upstream angle became closer to the horizon, scouring was reduced in this area. The depth of scour downstream was greater than the depth of scouring upstream. Angles of 50^∘, 70^∘, 110^∘ and 130^∘ had slight changes in the depth of the downstream scour, but compared to the angle of 90^∘, the depth of the downstream scour for these angles decreased significantly.

We review the general properties of the intracluster medium (ICM) in clusters that host a cooling flow, and in particular the effects on the ICM of the injection of hot plasma by a powerful active galactic nucleus (AGN). It is observed that, in some cases, the hot plasma produces cavities in the ICM that finally detach and rise, perhaps buoyantly. The gas dynamics induced by the rising bubbles can help in explaining the absence of a cooled gas component in clusters with a cooling flow. This scenario is explored using numerical simulations.

A variational approach using new wave functions to and muonic symmetric molecular ions is proposed. The present method is based on the calculations of the photodecay widths of muonically excited molecular states and their comparison with recent precise data. The numerical calculations were done with a short computation time. Our results are close to the report.

We present a new continuation method for computing implicitly defined manifolds. The manifold is represented as a set of overlapping neighborhoods, and extended by an added neighborhood of a boundary point. The boundary point is found using an expression for the boundary in terms of the vertices of a set of finite, convex polyhedra. The resulting algorithm is quite simple, allows adaptive spacing of the computed points, and deals with the problems of local and global overlap in a natural way. The algorithm is robust (the new points need only be near the boundary), and is well suited to problems with large embedding dimension, and small to moderate dimension.

In this paper, we perform our algorithm developed in [Yu & Lee, 2001] to present the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an interval of parameters for the 2-mode damped, driven sine-Gordon ODE.

In this paper, we will show how the statistics of the gravitational field is changed when the system is characterized by a non-uniform distribution of particles. We will show how the distribution functions W(F) and W(F,dF/dt), giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt, are modified by inhomogeneity. Then we will calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction. Finally we will test, by N-Body simulations, that the theoretical W(F) and dF/dt describes correctly the experimental data and we find that the stochastic force distribution obtained for the evolved system is in good agreement with theory. Moreover, we find that in an inhomogeneous background, the friction force is actually enhanced relative to the homogeneous case.

It is shown that the BSSN formulation of the Einstein equations, which forms the basis of most simulations in numerical relativity, explicitly uses the momentum constraints to evolve the conformal connection coefficients.

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or spacecraft) in the planar Sun–Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with the earlier ones regarding other planetary systems.

Neutron Fluence rate of a low intense Pu-Be source is measured by Neutron Activation Analysis (NAA) of ¹⁹⁷Au foils. Also, the neutron fluence rate distribution versus energy is calculated using the MCNP-4B code based on ENDF/B-V library. Theoretical simulation as well as our experimental performance are a new experience for Iranians to make reliability with the code for further researches. In our theoretical investigation, an isotropic Pu-Be source with cylindrical volume distribution is simulated and relative neutron fluence rate versus energy is calculated using MCNP-4B code. Variation of the fast and also thermal neutrons fluence rate, which are measured by NAA method and MCNP code, are compared.

A unique biolistic method of vaccination is operated by accelerating particulate vaccines with a high-speed gas jet generated by a convergent-divergent conical nozzle to sufficient momentum to penetrate the outer layer of human skin. The targeted cells elicit an immunological response. In this paper, Computational Fluid Dynamics (CFD) is utilized to simulate the operation of a prototype biolistics delivery system. The key features of transient gas dynamics and gas-particle interaction are discussed.

The influence of localized corrosion on cementless titanium-alloy modular total hip arthroplasty was analyzed using numerical and stochastic modeling. Corrosion depth influences maximum stress significantly, thereby reducing the load carrying capacity. Numerical analysis revealed that the stress levels due to corrosion in the modular implants are influenced not only by the pit geometry, but also by the contact properties of the taper junctions. Subsequently, crevice corrosion was economically modeled with two parameters related to physical and chemical properties of the materials involved. The solution introduces a dimensionless number that determines whether anoxic conditions will be reached. The analysis confirms the power-law relationship for the exponent variation with the concentration gradient variation assumed by others. The results may be used in averting the progression to rapid corrosion growth through infusion of oxygen in the crevice at the appropriate time intervals. Stochastic modeling of crevice area and maximum depth shows a power-law increase in dispersion measures with exponent of 0.63–0.64 though the average increase follows a more modest exponent of 0.13–0.15. A holistic approach, and continuous research towards the development of robust corrosion models is warranted so as to predict and enhance the design life of otherwise successful modular arthroplasties. A better understanding of the phenomenon may help alleviate early and catastrophic fractures.

