Coupled Boundary Research Articles

Non-axisymmetric, thermoelastic stress distribution in a solid containing an external crack

The non-axisymmetric thermal stress distribution in an infinite elastic solid containing an external stress-free crack with prescribed heat flux is investigated. The problem is formulated in terms of a complete set of harmonic functions and leads to a set of two mixed, coupled boundary value problems. The coupling is through two arbitrary constants which are determined by the condition that the displacements be finite near the edge of the crack. The problems are solved using a standard Hankel transform technique and expressions for the stress intensity factors are given.

Coupled Laminar Heat Transfer and Sublimation Mass Transfer in a Duct

Consideration is given to gas flow through a parallel-plate channel whose walls are coated with a sublimable material. The duct walls are thermally insulated from the environment, with the result that the heat of sublimation is supplied by the flowing gas stream. The formulation requires simultaneous consideration of the energy and diffusion equations along with highly coupled boundary conditions. An analytical solution is facilitated by employing a linear saturation state relationship for the vapor of the subliming solid, the suitability of which is given support by numerical comparisons. The resulting eigenvalue problem does not fall within the range of the conventional Sturm-Liouville system. A special integral condition was derived which serves as an orthogonality relation, while various numerical comparisons were made to verify the computational validity of the series solution. In particular, an independent boundary-layer solution is in excellent agreement with the series solution in the region just downstream of the entrance section. Numerical results are given for various quantities of interest including the bulk and wall temperatures and mass fractions, the wall heat flux, temperature and mass fraction profiles, and the length of the development region.

Mathematical Treatment of Competitive Surface and Volume Diffusion Processes

Equations are derived for the surface diffusion of atoms into a half-plane (the boundary of which is kept at constant concentration) under conditions in which atoms are simultaneously being lost into the bulk via a volume diffusion mechanism. Two coupled boundary valued problems arise which are solved by treating the volume diffusion as a perturbation. Methods of evaluating the coefficient D8 of surface diffusion are discussed. The final surface concentration Ŝ resulting from the parasitic effect of volume diffusion contains three leakage terms. These terms have the effect of altering the time dependence of the concentration. This formulation is useful in interpreting surface diffusion data obtained in the high-temperature range.

Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space

The propagation of mechanical and thermal disturbances in a half-space is studied by means of the solution of some transient boundary value problems, according to the coupled thermoelastic theory. The problems considered are those of a half-space under step time variations of strain, temperature, or stress uniformly distributed over the free surface. The coupled solution of Danilovskaya’s problem is thus included. The solution is obtained by the use of Fourier sine transforms, and the behaviors at short and long times, as well as the propagation of discontinuities, are studied.