Equations In Cylindrical Domains Research Articles

Local solutions for nonhomogeneous Navier–Stokes equations with large flux

The local existence of solutions to nonhomogeneous Navier–Stokes equations in cylindrical domains with arbitrary large flux is demonstrated. The existence is proved by the method of successive approximations. To show the existence with the lowest possible regularity the special Besov spaces called the Sobolev–Slobodetskii spaces are used. The inflow and outflow are prescribed on the parts of the boundary which are perpendicular to the ‐axis. Since the inflow and outflow are positive the crucial point of this paper is to verify that ‐coordinate of velocity is also positive. Finally, we conclude the local existence such that the velocity belongs to , the gradient of pressure to and the density to , where .

Qualitative properties of nonnegative solutions of some semilinear elliptic equations in cylindrical domains

Qualitative properties of nonnegative solutions of some semilinear elliptic equations in cylindrical domains

Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains

Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains

On the Rayleigh–Taylor instability for the two-phase Navier–Stokes equations in cylindrical domains

We are considering the two-phase Navier–Stokes equations with surface tension, modelling the dynamic behaviour of two immiscible and incompressible fluids in a cylindrical domain, which are separated by a sharp interface forming a contact angle with the fixed boundary. In the case that the heavy fluid is situated on top of the light fluid, one expects the effect which is known as Rayleigh–Taylor instability . Our main result implies the existence of a critical surface tension with the following property: In the case that the surface tension of the interface separating the two fluids is smaller than the critical surface tension, Rayleigh–Taylor instability occurs. On the contrary, if the surface tension of the interface is larger than the critical value, one has exponential stability of the flat interfaces. The last part of this article is concerned with the bifurcation of nontrivial equilibria in multiple eigenvalues. The invariance of the corresponding bifurcation equation with respect to rotations and reflections yields the existence of bifurcating subcritical equilibria.

Inverse Problems with Unknown Boundary Conditions and Final Overdetermination for Time Fractional Diffusion-Wave Equations in Cylindrical Domains

Inverse problems to reconstruct a solution of a time fractional diffusion-wave equation in a cylindrical domain are studied. The equation is complemented by initial and final conditions and partly given boundary conditions. Two cases are considered: (1) full boundary data on a lateral hypersurface of the cylinder are given, but the boundary data on bases of the cylinder are specified in a neighborhood of a final time; (2) boundary data on the whole boundary of the cylinder are specified in a neighborhood of the final time, but the cylinder is either a cube or a circular cylinder. Uniqueness of solutions of the inverse problems is proved. Uniqueness for similar problems in an interval and a disk is established, too.

Trace formulae of potentials for degenerate parabolic equations

In this paper, we analyze main properties of the volume and layer potentials as well as the Poisson integral for a multi-dimensional degenerate parabolic equation. As consequences, we obtain trace formulae of the heat volume potential and the Poisson integral which solve Kac's problem for degenerate parabolic equations in cylindrical domains.

Numerical Modeling of Heat Transfer in Gun Barrel with Experimental Validation

Transient heat transfer in a gun barrel has been investigated numerically in this paper. Numerical modeling is conducted with the objective to obtain temperature history of the gun barrel. From the temperature history, the maximum number of gun shots before the cook-off temperature of the gun barrel attained can be known. Gun barrel is a part of firearm functioned to control gas flow which is aimed to propel projectiles out of the barrel with high velocity. Each propelled projectile produces very high temperature caused by projectiles explosion and friction between projectiles and bore surface. If the temperature of the gun barrel reaches the cook-off temperature, the bore surface will be damaged. Heat conduction equation in cylindrical domain is used to model heat transfer inside the gun barrel. Numerical results are obtained by implementing the finite volume method. From the numerical simulations, we found that our numerical method has very small error compared to experimental data that are 1.68% and 0.95% for total heat transfer and maximum temperature of bore surface, respectively. Moreover, the maximum number of gun shots in order not to attain the cook-off temperature is 27 times with ten seconds per shot and rest time six seconds in every six gun shots. Â

On the Robin Problem for Second-Order Elliptic Equations in Cylindrical Domains

В полубесконечном цилиндре рассматривается поведение обобщенных решений дивергентных эллиптических уравнений второго порядка, удовлетворяющих на боковой поверхности цилиндра третьему краевому условию. Библиография: 10 названий.

