一类非均匀传输逆散射问题的混合交互关系研究

对一类带有传导边界条件的非均匀传输逆散射问题的混合交互关系进行探讨,并给出问题对应的Green函数远场G;与全场u、穿透场v的交互关系刻画,为重构散射体做好理论准备.

The improved element-free Galerkin method for three-dimensional transient heat conduction problems

With the improved moving least-squares (IMLS) approximation, an orthogonal function system with a weight function is used as the basis function. The combination of the element-free Galerkin (EFG) method and the IMLS approximation leads to the development of the improved element-free Galerkin (IEFG) method. In this paper, the IEFG method is applied to study the partial differential equations that control the heat flow in three-dimensional space. With the IEFG technique, the Galerkin weak form is employed to develop the discretized system equations, and the penalty method is applied to impose the essential boundary conditions. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the transient heat conduction equations and the boundary and initial conditions are time dependent, the scaling parameter, number of nodes and time step length are considered in a convergence study.

Freezing of Water in a Slab with Boundary Conditions of the Third Kind

Predictions for freezing heat transfer in a slab with convective boundary conditions at the cold surfaceare obtained from heat balance integral approximations, which consider conduction as the only modeof heat transfer in both the solid and liquid and consider durations of precooling and freezing in theheat transfer process. The thermal penetration dimensionless parameter or is presented to distinguishtwO cases of freezing, and analytical results for α≥ 1 are given in this paper. An experimental investigation on freezing of water is reported for comparison with the one-dimensional conduction model toshow that experimental modeling for freezing heat transfer with convective boundary conditions usingPeltter devices is feasible. The comparison also demonstrated that the freezing rate in this case wasdecreased by natural convection in the liquid just as freezing with boundary conditions of the first kindand phase change approximately proceeds linearly with time rather than with square root of time atthe initiation of freezing.

Heat Transfer Characteristics of Laminar Flow in Internally Finned Tubes under Various Boundary Conditions

Numerical solutions for fully developed laminar flow in internally finned tubes with trapezoidal and triangular fin profiles were given with Finite Element Method (FEM): The heat transfer characteristics were obtained and compared under the boundary conditions of uniform heat flux, uniform wall temperature, and the third boundary condition with finite wall thermal conductivity considered. The numerical results show that boundary conditions have pronounced effects on the temperature field.Furthermore, a new mechanism on the heat transfer augmentation of internally finned tubes is proposed.

Conjugate Heat Transfer Characterization in Cooling Channels

Cooling technology of gas turbine blades,primarily ensured via internal forced convection,is aimed towards withdrawing thermal energy from the airfoil.To promote heat exchange,the walls of internal cooling passages are lined with repeated geometrical flow disturbance elements and surface non-uniformities.Raising the heat transfer at the expense of increased pressure loss;the goal is to obtain the highest possible cooling effectiveness at the lowest possible pressure drop penalty.The cooling channel heat transfer problem involves convection in the fluid domain and conduction in the solid.This coupled behavior is known as conjugate heat transfer.This experimental study models the effects of conduction coupling on convective heat transfer by applying iso-heat-flux boundary condition at the external side of a scaled serpentine passage.Investigations involve local temperature measurements performed by Infrared Thermography over flat and ribbed slab configurations.Nusselt number distributions along the wetted surface are obtained by means of heat flux distributions,computed from an energy balance within the metal domain.For the flat plate experiments,the effect of conjugate boundary condition on heat transfer is estimated to be in the order of 3%.In the ribbed channel case,the normalized Nusselt number distributions are compared with the basic flow features.Contrasting the findings with other conjugate and convective iso-heat-flux literature,a high degree of overall correlation is evident.

Finite Element Method Formulation in Polar Coordinates for Transient Heat Conduction Problems

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method(FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

Controllability of the Heat Equation with a Control Acting on a Measurable Set

The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.