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 of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition

Abstract: This paper examined the hydromagnetic boundary layer flow with heat and mass transfer over a vertical plate in the presence of magnetic field and a convective heat exchange at the surface with the surrounding has been studied. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations and an efficient numerical technique is implemented to solve the reduced system. A comparison study with the previous results shows a very good agreement. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters. Key words: Vertical plate, convective boundary condition, heat and mass transfer, magnetic field, similarity solution.

Flow past a suddenly heated vertical plate in a porous medium

Abstract: An analysis is presented for the steady free convection flow about a semi-infinite vertical flat plate that is embedded in a saturated porous medium at high Rayleigh numbers. Similarity solutions are obtained for a class of problems where the wall temperature varies as a power of the distance from the leading edge of the plate. The existence and uniqueness of the solutions are considered. The approach to this steady-state solution is also considered by investigating the temporal development of the flow when the temperature of the plate is impulsively increased from that of the surroundings. A numerical solution is presented that matches the small and large time solutions. For some temperature distributions on the plate it is found that the velocity achieves its maximum value within the boundary layer. For these the disturbance from the leading edge of the plate travels fastest within the boundary layer. An asymptotic solution valid at large times is presented and the approach of the numerical solution to this asymptotic solution is illustrated. For the situation in which the plate is impulsively heated to a constant temperature an analysis is presented for the early stages of the departure from the one-dimensional solution.

An analytic description of converging shock waves

Abstract: The similarity solution describing the motion of converging spherical and cylindrical shocks is governed by a set of three ordinary differential equations. Previous descriptions of the shock motion have been based on numerical solutions of these differential equations. In the present paper a study of the singular points of the differential equations leads to an analytic description of the flow and a determination of the similarity exponent which is in excellent agreement with the earlier numerical values. Limiting values of the ratio of specific heats are considered. It is shown that as the ratio tends to unity the shock becomes ‘freely propagating’ and the first terms in a power series for the similarity exponent are obtained. Large values of the ratio of specific heats are briefly considered and provide a further check on the analytic description of this paper. Finally in the Appendix the condition for the pressure to have a maximum is clarified and the location of the maximum provides further strong evidence of the high accuracy of the analytic approach of this paper.

Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating

Abstract: The present paper is concerned with the analysis of inherent irreversibility in hydromagnetic boundary layer flow of variable viscosity fluid over a semi-infinite flat plate under the influence of thermal radiation and Newtonian heating. Using local similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilized to compute the entropy generation number. The effects of magnetic field parameter, Brinkmann number, the Prandtl number, variable viscosity parameter, radiation parameter and local Biot number on the fluid velocity profiles, temperature profiles, local skin friction and local Nusselt number are presented. The influences of the same parameters and the dimensionless group parameter on the entropy generation rate in the flow regime and Bejan number are calculated, depicted graphically and discussed quantitatively. It is observed that the peak of entropy generation rate is attained within the boundary layer region and plate surface act as a strong source of entropy generation and heat transfer irreversibility.

Integral Solution for the Mean Flow Profiles of Turbulent Jets, Plumes, and Wakes

Abstract: Integral methods are used to derive similarity solutions for several quantities of interest including the cross-stream velocity, Reynolds stress, the dominant turbulent kinetic energy production term, and eddy diffusivities of momentum and heat for axisymmetric and planar turbulent jets, plumes, and wakes. A universal constant is evaluated for axisymmetric and planar plumes