Large Time Existence of Special Strong Solutions to MHD Equations in Cylindrical Domains

We investigate the problem of the existence of regular solutions to the three-dimensional MHD equations in cylindrical domains with perfectly conducting boundaries and under the Navier boundary conditions for the velocity field. We show that if the initial and external data do not change too rapidly along the axis of the cylinder, then there exists a unique regular solution for any finite time.

Global solvability of the rotating Navier-Stokes equations with fractional Laplacian in a periodic domain

We consider existence of global solutions to equations for three-dimensional rotating fluids in a periodic frame provided by a sufficiently large Coriolis force. The Coriolis force appears in almost all of the models of meteorology and geophysics dealing with large-scale phenomena. In the spatially decaying case, Koh et al. (J Differ Equ 256:707–744, 2014) showed existence for the large times of solutions of the rotating Euler equations provided by the large Coriolis force. In this case the resonant equation does not appear anymore. In the periodic case, however, the resonant equation appears, and thus the main subject in this case is to show existence of global solutions to the resonant equation. Research in this direction was initiated by Babin et al. (Indiana Univ Math J 48:1133–1176, 1999) who treated the rotating Navier-Stokes equations on general periodic domains. On the other hand, Golse et al. (Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains. Instability in Models Connected with Fluid Flows. I. Springer, New York, pp 301–338. arXiv:0704.0337v1 , 2008) considered bursting dynamics of the resonant equation in the case of a cylinder with no viscosity. Thus we may not expect to show global existence of solutions to the resonant equation without viscosity in the periodic case. In this paper we show existence of global solutions for fractional Laplacian case (with its power strictly less than the usual Laplacian) in the periodic domain with the same period in each direction. The main ingredient is an improved estimate on resonant three-wave interactions, which is based on a combinatorial argument.

Performance Evaluation of Various Phase Change Materials for Thermal Energy Storage of A Solar Cooker via Numerical Simulation

In this paper, thermal performance of various phase change materials (PCMs) used as thermal energy storage in a solar cooker has been investigated numerically. Heat conduction equations in cylindrical domain are used to model heat transfer of the PCMs. Mathematical model of phase change problem in the PCM storage encompasses heat conduction equations in solid and liquid region separated by moving solid-liquid interface. The phase change problem is solved by reformulating heat conduction equations with emergence of moving boundary into an enthalpy equation. Numerical solution of the enthalpy equation is obtained by implementing Godunov method and verified by analytical solution of one-dimensional case. Stability condition of the numerical scheme is also discussed. Thermal performance of various PCMs is evaluated via the stored energy and temperature history. The simulation results show that phase change material with the best thermal performance during the first 2.5 hours of energy extraction is shown by erythritol. Moreover, magnesium chloride hexahydrate can maintain temperature of the PCM storage in the range of 110-116.7°C for more than 4 hours while magnesium nitrate hexahydrate is effective only for one hour with the PCM storage temperature around 121-128°C. Among the PCMs that have been tested, it is only erythritol that can cook 10 kg of the loaded water until it reaches 100°C for about 3.5 hours.Article History: Received June 22nd 2016; Received in revised form August 26th 2016; Accepted Sept 1st 2016; Available onlineHow to Cite This Article: Tarwidi, D., Murdiansyah, D.T, Ginanja, N. (2016) Performance Evaluation of Various Phase Change Materials for Thermal Energy Storage of A Solar Cooker via Numerical Simulation. Int. Journal of Renewable Energy Development, 5(3), 199-210.http://dx.doi.org/10.14710/ijred.5.3.199-210

