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axisymmetric flow simulations of fiber suspensions as described by 3D probability distribution function

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS 2020年 284卷

作者： Ferec, Julien Mezi, Dihya Advani, Suresh G. Ausias, Gilles Univ Bretagne Sud IRDL UMR CNRS 6027 F-56100 Lorient France Univ Delaware Ctr Composite Mat Dept Mech Engn 101 Acad St Newark DE 19716 USA

Numerical models are developed to examine fiber suspension flows through axisymmetric geometries, such as a circular pipe, a center-gated disk and a die exit. The fiber orientation micro-structure is fully described by using the entire probability distribution function (PDF) in 3D instead of the second and fourth moments of the PDF, which introduce errors due to the closure approximation when using orientation tensor descriptions. A Newtonian suspending fluid is considered for the constitutive relationship and simulations are performed with and without coupling the flow and fiber orientation. Results are compared with numerical simulations obtained by using the standard evolution equation for the second-order orientation tensor and the IBOF closure approximation. It is found that the IBOF closure approximation does a relatively good job of matching the exact orientation results given by the probability distribution function. For the three explored flows, the difference between the predicted orientation results using the coupled and decoupled approaches is not significant. There is a noticeable difference in the velocity field solutions, specifically at the die exit where the coupled approach increases the die swell ratio when the fibers enter the inlet with random orientation state.

关键词： Fiber suspension Polymer composite Fiber orientation Numerical modeling Probability distribution function axisymmetric flow

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axisymmetric flow due to a stretching sheet with partial slip

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2007年第7-8期54卷 1169-1183页

作者： Ariel, P. Donald Trinity Western Univ Dept Math Sci Langley BC V2Y 1Y1 Canada

The steady, laminar, axisymmetric flow of a Newtonian fluid due to a stretching sheet when there is a partial slip of the fluid past the sheet has been investigated. The flow is governed by a third-order non-linear boundary value problem whose exact numerical solution has been obtained non-iteratively in terms of the non-dimensional slip parameter lambda. A perturbation solution valid for small lambda and an asymptotic solution valid for large lambda have been derived. Finally a solution based upon He's homotopy perturbation method has been developed. The latter, being analytical, is elegant but is sufficiently accurate for all values of lambda. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： axisymmetric flow partial slip homotopy perturbation method Ackroyd's method Samuel and Hall method perturbation solution asymptotic solution

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axisymmetric flow AND HEAT TRANSFER OF THE CARREAU FLUID DUE TO A RADIALLY STRETCHING SHEET: NUMERICAL STUDY

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JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS 2017年第3期58卷 410-418页

作者： Khan, M. Hashim Quaid I Azam Univ Dept Math Islamabad 44000 Pakistan

The prime objective of this article is to study the axisymmetric flow and heat transfer of the Carreau fluid over a radially stretching sheet. The Carreau constitutive model is used to discuss the characteristics of both shear-thinning and shear-thickening fluids. The momentum equations for the two-dimensional flow field are first modeled for the Carreau fluid with the aid of the boundary layer approximations. The essential equations of the problem are reduced to a set of nonlinear ordinary differential equations by using local similarity transformations. Numerical solutions of the governing differential equations are obtained for the velocity and temperature fields by using the fifth-order Runge-Kutta method along with the shooting technique. These solutions are obtained for various values of physical parameters. The results indicate substantial reduction of the flow velocity as well as the thermal boundary layer thickness for the shear-thinning fluid with an increase in the Weissenberg number, and the opposite behavior is noted for the shear-thickening fluid. Numerical results are validated by comparisons with already published results.

