Similarity solution

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

Eigenvalues in trailing edge flows

Abstract: A wake similarity solution for symmetric uniform shear flows merging at the trailing edge of a flat plate has associated with it an eigenfunction problem which was overlooked by Hakkinen and O'Neil (1967). An asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a two-dimensional channel.

Unsteady Solution of the Boundary Layer Equations with Application to Space Shuttle Tiles.

Abstract: : Wind tunnel tests were conducted on space shuttle orbiter insulating articles. The data, processed by a heat estimation computer program, revealed a large discrepancy in magnitude of the heat transfer coefficient over the space shuttle tile when compared to that yielded by flat plate theory and thin skin test results. A suggested cause of this discrepancy was the nonisothermal wall effect. An unsteady compressible to investigate these effects. The boundary layer equations were transformed, using the Dorodnitsyn transformation to allow the equations to be solved similar to incompressible equations. These equations were then transformed to the computational plane and approximated by finite differences. Optimized successive overrelaxation was used to solve the difference equations. The grid used for this program is optimized based on the Blasius solution. Upon running this program, leading edge startup problems arose so a similarity solution is assumed at the leading edge which corrects the problem. The program was verified with an incompressible case which was in good agreement with the Blasius solution, and a compressible case with an isothermal wall which agreed well with approximate theory. The isothermal case showed the solution was dependent on the grid. The steady state and transient nonisothermal wall cases displayed the same trend as the approximate nonisothermal solution. All cases had the same dramatic decrease in the heat transfer coefficient and the subsequent recovery in the streamwise direction. (Theses)

Charge carrier dynamics in alpha particle tracks

Abstract: An alpha particle event in a semiconductor device is modeled as the instantaneous generation of holes and electrons. The resulting axisymmetric potential of charge carriers is shown to be represented by a similarity solution of the drift-diffusion equations. The ordinary differential equations (ODEs) that arise are integrated numerically, after two quadratures. The results help to clarify the field funneling mechanism in dynamic random access memory (DRAM) storage devices.

Convective mass transfer effect on short-time liquid phase epitaxial growth

Abstract: The effect of slider velocity on the growth rate and epilayer thickness in liquid phase epitaxial (LPE) growth has been studied numerically by means of the boundary layer theory. The governing equations and boundary conditions under the boundary layer approximation have been developed and the melt velocity profile and growth rate have been solved by means of a similarity method and finite difference scheme. The simulation shows that two growth mechanisms occur during the LPE process. In the initial period of epitaxial growth the slider motion induces a disturbance in the melt; convective mass transfer predominates and the epilayer grows rapidly. After the melt has settled down, the mass transfer rate is controlled by diffusion and a concentration gradient is established to maintain the diffusion. Since the Sakiadis flow dominates the fluid motion in the sliding process and the boundary layer is fully developed at a position far from the leading edge, the epilayer thickness is uniform. In the initial growth period the velocity profile near the growth interface decreases drastically, resulting in a very short convective mass transfer region in the entire LPE growth.

Matched asymptotic expansions to similarity solutions of shock diffraction

Abstract: Formal asymptotic expansions with differently scaled variables are matched to obtain a uniform approximation to the similarity solution of the shock-wedge diffraction problem.