Moving Boundary Value Research Articles

A Class of Moving Boundary Problems Arising in Drying Processes

Various representations of equilibrium drying processes are presented in a coherent framework as a class of moving boundary value problems involving the hysteresis phenomenon. The class splits into two subclasses of problems, called here implicit models and jump models; individual problems are categorized as sorption models, wet and dry models, and hysteresis-jump models. The mathematical model for the evolution of moisture, humidity, temperature, and pressure consists of a strongly coupled system of quasilinear partial differential equations, which is parabolic in the physical domain, together with the associated jump conditions of the Rankine–Hugoniot type. Whereas previous work on these models dealt with the numerical results, the present study addresses the mathematical wellposedness of the problems. The wet and dry jump model for a slab is stated, in both the classical and the weak formulations. Some results on local existence and uniqueness are obtained by using existing theory and the embedding tec...

Basic Concepts of Structure Formation During Processing of Thermoplastic Materials

Abstract A report is given of progress achieved during a 5-year period for describing the solidification of polymers by crystallization. Emphasis is placed on the fact that the classical quasi-equilibrium treatment of solidification under heat transfer conditions (as known under the heading of moving boundary value problems) is unable to predict any texturing in one-component systems. For polymers which are notorious for their slow approach to thermodynamic equilibrium, the local equilibrium theories, which are popular in metallurgy, are not discussed. In the present paper we show how to cope with nucleation under changing temperature conditions. Use is made of an adaptation of Avrami's theory to nonisothermal conditions, as recently proposed. Experimental work is extended to conditions of flow, where nucleation is enhanced. We show the possibility of theoretically describing this latter phenomenon.

High speed numerical technique to solve coupled moving boundary value heat problems

This paper presents a numerical scheme to solve the moving boundary value problem in phase change material and will elaborate the difficulties with the algorithm. A discussion on the extension of the algorithm to higher dimension is also presented. A table of the computer time taken during iterations is presented and figures to show the effectiveness of the algorithm are also given. The numerical scheme developed in this paper needs only CN multiplication operations to solve for solutions at N points, where C is a constant less than or equal to 5 at each iteration. Graphs of solutions are presented with different Stefan numbers. A graph for the interface is also presented in this paper. This paper presents a table with time analysis, required for each iteration.

A modified stefan problem related to transport-controlled stress corrosion cracking

A moving boundary value problem is proposed and analytically solved for environmental crack propagation where the transport of the deleterious species is the controlling mechanism of the plateau stage of subcritical crack growth. The concentration of the corrodant diffuses along the surfaces of the crack from a stationary environmental reservoir to the moving crack tip. A minimum concentration of gas at the crack tip is required to sustain crack propagation at a given temperature. The magnitude of the crack velocity is proportional to the mass flux at the crack tip, while the diffusivity of the gas is theoretically related to the evolving crack tip opening displacement. Under a transformation of coordinates, this moving boundary value problem is mapped onto the classic Stefan problem and solved. Because the theory is based primarily on gas transport and the mechanical response of the specimen to an applied load, it can be applied to a wide class of materials and environments.

Fasteners in composite plates: effects of interfacial friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.

Propagation of fire fronts in forests

A moving boundary value problem is considered to investigate the one-dimensional propagation of fire fronts in forests. The problem is solved by the finite difference method with real physical parameters of forests. The theoretical and experimental results are compared to determine the sensitivity of the model for forecasting and control of forest fires.

Invariant imbedding and solid-fluid reactions—I: The unreacted core model

Invariant imbedding is used to develop a straightforward numerical technique for solving the moving boundary value problems in solid-fluid reactions. T

Computational Methods For Obstacle Problems

It is well known that a wide class of linear and nonlinear obstacle, unilateral, contact, free and moving boundary value problems arising in pure an applied engineering sciences can be studied in the unified framework of variational inequalities. The main advantage of this formulation is that the location of the obstacle (free, contact) becomes an essential part of the solution and no special technique is needed to locate it. In this paper, we use the auxiliary principle technique to suggest and analyze a novel and general iterative algorithm for solving a new class of variational inequalities. Several known iterative methods can be obtained as special cases of our main result.

Superconducting-to-Normally Conducting Transitions in Strip Transmission Line Structures

A theoretical and experimental investigation of superconducting-to-normally conducting transitions in strip transmission line structures is presented. The theoretical analysis is based on a macroscopic model, which is the transmission line analog of the Pippard model. It is assumed that during the transition a superconducting-normally conducting (S-N) interface propagates along the transmission line structure. This situation is treated theoretically as a moving boundary value problem. The S-N interface propagation velocity is determined explicitly in terms of the current that induces the transition, the operating temperature, and the superconductive penetration depth. Experimental results indicate that the model is useful for predicting the transition time of a strip transmission line structure.