Showing papers on "Similarity solution published in 1969"
TL;DR: In this article, an analysis of the effects of buoyancy forces in laminar forced-convection on a vertical flat plate is made, and an approximate similarity solution is given by introducing the assumption that a role of Gr/Re2 in stream function is negligibly small as compared with η.
Abstract: An analysis is made for the effects of buoyancy forces in laminar forced-convection on a vertical flat plate. In general, since it is difficult to obtain an exact solution, an approximate similarity solution is given by introducing the assumption that a role of Gr/Re2 in stream function, [numerical formula] is negligibly small as compared with η. The validity of this assumption is examined by comparing with the experimental data of Kliegel. Numerical calculations are performed for both the constant fluid properties and the variable fluid properties, and the results are compared with Szewczyk's solution previously obtained by perturbation analysis. The velocity and temperature distribution, the friction factor and heat transfer coefficient are given for various values of the parameter Gr/Re2.
60 citations
TL;DR: In this paper, an exact similarity solution for the flow of a fluid-particle suspension over an infinitely large disk rotating at a constant velocity is given for the case where the boundary layer thicknesses of the particle cloud and the fluid are approximately equal.
Abstract: An exact similarity solution is given for the flow of a fluid‐particle suspension over an infinitely large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The boundary‐layer thicknesses of the particle cloud and the fluid are found to be approximately equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques.
23 citations
TL;DR: In this paper, the problem of ion transfer in the fluid phase of an electrodialysis stack with parallel flow is considered for two extreme cases: (a) undisturbed laminar flow with purely diffusive mixing; and (b) perfectly mixed flow.
Abstract: The problem of ion transfer in the fluid phase of an electrodialysis stack with parallel flow is considered for two extreme cases: (a) undisturbed laminar flow with purely diffusive mixing; and (b) perfectly mixed flow. Case (a) leads to a thin concentration boundary layer imbedded in the flow near the membrane surface. It is shown that for practically relevant parameters the solution may be approximated by a closed‐form similarity solution, and this is compared with the more exact numerical solution. Case (b), which represents the ideal situation, is presented for comparison.
11 citations
TL;DR: In this article, a similarity solution for spherically symmetric flow following an explosion in a rarefied atmosphere is extended by requiring it to satisfy the hydrodynamic energy conservation equation.
Abstract: A similarity solution recently given by Stuart for spherically symmetric flow following an explosion in a rarefied atmosphere is extended by requiring it to satisfy the hydrodynamic energy conservation equation. This additional constraint allows one to determine the functional form of the pressure and density and avoids the necessity of making the virial theorem approximation. The differential equation for the radius of the disturbance is different from the earlier theory, especially at late times when it shows that the kinetic energy eventually is completely transformed into internal energy, but the disturbance velocities are identical in the limit as R → 0.
9 citations
TL;DR: In this paper, the problem of concentration build-up at the membrane surface in the mass-transfer entry length in fully developed turbulent flow is formulated, taking into account incomplete salt rejection at membrane and axial variation of the osmotic pressure.
3 citations
20 Jan 1969
TL;DR: In this article, a simple interaction analysis based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave was proposed to calculate the major features of the interaction between a laminar boundary layer and a supersonic corner expansion wave.
Abstract: There are three distinct effects involved in the interaction of a laminar boundary layer and a supersonic corner expansion wave. These are: the upstream influence effect causing some pressure decay ahead of the corner, transverse pressure gradients in the immediate neighborhood of the corner, and the interaction of the boundary layer downstream with the external flow. Arguments are presented to suggest that, when the flow is locally hypersonic and the wall is highly cooled, the dominant effect is the downstream interaction process. Hence the major features can be calculated by using a simple interaction analysis down stream of the corner based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave. Numerical results are obtained by using the "cold wall" similarity solution to the boundary-layer equations. These show that pressure decay extends over a region which can be many times larger than the original plate length used to generate the boundary layer.