Similarity solution

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

Similarity Solution for Unsteady MHD Flow Near a Stagnation Point of a Three-Dimensional Porous Body with Heat and Mass Transfer, Heat Generation/Absorption and Chemical Reaction

Abstract: The problem of unsteady mixed convection heat and mass transfer near the stagnation point of a three-dimensional porous body in the presence of magnetic field, chemical reaction and heat source or sink is analyzed. An efficient, iterative, tri-diagonal implicit finite difference method is used to solve the transformed similarity equations in the boundary layer. Three cases were considered, namely, accelerating flow, decelerating flow and the steady-state case. The obtained results are presented in graphical and tabulated forms to illustrate the influence of the different physical parameters such as the magnetic field parameter, transpiration parameter, unsteadiness parameter, ratio of velocity gradients at the edge of the boundary layer parameter, heat generation/absorption parameter and the chemical reaction parameter on the velocity components in the x-and y- directions, temperature and concentration distributions, as well as the skin-friction coefficients and Nusselt and Sherwood numbers.

Real-Gas Effects on Mean Flow and Temporal Stability of Binary-Species Mixing Layers

Abstract: Real-gas effects on the mean flow and inviscid stability of temporal mixing layers are examined for supercritical heptane/nitrogen and oxygen/hydrogen mixtures. The analysis is based on the compressible Navier–Stokes equations for conservation of mass, momentum, total energy, and species mass, with heat and species-mass fluxes derived from fluctuation-dissipation theory and incorporating Soret and Dufour effects. An approximate form of the equations is used to obtain a system of similarity equations for the streamwise velocity, the temperature, and the mass fraction. The similarity profiles show important real-gas nonideal-mixture effects, particularly for the temperature, in departing from the incompressible error-function similarity solution. Realistic Schmidt and Prandtl numbers were found to be important to the similarity profiles. A linear, inviscid stability analysis is then performed using the similarity profile, as well as analytical error-function profiles, as its basic flow. The stability analysis shows that the similarity profile has larger growth rates at a given wavelength and a shorter more unstable wavelength than the error-function profiles and than an incompressible flow. The similarity profile also has a larger range of unstable wavelengths than the error-function profiles.