Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

Abstract: Numerical modeling of Si homoepitaxial deposition from in the horizontal reactor has been undertaken employing the steady‐state, fully parabolic flow approximation for the heat, momentum, and mass‐transfer equations. Reactants are assumed to be dilute in their carrier gas. The resulting set of partial differential equations are discretized using finite elements and solved using the method of lines. The effect of a third dimension, the side temperature boundary conditions, and natural convection are explored. Given recent kinetics data on the silane decomposition and silylene insertion reactions, it is shown that a quasi‐thermodynamic equilibrium exists in the heated region above the surface, at least for hydrogen gas ambients. The combination of a fast silylene surface reaction and a slow silane surface reaction implies that the effective surface reaction rate is governed by the homogeneous thermodynamic equilibrium in the gas phase and diffusion through a thin mass‐transfer boundary layer near the surface. Examples of how tilting the susceptor contributes to growth uniformity are presented, and the effectiveness of similarity solution models at predicting this enhanced axial uniformity is tested.

Sakiadis flow of an upper-convected Maxwell fluid

Abstract: The flow of an upper-convected Maxwell (UCM) fluid is studied theoretically above a rigid plate moving steadily in an otherwise quiescent fluid. It is assumed that the Reynolds number of the flow is high enough for boundary layer approximation to be valid. Assuming a laminar, two-dimensional flow above the plate, the concept of stream function coupled with the concept of similarity solution is utilized to reduce the governing equations into a single third-order ODE. It is concluded that the fluid's elasticity destroys similarity between velocity profiles; thus an attempt was made to find local similarity solutions. Three different methods will be used to solve the governing equation: (i) the perturbation method, (ii) the fourth-order Runge–Kutta method, and (iii) the finite-difference method. The velocity profiles obtained using the latter two methods are shown to be virtually the same at corresponding Deborah number. The velocity profiles obtained using perturbation method, in addition to being different from those of the other two methods, are dubious in that they imply some degree of reverse flow. The wall skin friction coefficient is predicted to decrease with an increase in the Deborah number for Sakiadis flow of a UCM fluid. This prediction is in direct contradiction with that reported in the literature for a second-grade fluid.