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: Investigation of unsteady magnetohydrodynamic nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects found that the nanofuid viscosities declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.
Abstract: The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid’s viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.
36 citations
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...[10] scrutinized the micro-polar fluids flow through a stretching sheet....
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TL;DR: In this article, the authors investigated the impact of the exponential heat source in the transport of nano micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating and convective condition effects.
Abstract: The study of novel exponential heat source phenomena across a flowing fluid with a suspension of microparticles and nanoparticles towards a convectively heated plate has been an open question. Therefore, the impact of the exponential heat source in the transport of nano micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating and convective condition effects has been analytically investigated. Influence of chemical reaction has also been exhibited in this discussion.,The leading equations are constructed via conservation equations of transport, micro-rotation, energy and solute under the non-transient state situation. Suitable stretching transformations are used to transform the system of partial differential equations to ordinary. The transformed ODEs admit numerical solution via Runge–Kutta fourth order method along with shooting technique.,The effects of pertinent physical parameters characterizing the flow phenomena are presented through graphs and discussed. The inclusion of microparticles and nanoparticles greatly affects the flow phenomena. The impact of the exponential heat source (EHS) advances the heat transfer characteristics significantly compared to usual thermal-based heat source (THS). The thermal performance can be improved through the effects of a magnetic dipole, viscous heating, Joule heating and convective condition.,The effectiveness of EHS phenomena in the dynamics of nano micropolar fluid past an elongated plate which is convectively heated with regression analysis is for the first time investigated.
33 citations
TL;DR: In this paper, similar solutions for the problem of a continuously moving surface in a stationary incompressible fluid, including the combined effects of convection, diffusion, wall velocity and thermophoresis are derived for the case in which both the surface temperature and stretching velocity vary as a power law.
Abstract: Similarity solutions for the problem of a continuously moving surface in a stationary incompressible fluid, including the combined effects of convection, diffusion, wall velocity and thermophoresis are derived for the case in which both the surface temperature and stretching velocity vary as a power law. Calculations for an isothermal moving plate clearly show the importance of thermophoresis on particle deposition.
24 citations
TL;DR: In this article, the effects of a chemical reaction on an unsteady flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium are investigated.
Abstract: An analysis is presented to investigate the effects of a chemical reaction on an unsteady flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation. The resulting nonlinear coupled differential equations are solved numerically by using a fourth-order Runge–Kutta scheme together with shooting method. The influence of pertinent parameters on velocity, angular velocity (microrotation), temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number has been studied and numerical results are presented graphically and in tabular form. Comparisons with previously published work are performed and the results are found to be in excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21090
23 citations
TL;DR: In this article , the authors considered the effects of Brownian motion and thermophoresis on the micropolar fluid at exponentially stretching curved surfaces and developed a mathematical model under the flow assumptions in partial differential equations.
Abstract: The present study considers heat transfer analysis of micropolar nanofluid flow over an exponentially stretching curved surface. The effects of Brownian motion and thermophoresis on the micropolar fluid at exponentially stretching curved surfaces are considered. The chemical reaction and slip effects are analyzed at exponentially stretching curved surface. Using boundary layer approximations, the mathematical model under the flow assumptions is developed in partial differential equations. The partial differential equations are transformed into ordinary differential equations using the dimensionless similarity variables. The dimensionless system is solved through numerical technique. The involving physical parameter effects are presented through graphs and tables. The f′(η) is enhanced due to rising the values of the curvature parameter. If the curvature is increasing, the bending of the sheet is more which enhances the motion of the fluid particles due to the action of centrifugal force. The Schmidt number enhances which reduces the concentration profile because Sc is directly proportional to the momentum diffusivity and inversely proportional to the mass diffusivity, and consequently, greater the values of Sc conformed to the small mass diffusivity which declines the concentration function.
17 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