Similarity solution

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

Stability of streamwise vortices

Abstract: A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Momentum and heat transfer over a continuous moving surface in a non-Darcian fluid

Abstract: The momentum and heat transfer characteristics associated with the boundary layer on a continuous moving flat surface in a non-Darcian fluid have been investigated exploiting a local similarity solution procedure. The full boundary layer equations, which describe the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables, deduced from a scale analysis on the momentum and energy conservation equations. Details are provided for the effects of convective inertia and porous inertia on the velocity and temperature profiles. The resulting friction and heat transfer characteristics are found to be substantially different from those of forces convection over a stationary flat plate. Furthermore, useful asymptotic expressions for the local Nusselt number are presented in consideration of possible physical limiting conditions.

Similarity Solution of Freezing or Melting Processes with Variable Thermal Properties

Abstract: Freezing or melting processes, using substances with variable thermal properties, taking place in a body with variable cross-sectional area, are considered. The method of obtaining the similarity s...

Self similar flow under the action of monochromatic radiation behind a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas

Abstract: The propagation of a cylindrical shock wave in a self-gravitating, rotating axisymmetric dusty gas under the action of monochromatic radiation with a constant intensity per unit area, which has variable azimuthal and axial components of fluid velocity, is investigated The gas is assumed to be grey and opaque, and the shock is assumed to be transparent The dusty gas is considered as a mixture of non-ideal gas and small solid particles, in which solid particles are continuously distributed To obtain some essential features of shock propagation, small solid particles are considered as a pseudo-fluid, and it is assumed that the equilibrium flow condition is maintained in the entire flow-field Similarity solutions are obtained as well as the effects of the variation of the radiation parameter, the gravitation parameter, the non-idealness parameter of the gas, the mass concentration of solid particles in the mixture, the ratio of the density of solid particles to the initial density of the gas are worked out in detail The similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the radiation parameter and the gravitation parameter It is found that radiation parameter dominates the effect of dusty gas parameters on the variation of radiation heat flux The total energy of the flow-field behind the shock front is not constant but varies as fourth power of the shock radius