Micropolar flow past a stretching sheet
01 Nov 1985-Zeitschrift für Angewandte Mathematik und Physik (Springer International Publishing)-Vol. 36, Iss: 6, pp 845-853
TL;DR: In this paper, the flow of an incompressible, constant density micropolar fluid past a stretching sheet is studied using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newton algorithm.
Abstract: This paper studies the flow of an incompressible, constant density micropolar fluid past a stretching sheet. The governing boundary layer equations of the flow are solved numerically using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newton algorithm. The flow pattern depends on three non-dimensional parameters. Some interesting results are illustrated graphically and discussed.
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TL;DR: In this paper , the effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms.
Abstract: The goal of this research is to check irregularity in heat generation, chemical reaction and thermal radiation effect an unsteady micropolar fluid flow. With the help of suitable similarity variables, the group of governing system of PDE and their associative boundary conditions are converted into the family of ODE and then solved using the HAM. The effect of various and important dimensionless parameters on the momentum, micro-rotation, energy and concentration equations have been discussed with graphical representation as well as tabular forms. It is observed that buoyancy force parameter, mixed convection parameter and permeability parameter enhance the velocity distribution while micropolar reduces the velocity profile. The temperature profiles are boosted for time and space dependent heat generation and absorption parameter respectively but reverse trend is observed for Prandtl number and unsteadiness parameter. Skin-friction factor, mass transfer rate and heat transfer rate have been listed and displayed in tables.
5 citations
TL;DR: In this paper, the model of boundary-layer equations for a perfectly conducting fluid was applied to study the heat transfer with one relaxation time from a non-isothermal stretching sheet on the flow of a polar fluid.
Abstract: The model of boundary-layer equations for a perfectly conducting fluid proposed by M. Ezzat [1] is applied to study the heat transfer with one relaxation time from a non-isothermal stretching sheet on the flow of a polar fluid. The method of the successive approximation is adopted for the solution of two-dimensional problem. The effects of various material parameters on the velocity, angular velocity, and temperature are discussed and illustrated graphically.
5 citations
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TL;DR: In this article , the steady incompressible second-grade micropolar fluid flow over a nonlinear vertical stretching Riga sheet is studied, where velocity slip and zero mass flux are considered at the solid surface of Riga shape such that the friction of nanoparticle maintains itself with strong retardation.
Abstract: The main purpose of this work is to study the steady incompressible second-grade micropolar fluid flow over a nonlinear vertical stretching Riga sheet. Velocity slip and zero mass flux are considered at the solid surface of Riga shape such that the friction of nanoparticle maintains itself with strong retardation. The influence of Lorentz forces produced by the Riga plate is an important aspect of the study. The influences of thermophoresis and Brownian motion under the heat generation and e bouncy forces are studied on the nonlinear vertical Riga sheet. The mathematical model is developed under the flow assumptions. The mathematical model in terms of partial differential equations is formed by implementing the boundary layer approximations. The partial differential equations are further reduced to ordinary differential equations by means of suitable transformations. The ordinary differential equations are solved through the numerical procedure. The variations in the horizontal movement of nanofluid, thermal distribution and concentration distribution of the nanoparticle have been noted for different fluid parameters. The values of velocity profile and temperature profile are larger in the case of injection ([Formula: see text] as compared to suction ([Formula: see text]). The values of concentration distribution are smaller in the case of injection ([Formula: see text] as compared to suction ([Formula: see text]. The validation of this analysis with decay literature is provided in the form of tables.
5 citations
TL;DR: In this article, the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field was studied using the Adomian decomposition with Padé approximants.
Abstract: Abstract In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems
4 citations
References
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TL;DR: In this paper, a plastischem material fliesst aus einem Spalt with einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist.
Abstract: Eine Platte aus plastischem Material fliesst aus einem Spalt mit einer Geschwindigkeit, die proportional zum Abstand vom Spalt ist. Eine exakte Losung der Grenzschichtgleichungen fur die von der Platte erzeugte Luftbewegung wird gegeben. Oberflachenreibung und Warmeleitungskoeffizient werden berechnet.
3,317 citations
TL;DR: In this article, the boundary layer flow over a semi-infinite flat plate is studied and the partial differential equations of motion are reduced to 2 couple differential equations and numerical solutions for different values of the parameters are obtained.
523 citations
01 Aug 1980
TL;DR: A pack of FORTRAN subprograms for the numerical solution of nonlinear equations and nonlinear least-squares problems and this report provides an overview of the algorithms and software in the package.
Abstract: MINPACK-1 is a pack of FORTRAN subprograms for the numerical solution of nonlinear equations and nonlinear least-squares problems. This report provides an overview of the algorithms and software in the package, and includes the documentation and program listings.
415 citations
TL;DR: In this paper, two different boundary conditions for the spin are considered: vanishing spin and vanishing surface moment, and the equations of motion are reduced to dimensionless forms which include three dimensionless parameters, and integrated numerically by a Runge-Kutta method.
Abstract: Plane and axially symmetric flows of a micropolar fluid, in contact with an infinite plate, and tending to potential flow at infinity, with a stagnation point on the plate, are considered Two different boundary conditions for the spin are considered: (a), vanishing spin; and (b), vanishing surface moment The equations of motion are reduced to dimensionless forms which include three dimensionless parameters, and integrated numerically by a Runge—Kutta method Results are presented both in tabular and graphical form, and the effects of the values of the parameters on the flow are discussed
173 citations
TL;DR: Chow, Mallet-Paret, and Yorke have recently proposed an algorithm for computing Brouwer fixed points of C^2 maps as discussed by the authors, and a numerical implementation of that algorithm is presented here.
158 citations