In this paper, the unsteady fully developed forced convective flow of viscous incompressible biofluid that contains both nanoparticles and gyrotactic microorganisms in a horizontal micro-channel is studied. Buongiorno’s model is employed. The upper channel wall is either expanding or contracting and permeable and the lower wall is static and impermeable. The plate separation is therefore a function of time. Velocity, temperature, nanoparticle species (mass) and motile microorganism slip effects are taken into account at the upper wall. By using the appropriate similarity transformation for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing partial differential conservation equations are reduced to a set of similarity ordinary differential equations. These equations under prescribed boundary conditions are solved numerically using the Runge–Kutta–Fehlberg fourth-fifth-order numerical quadrature in the MAPLE symbolic software. Excellent agreement between the present computations and solutions available in the literature (for special cases) is achieved. The key thermofluid parameters emerging are identified as Reynolds number, wall expansion ratio, Prandtl number, Brownian motion parameter, thermophoresis parameter, Lewis number, bioconvection Lewis number and bioconvection Péclet number. The influence of all these parameters on flow velocity, temperature, nanoparticle volume fraction (concentration) and motile microorganism density function is elaborated. Furthermore, graphical solutions are included for skin friction, wall heat transfer rate, nanoparticle mass transfer rate and microorganism transfer rate. Increasing expansion ratio is observed to enhance temperatures and motile microorganism density. Both nanoparticle volume fraction and microorganism increases with an increase in momentum slip. The dimensionless temperature and microorganism increases as wall expansion increases. Applications of the study arise in advanced nanomechanical bioconvection energy conversion devices, bio-nano-coolant deployment systems, etc.

Computational blood flow studies are providing an increasingly important complement to clinical experiments in 21st century biomedical engineering. Motivated by probing deeper into this topic, a theoretical and numerical study is presented of the flow induced by an impulsive acceleration to steady state hemodynamics in a curved tube which is investigated as a boundary layer developing with time from the curved entrance to a straight tube (blood vessel). The transient processes are simulated with a finite volume method solution of the Navier–Stokes equations. The rapid growth of the boundary layer with the core flow is captured in the curved entrance, along the tube to an axisymmetric flow in the downstream. Secondary flow patterns, centrifugal pressures and total head contours are correlated with longitudinal velocity distributions across various sections. It is observed that the entrance zone is controlled by uniform inlet velocity and centrifugal forces. The high pressure drop in the onset flow is associated with strong acceleration which is comparable to generating systolic pressures. The simulations further indicate that a sustained increment in volumetric flow rate is necessary to maintain the pressure wave in the aorta. Furthermore, the velocity distributions are shown to approach Hagen–Poiseuille flow in the downstream zone. The complex hemodynamic characteristics are visualized effectively with computational simulations and the study demonstrates the excellent ability of this approach in elaborating critical flow details in aortic hemodynamics.

Microchannels have the potential to be ultra compact, very efficient heat exchangers, which capitalize on the large surface area to volume ratio of the channels, to transport high heat fluxes with small thermal resistance. This paper describes a 3-D developing flow model by using Navier stoke equations with electric double layer (EDL) effect to model the flow field in microchannel. The electric potential distribution is simulated using a Poisson-Boltzmann equation. Results comparing the performances of the microchannel under different nondimensionalized electric potential are shown and discussed. Nusselt numbers for each case such as with or without EDL effect is also calculated; so that the actual effectiveness of the micro-channel can be understand.

Natural fibers are extracted from natural resources such as stems of plants. In contrast to synthetic fibers (e.g., carbon fibers), natural fibers are from renewable resources and are eco-friendlier. Plant fibers are important members of natural fibers. Review papers discussing the microstructures, performances and applications of natural plant fiber composites are available in the literature. However, there are relatively fewer review reports focusing on the modeling of the mechanical properties of plant fiber composites. The microstructures and mechanical behavior of plant fiber composites are briefly introduced by highlighting their characteristics that need to be considered prior to modeling. Numerical works that have already been carried out are discussed and summarized. Unlike synthetic fibers, natural plant fiber composites have not received sufficient attention in terms of numerical simulations. Existing technical challenges in this subject are summarized to provide potential opportunities for future research.

This paper describes and analyzes a proposal for a pay-for-cuts carbon treaty and illustrates how it would work with numerical simulations for 186 countries. A treaty board would pay each country’s government an amount P for each CO₂ ton the country cuts by any method. Each government would decide how to get its firms and households to cut CO₂ emissions; the board would encourage a carbon tax or cap-and-trade but not require it. $R_i$ is the number of tons that country i reduces its CO₂ emissions. $R_i$ equals country i’s base emissions minus its actual emissions which are publicly available data. Country i’s government would receive $P{R}_i$ from the board. The board’s $P{R}_i$ payments would be financed by country government contributions to the board. A formula would give each country’s government the amount it must contribute each year. The formula would aim to make government contributions equal to the board’s $P{R}_i$ payments and equitably distribute the burdens from cutting world emissions. Representatives of the countries would have to approve the board’s most important decisions.

In this research, 3D analysis model of air-to-air hexagonal plastic plate heat exchanger (HX) is developed numerically and compared with the available experiment. The heat transfer performances with polypropylene (PP) and aluminum (Al) indicate that PP HX can transfer heat as good as Al under this HX application. On the basis of this model, the crest length, the crest pitch and the inlet and outlet chamfer size are designed as three key parameters to improve the heat transfer performances of HX.