Numerical Analysis of MEMS Technology Integrated in a Small-Caliber Projectile

In this paper, numerical analysis of small-caliber projectile during external ballistic is presented. This work is aimed to find safe location to install microelectromechanical system (MEMS) inside small-caliber projectile based on history and distribution of temperature. The MEMS technology is applied to increase performance of the projectile and it must be protected from damage due to high temperature during internal and external ballistic. Heat conduction equation in cylindrical domain is used to describe transient temperature of small-caliber projectile. Finite element method with the appropriate boundary conditions is adopted to solve the heat conduction equation and to obtain temperature distribution inside projectile. Numerical results show that heat transfer behavior of the projectile at any point is greatly affected by the value of thermal conductivity of material while the external convection does not significantly effect to the heat distribution. The maximum temperatures obtained from temperature history are below threshold value of MEMS damage that is 71 oC. The MEMS technology can be installed anywhere inside the small-caliber projectile except at near top and bottom of projectile surface.

Stability of two-dimensional solutions to the Navier–Stokes equations in cylindrical domains under Navier boundary conditions

The Navier–Stokes motions in a cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that norms bounded with respect to time are controlled by the same constant for all t∈R+. Assuming that the initial velocity and the external force are sufficiently close to the initial velocity and the external force of a two-dimensional solution, we prove existence of global three-dimensional solutions which remain close to the two-dimensional solution for all time. In this sense we have stability of two-dimensional solutions. Thanks to the Navier boundary conditions the nonlinear term in the two-dimensional Navier–Stokes equations does not influence the energy estimate. This implies that the global two-dimensional solution is proved without any structural restrictions on the external force, initial data or viscosity.

О решениях эллиптических уравнений второго порядка в цилиндрических областях

О решениях эллиптических уравнений второго порядка в цилиндрических областях

On boundary value problems for Maxwell set of equations in cylindrical domain

In this article solution of the Maxwell set of equations in cylindrical domain with homogeneous boundary conditions is constructed. New approach of expansion of unknown functions into series by two sets of functions orthogonal over the cross-section of domain is used. It is shown that the mixed type conjugation problem, to which the diffraction problem of electromagnetic wave on thin conducting lateral screen placed inside of the waveguide is reduced, is equivalent to two infinite sets of linear algebraic equations.

Global existence of strong solutions to micropolar equations in cylindrical domains

The micropolar equations are a useful generalization of the classical Navier–Stokes model for fluids with microstructure. We prove the existence of global and strong solutions to these equations in cylindrical domains in . We do not impose any restrictions on the magnitude of the initial and external data, but we require that they cannot change in the x3‐direction too fast. Copyright © 2014 John Wiley & Sons, Ltd.

Calderón problem for Maxwell's equations in cylindrical domain

We prove some uniqueness results in determination ofthe conductivity, the permeability and the permittivity ofMaxwell's equations in a cylindrical domain$\Omega \times (0,L)$ from partial boundary map.More specifically, for an arbitrarily given subboundary$\Gamma_0 \subset \partial\Omega$, we prove thatthe coefficients of Maxwell's equations can be uniquelydetermined in the subdomain$(\Omega \setminus$ [the convex hull of $\Gamma_0])$$ \times (0,L)$ by the boundary map only for inputs vanishingon $\Gamma_0 \times (0,L)$.

Asymptotic behavior of elliptic nonlocal equations set in cylinders

In this paper the asymptotic behavior of elliptic nonlocal equations in cylindrical domains is studied. These equations are associated with symmetric pure jump Levy stochastic processes and are generalisation of equations involving the fractional Laplacian operator. First we consider the existence and uniqueness of weak solutions in appropriate Hilbert spaces associated with the Levy measure and then study the asymptotic behavior in cylinders.

Long-time behavior of micropolar fluid equations in cylindrical domains

In this paper we investigate the existence of the H1-uniform attractor and long-time behavior of solutions to non-autonomous micropolar fluid equations in three dimensional cylindrical domains. In our considerations we take into account that the existence of global and strong solutions is proved under the assumption on smallness of change of the initial and the external data along the axis of the cylinder. Therefore, we refine the concept of the uniform attractor by adopting the idea which was proposed by J.W. Cholewa and T. Dłotko (1998) in [9].

Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translations of the front. In the case of stationary ergodic reactions, the fronts are proved to propagate with a deterministic positive speed. Our results extend to reaction-advection-diffusion equations with periodic advection and diffusion.