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Showing papers on "Similarity solution published in 1975"


Journal ArticleDOI
TL;DR: In this article, the effects of blowing and suction on free convection boundary layers on bodies of general shape are considered and a numerical solution is obtained for a horizontal circular cylinder with both constant blowing and SUction.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the similarity solution for the steady incompressible laminar boundary layer flow of a micropolar fluid past an infinite wedge was presented, and the governing equations have been solved numerically using fourth order Runge-Kutta-Gill method.
Abstract: This paper presents the similarity solution for the steady incompressible laminar boundary layer flow of a micropolar fluid past an infinite wedge. The governing equations have been solved numerically using fourth orderRunge-Kutta-Gill method. The results indicate the extent to which the velocity and microrotation profiles, and the surface shear stress are influenced by coupling, microrotation, and pressure gradient parameters. The important role played by the standard length of the micropolar fluid in determining the structure of the boundary layer has also been discussed.

33 citations


Journal ArticleDOI
TL;DR: In this article, the equations of motion for the laminar boundary layer flow over a rotating disc have been derived for a fluid which obeys a Rivlin-Ericksen type of constitutive equation and whose material parameters are assumed to be arbitrary functions of the second invariant of the rate of deformation tensor.
Abstract: The equations of motion for the laminar boundary layer flow over a rotating disc have been derived for a fluid which obeys aRivlin-Ericksen type of constitutive equation and whose material parameters are assumed to be arbitrary functions of the second invariant of the rate of deformation tensor. The analysis establishes the conditions under which a true similarity solution is possible. An inspectional analysis yields a relationship between the moment coefficient, a generalizedReynolds number and a modifiedWeissenberg number which incorporates a variable relaxation time with a process time characteristic of the boundary layer flow on the disc. Experimental data obtained are analysed in terms of the derived relationship and the agreement between the two, after the determination of the unknown constants, is found to be quite sound. A brief discussion follows which emphasizes the role of geometry, regime of flow and viscoelastic material parameters in giving a wide variety of flow phenomena.

16 citations


Journal ArticleDOI
TL;DR: In this paper, a solution to the integro-differential equation of batch grinding has been presented which maps the trajectory of particle size spectra of continuous size and time domains.

13 citations


Journal ArticleDOI
TL;DR: In this paper, a predictive model based solely on the conservation equations of both phases is presented for the study of the effect of the gas-side resistance in multicomponent absorption with chemical reaction in a laminar liquid film.

12 citations


Journal ArticleDOI
TL;DR: In this paper, similarity solutions are developed for a wide class of particulate processes that are governed by a general population balance equation for the inhomogeneous size distribution density function, termed self-preserving since neither particle size nor time appears explicitly in the solution.

10 citations


Journal ArticleDOI
TL;DR: In this article, a one-dimensional population balance governing the particle size distribution in a system where particles change their sizes due to both coagulation and individual growth is studied for the possibility of a similarity solution.

9 citations



Journal ArticleDOI
TL;DR: In this paper, a similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972).
Abstract: The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

7 citations


Journal ArticleDOI
TL;DR: In this paper, the fundamental equations of a two-dimensional turbulent jet without pressure gradient in the lateral direction are used to derive a similarity solution for particulate mass transfer across an air curtain.

7 citations


Proceedings ArticleDOI
01 May 1975
TL;DR: In this paper, the slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived for accurate merged shock layer solutions on a sphere.
Abstract: The slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived. The more realistic multicomponent species slip conditions are shown to be necessary for accurate merged shock layer solutions on a sphere. These slip conditions are used in a first-order similarity solution of the Navier-Stokes equations with nonequilibrium chemistry for the merged shock layer. Results of this quick numerical solution are compared with a time dependent solution around the sphere and with measured arc jet results at low Reynolds numbers. The similarity solution, unlike the time dependent solution, shows smooth radial profiles of the pressure and smooth variations of velocity slip, skin friction, temperature slip and heat transfer around the body. The present first-order similarity solution is valid up to 25 deg from the stagnation point and takes less than 1% of the computer time to run a time dependent scheme. The smaller stand-off distance obtained from the similarity solution is supported by experimental data. The measured heat flux is closer to the similarity solution than the time dependent method at the stagnation point and shows the proper variation with circumferential angle up to at least 40 deg.



Journal ArticleDOI
TL;DR: In this paper, the nonlinear, partial differential equations describing the compressible flow of a viscous and heat conducting gas in a cone are reduced to two coupled, ordinary, nonlinear differential equations by means of a self-similar transformation.
Abstract: The nonlinear, partial differential equations describing the compressible flow of a viscous and heat conducting gas in a cone are reduced to two coupled, ordinary, nonlinear differential equations by means of a self‐similar transformation. These are solved numerically for the velocity and temperature distributions in the cone. It is shown that for given flow numbers R, P, and M, laminar flows exist only up to a critical cone angle ϑ0.

Journal ArticleDOI
TL;DR: In this article, an asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a 2D channel.
Abstract: A wake similarity solution for symmetric uniform shear flows merging at the trailing edge of a flat plate has associated with it an eigenfunction problem which was overlooked by Hakkinen and O'Neil (1967). An asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a two-dimensional channel.