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 article, the effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated and self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method.
189 citations
Cites background from "Micropolar flow past a stretching s..."
...[11] extended the work of Sankara and Watson [10] by considering the mass suction or injection through the porous sheet....
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...An important contribution in micropolar flow dynamics was made by Sankara and Watson [10], when they investigated the flow of micropolar fluids past a stretching sheet....
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TL;DR: In this paper, an analysis is presented to study dual nature of solution of mass transfer with first order chemical reaction in boundary layer stagnation-point flow over a stretching/shrinking sheet.
169 citations
Cites background from "Micropolar flow past a stretching s..."
...[4], Sankara and Watson [5], Chen and Char [6], Vajravelu and Rollins [7] and Chamkha [8] by considering different types of fluid and various physical conditions....
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TL;DR: Probability one homotopy algorithms as mentioned in this paper are a class of methods for solving nonlinear systems of equations that are globally convergent with probability one, and if constructed and implemented properly, are robust, numerically stable, accurate, and practical.
Abstract: Probability one homotopy algorithms are a class of methods for solving nonlinear systems of equations that are globally convergent with probability one These methods are theoretically powerful, and if constructed and implemented properly, are robust, numerically stable, accurate, and practical The concomitant numerical linear algebra problems deal with rectangular matrices, and good algorithms require a delicate balance (not always achieved) of accuracy, robustness, and efficiency in both space and time The author's experience with globally convergent homotopy algorithms is surveyed here, and some of the linear algebra difficulties for dense and sparse problems are discussed
159 citations
TL;DR: In this article, an analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method.
Abstract: An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet. Using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value, steady flow is possible. The dual solutions for velocity and temperature distributions are obtained. With increasing values of the mass suction parameter, the skin friction coefficient increases for the first solution and decreases for the second solution.
136 citations
TL;DR: Homotopy algorithms for solving nonlinear systems of (algebraic) equations, which are convergent for almost all choices of starting point, are globally convergent with probability one and exhibit a large amount of coarse grain parallelism.
123 citations
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38 citations
TL;DR: In this paper, a viscous fluid is injected through a rotating porous disc onto a coaxial, rotating solid disc, and the resulting nonlinear ordinary differential equations are solved by three methods: series expansion for small cross-flow Reynolds number, asymptotic expansion for large number, and numerical integration using a homotopy method.
Abstract: A viscous fluid is injected through a rotating porous disc onto a coaxial, rotating solid disc. The resulting nonlinear ordinary differential equations are solved by three methods: series expansion for small cross-flow Reynolds numberR, asymptotic expansion for largeR, and numerical integration using a homotopy method. Lift and torque are discussed.
34 citations
TL;DR: A numerical implementation of S.N. Chow and J. Yorke's proposed algorithm for computing fixed points of C2 maps that is globally convergent with probability one is presented here, where careful attention has been paid to computational efficiency, accuracy, and robustness.
32 citations
TL;DR: In this article, a globally convergent homotopy algorithm is applied to the boundary value problem, and numerical results for a wide range of parameter values are reported for a variety of problems.
20 citations
TL;DR: In this paper, a search for similar solutions reveals as only possible similar boundary layer flow in micropolar fluids the flow near a stagnation point, and the corresponding equations have been solved numerically by means of a shooting method.
Abstract: A search for similar solutions reveals as only possible similar boundary layer flow in micropolar fluids the flow near a stagnation point. The corresponding equations have been solved numerically by means of a shooting method. Consideration is given not only to the coupling parameterC1 and the microdiffusivity parameterC2 but also to the microinertia parameterC3. It is shown that macroscopic properties of steady boundary layer flows are not very much affected by these parameters, while the microrotation and therefore the inner structure of the layer is very sensitive to all three parameters. These properties of the microstructure can become important in certain unsteady flow problems; then also the macroscopic behaviour may be different to the behaviour of Newtonian fluids.
14 citations