A simple boundary condition at semiconductor-insulating substrate interface of a TFT

The authors construct a bridge between a microscale view and a nanoscale one in continuum mechanics. When the size of structure reduces to nanolevel, the ratio of surface to volume increases. Then, the surface stresses, which like to surface tension in fluid, influence on bulk stresses. In the present paper, the authors analyze a problem that anisotropic nanothin layers are deposited on a half substrate. Interface stresses and interface elasticity are taken into account for the boundary condition for each layer. Furthermore, misfit dislocation networks which generate from a mismatch of lattice parameters in crystals composing multilayers exist at each interface. A complicated interaction between misfit dislocation networks located at different interfaces will be demonstrated, and the results in the theory will be compared with those in a molecular dynamic method using a generalized embedded atomic potential.

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Free convection beneath a heated horizontal plate in a rapidly rotating system

Journal of Fluid Mechanics ◽

10.1017/s0022112007007252 ◽

2007 ◽

Vol 586 ◽

pp. 491-506

Author(s):

ROBERT J. WHITTAKER ◽

JOHN R. LISTER

Keyword(s):

Boundary Layer ◽

Thermal Boundary Layer ◽

Ekman Layer ◽

Outer Edge ◽

Horizontal Plate ◽

Rotating System ◽

Plate Temperature ◽

System Equation ◽

Simple Boundary ◽

Simple Boundary Condition

Laminar flow beneath a finite heated horizontal plate in a rapidly rotating system is considered in both axisymmetric and planar geometries. In particular, we examine the case where the Ekman layer is confined well within a much deeper (yet still thin) thermal boundary layer. This situation corresponds to the regime E−3/2 ≪ Ra ≪ E−5/2, where E and Ra are the natural Ekman and Rayleigh numbers for the system (equation (2.6)). The outward flux of buoyant fluid from beneath the plate occurs primarily in the Ekman layer, while outward flow in the thicker thermal boundary layer is inhibited by a dominant thermal-wind balance. The O(Ra−1/2E−3/4 thickness of the thermal boundary layer is determined by a balance between Ekman suction and diffusion. There are several possible asymptotic regimes near the outer edge of the plate, differing only by logarithmic factors, but in all cases the edge corresponds to a simple boundary condition on the interior flow. With a uniform plate temperature, the dimensionless heat transfer (equation (7.6)) is given by a Nusselt number $\Nu\,{\sim} \tfrac{1}{2}\Ra^{1/2}\Ek^{3/4}[\ln (\Ra^{-1} \Ek ^{-5/2})]^{1/2}$. The solution for a uniform plate heat flux is also presented.

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One-Dimensional Fin-Tip Boundary Condition Correction II

Heat Transfer Engineering ◽

10.1080/01457630152496304 ◽

2001 ◽

Vol 22 (5) ◽

pp. 35-40 ◽

Cited By ~ 1

Author(s):

D. C. Look Jr ◽

Arvind Krishnan

Keyword(s):

Boundary Condition ◽

One Dimensional

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