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A finite element method dealing with an open boundary condition for the analysis of long wave problem is presented. The key feature of the method is that spurious reflective waves which occurred for the initial transient state on the open boundary can be eliminated by introducing a subdomain technique. For the numerical outflow boundary condition, the progressive wave condition, based on the shallow water long wave theory, is successfully employed. This method is quite suitable for practical analysis because of its adaptability for the arbitrary configuration of the open boundary and shape of elements adjacent to the open boundary. This method is numerically verified for flow in a one dimensional channel and the two dimensional tidal current in Tokyo Bay. The numerical results are compared with analytical solutions and observed data obtained by field measurements. These results are all in close agreement.

The paper has the purpose of proposing a new open boundary condition to be used in conjunction with the finite integration technique (FIT) for the modelling of passive on‐chip components.

This boundary condition is ensured by using a virtual layer that surrounds the computational domain.

The paper proves which are the optimal material properties of the equivalent layer of open boundary.

When modelling passive on‐chip components with FIT, the method proposed is more efficient than the strategic dual image technique.

The paper shows the advantage of this approach – that the analysis algorithm remains unchanged, while saving the field‐circuit compatibility properties, such as current conservation.

Numerical simulation of a fluid flow involves the specification of boundary conditions along all or part of the boundary. Designs a means of handling outflow boundary conditions for the incompressible Navier‐Stokes equations. Addresses through‐flow problems involving the specification of outflow conditions at the synthetic boundary. This outflow boundary condition is applicable to a developing flow problem. The underlying objectives behind designing the boundary condition at the truncated boundary are three‐fold, namely: matching with Navier‐Stokes equations inside the domain; taking both non‐linear and diffusive contributions into account; and ensuring the discrete divergence‐free condition. In order to meet these requirements, follows the concept of a free boundary condition by taking the outflow nodal values of u, v and p as unknowns, which are coupled with the interior unknowns through the surface integrals in the momentum equations. The computed solutions can be legitimately regarded as solutions to conservation equations under consideration when both components of the surface traction vector approach zero. With the convergent property accommodated in the present mixed finite element analysis, the task remains to simply improve the accuracy. Demonstrates the capability of the proposed non‐linear outflow boundary conditions through several benchmark tests.

The purpose of this numerical study is to investigate the effects of inclination angle and non‐isothermal wall boundary conditions in a partially open cavity filled with a porous medium.

In this study, the governing dimensionless equations were written using Brinkman‐Forchheimer model. They are numerically solved by using finite volume method with SIMPLE solution algorithm by applying open boundary conditions in one side. The opposed side of the open cavity is under non‐isothermal boundary conditions.

Results are presented by streamlines, isotherms, velocity and temperature profiles as well as the local and mean Nusselt numbers for different values of the governing parameters such as Grashof numbers, porosity, amplitude of sinusoidal function and inclination angle of the cavity. It is found that inclination angle is the most important parameter on the temperature and flow field.

The originality of this study is the open sided enclosure filled with porous media and non‐isothermal wall.

A numerical model of the inclined open thermosyphon has been developed using a finite difference algorithm to solve the vorticity vector potential form of the Navier‐Stokes equations. The model simulates flow in an inclined cylinder whose bottom end is sealed and whose top is connected to uniform temperature reservoir, a configuration typical of evacuated tubular solar absorbers. The solution domain includes the cylinder only without the reservoir; therefore a special set of boundary conditions has been derived for the vector potential at the top end which is a flow‐through surface. Steady flow is simulated at various combinations of Rayleigh number, aspect ratio and mode of heating. An experimental set‐up has also been developed in order to investigate the development of different flow patterns previously predicted by analytical and numerical workers, as well as to observe more closely the behaviour of the fluid at the orifice. Velocity profiles were measured at the orifice using laser doppler anemometry, and compared with predictions from the numerical model.

The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions.

The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other.

The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions.

The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

Parameters of the perfectly matched layer (PML) for 2D magnetic field in a region bounded by circular boundary are rigorously calculated for the case of symmetrical or antisymmetrical boundary conditions. The PML consists of a single or double layer of elements, whose artificial parameters are calculated by minimizing an error function of potential difference between the nodal potentials of the PML and of the original grid expanding to infinity.

The purpose of this paper is to numerically study thermo‐magnetic convection and heat transfer of paramagnetic fluid placed in a micro‐gravity condition (g≈0) and under a uniform vertical gradient magnetic field in an open square cavity with three cold sidewalls.

This magnetic force is proportional to the magnetic susceptibility and the gradient of the square of the magnetic induction. The magnetic susceptibility is inversely proportional to the absolute temperature based on Curie's law. Thermal convection of a paramagnetic fluid can therefore take place even in a zero‐gravity environment as a direct consequence of temperature differences occurring within the fluid due to a constant internal heat generation placed within a magnetic field gradient.

Effects of magnetic Rayleigh number, γRa, Prandtl number, Pr, and paramagnetic fluid parameter, m, on the flow pattern and isotherms as well as on the heat absorption are presented graphically. It is found that the heat transfer rate is suppressed in increased of the magnetic Rayleigh number and the paramagnetic fluid parameter for the present investigation.

It is possible to control the buoyancy force by using the super conducting magnet. To the best knowledge of the author no literature related to magnetic convection for this configuration is available.

This study aims to simulate Hunter turbine in Computer Forensic Examiner (CFX) environment dynamically. For this purpose, the turbine is designed in desired dimensions and simulated in ANSYS software under a specific fluid flow rate. The obtained values were then compared with previous studies for different values of angles (θ and α). The amount of validation error were obtained.

In this research, at first, the study of fluid flow and then the examination of that in the tidal turbine and identifying the turbines used for tidal energy extraction are performed. For this purpose, the equations governing flow and turbine are thoroughly investigated, and the computational fluid dynamic simulation is done after numerical modeling of Hunter turbine in a CFX environment.

The failure results showed; 11.25% for the blades to fully open, 2.5% for blades to start, and 2.2% for blades to close completely. Also, results obtained from three flow coefficients, 0.36, 0.44 and 0.46, are validated by experimental data that were in high-grade agreement, and the failure value coefficients of (0.44 and 0.46) equal (0.013 and 0.014), respectively.

In this research, at first, the geometry of the Hunter turbine is discussed. Then, the model of the turbine is designed with SolidWorks software. An essential feature of SolidWorks software, which was sorely needed in this project, is the possibility of mechanical clamping of the blades. The validation is performed by comparing the results with previous studies to show the simulation accuracy. This research’s overall objective is the dynamical simulation of Hunter turbine with the CFX. The turbine was then designed to desired dimensions and simulated in the ANSYS software at a specified fluid flow rate and verified, which had not been done so far.