Similarity solution

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

Surface phenomena in the hydrodynamics of an incompressible fluid

Abstract: By taking as an example the outflow of an incompressible fluid through a hole with small geometric parameters under the conditions of supersmall pressures, we attempted to evaluate the effect of surface phenomena on its flow by the similarity method. The Navier–Stokes differential equation was supplemented by parameters allowing for the effect of surface forces. The modified Navier–Stokes equation was subjected to similarity conversion. This yielded a dimensionless group that includes the whole range of variable parameters affecting the fluid flow, namely, the generalized criterion Pv. The graphic dependence of the coefficient of the fluid flow rate on the generalized criterion Pv is presented on the basis of experimental data.

On similarity solution of an unsteady laminar boundary layer along a flat plate

Abstract: A unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow, inside a boundary layer along a flat plate. Though previously, attempts were made to obtain similarity solutions of a steady boundary layer flow neglecting viscous dissipation term in the energy conservation equation but the treatments were not complete. Here we have taken account of the viscous dissipation term. In the steady case it has been shown that for a similarity solution of both velocity and temperature, there should be a relation between the undisturbed flow outside the boundary layer and the temperature of the plate. It has been shown that the similarity solution exists in the unsteady case if we neglet the viscous dissipation term in the energy equation.

On Obtaining Non-Similar Solutions from Similar Solutions

Abstract: We have seen in the earlier chapters, that a similarity representation is obtainable for a boundary value problem provided the governing differential equations and the associated boundary conditions are invariant under a group of transformations. However, if any of the equations and boundary conditions is not invariant under a group, then the problem becomes nonsimilar.

The effect of sudden source buoyancy flux increases on turbulent plumes

Abstract: Building upon the recent experimentally verified modelling of turbulent plumes which are subject to decreases in their source strength (Scase et al., J. Fluid Mech., vol. 563, 2006b, p. 443), we consider the complementary case where the plume’s source strength is increased. We consider the effect of increasing the source strength of an established plume and we also compare time-dependent plume model predictions for the behaviour of a starting plume to those of Turner (J. Fluid Mech., vol. 13, 1962, p. 356). Unlike the decreasing source strength problems considered previously, the relevant solution to the time-dependent plume equations is not a simple similarity solution. However, scaling laws are demonstrated which are shown to be applicable across a large number of orders of magnitude of source strength increase. It is shown that an established plume that is subjected to an increase in its source strength supports a self-similar ‘pulse’ structure propagating upwards. For a point source plume, in pure plume balance, subjected to an increase in the source buoyancy flux F0, the rise height of this pulse in terms of time t scales as t 3/4 while the vertical extent of the pulse scales as t 1/4 . The volume of the pulse is shown to scale as t 9/4 . For plumes in pure plume balance that emanate from a distributed source it is shown that the same scaling laws apply far from the source, demonstrating an analogous convergence to pure plume balance as that which is well known in steady plumes. These scaling law predictions are compared to implicit large eddy simulations of the buoyancy increase problem and are shown to be in good agreement. We also compare the predictions of the time-dependent model to a starting plume in the limit where the source buoyancy flux is discontinuously increased from zero. The conventional model for a starting plume is well approximated by a rising turbulent, entraining, buoyant vortex ring which is fed from below by a ‘steady’ plume. However, the time-dependent plume equations have been defined for top-hat profiles assuming only horizontal entrainment. Therefore, this system cannot model either the internal dynamics of the starting plume’s head or the extra entrainment of ambient fluid into the head due to the turbulent boundary of the vortex ring-like cap. We show that the lack of entrainment of ambient fluid through the head of the starting plume means that the time-dependent plume equations overestimate the rise height of a starting

Heat and Mass transfer effects on Hydro magnetic Blood flow through a Parallel Plates when Lower Plate Stretches Exponentially

Abstract: In this study, we have analyzed heat and mass transfer effects on unsteady blood flow along a parallel plate channel with heat source and chemical reaction. Strength of magnetic field B 0 is applied perpendicularly. The governing higher order nonlinear PDEs are solved by converting into ODEs under the similarity transformations of exponential form by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of η and t with respect to the chosen boundary conditions. The effects of different pertinent parameters appeared in this model viz thermal Grashof number Gr , mass Grashof number Gm, Prandtl number Pr , heat generation/absorption parameter N , Magnetic field M and decay parameter λ on axial flow transport with the normal velocity are analyzed in detail. KEYWORDS: Blood flow, Similarity solution, Decay parameter, Heat source, Mass transfer, Chemical reaction. NOMENCLATURE: M Magnetic parameter λ Decay parameter