关键词： axisymmetric flow Carreau fluid heat transfer radially stretching sheet shooting technique

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axisymmetric flow with heat transfer over exponentially stretching sheet: A computational approach

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2020年 554卷

作者： Shahzad, Azeem Ali, Ramzan Kamran, Muhammad Khan, Salah Ud-Din Khan, Shahab Ud-Din Farooq, Aamir Univ Engn & Technol Dept Basic Sci Taxila 47050 Pakistan Univ Cent Asia 310 Lenin St Naryn 722918 Kyrgyzstan COMSATS Univ Islamabad Dept Math Wah Campus Islamabad 47040 Pakistan King Saud Univ Coll Engn Sustainable Energy Technol SET Ctr POB 800 Riyadh 11421 Saudi Arabia Natl Tokamak Fus Program PO Nilore Islamabad 45650 Pakistan Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China

This study perform an accurate numerical analysis of axisymmetric flow and heat transfer of an electrically conducting fluid over a radially stretching surface. The flow phenomena occurs due to stretching of surface along radial direction with exponential velocity. The governing highly nonlinear partial differential equations are transformed into ordinary differential equations by invoking new similarity transformations. Numerical analysis for flow behavior is performed using Shooting technique. The velocity and thermal profiles are shown for various values of dimensionless physical parameters and discussed in detail. Further skin friction coefficient and nusselt number are tabulated and examined for various values of pertinent parameters. (C) 2020 Elsevier B.V. All rights reserved.

关键词： axisymmetric flow Heat transfer Exponential stretching

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axisymmetric flow of hybrid nanofluid due to a permeable non-linearly stretching/shrinking sheet with radiation effect

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INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID flow 2021年第7期31卷 2330-2346页

作者： Rosca, Natalia C. Rosca, Alin V. Pop, Ioan Babes Bolyai Univ Dept Math Fac Math & Comp Sci Cluj Napoca Romania Babes Bolyai Univ Dept Stat Forecasts Math Fac Econ & Business Adm Cluj Napoca Romania

Purpose This paper aims to report theoretical and numerical results for the problem of laminar axisymmetric flow of hybrid nanofluid over a permeable non-linearly stretching/shrinking sheet with radiation effect. Design/methodology/approach The numerical solutions of the arising boundary value problem are obtained using the function bvp4c from MATLAB for different values of the governing parameters. Findings It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the stretching/shrinking and suction parameters. To establish which of these solutions are stable and which are not, a stability analysis has been performed. Originality/value To the best of the authors' knowledge, present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Mustafa et al. (2015) to the case of hybrid nanofluids.

关键词： Stability analysis Numerical solution axisymmetric flow Non-linear stretching shrinking sheet Radiation effect

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axisymmetric flow of a Nanofluid Over a Radially Stretching Sheet with Convective Boundary Conditions

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CURRENT NANOSCIENCE 2012年第3期8卷 328-334页

作者： Mustafa, M. Hayat, T. Alsaedi, A. NUST RCMS Islamabad 44000 Pakistan Quaid I Azam Univ 45320 Dept Math Islamabad 44000 Pakistan King Abdulaziz Univ Fac Sci Dept Math Jeddah 21589 Saudi Arabia

This article addresses the flow of nanofluid towards a radially stretching sheet with convective boundary conditions. The Brownian motion and thermophoresis effects are taken into consideration. The governing equations are reduced to a system of coupled ordinary differential equations through similarity transformations. Analytic solutions valid for all the values of embedding parameters have been obtained by homotopy analysis method (HAM). In addition numerical solutions are computed through a shooting technique using computational software Mathematica. The behaviors of key parameters such as Brownian motion parameter (Nb), thermophoresis parameter (Nt), Biot number (Bi), Prandtl number (Pr) and Lewis number (Le) have been thoroughly examined. It is observed that increase in the strength of Brownian motion effect rises the temperature significantly. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Nb is increased. Moreover it is noticed that temperature and nanoparticles concentration are increasing functions of Biot number (Bi). A comparative study between analytic and numerical solution shows an excellent agreement.

关键词： Nanofluid axisymmetric flow radially stretching sheet convective boundary conditions similar solutions

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axisymmetric flow and heat transfer over an unsteady stretching sheet in power law fluid

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JOURNAL OF MOLECULAR LIQUIDS 2016年 221卷 386-393页

作者： Ahmed, Jawad Mahmood, Tariq Iqbal, Zahid Shahzad, Azeem Ali, Ramzan Univ Engn & Technol Dept Basic Sci Taxila 47050 Pakistan HITEC Univ Fac Sci Dept Math Taxila Cantt Pakistan Univ Cent Asia Bishkek 720001 Kyrgyzstan

An analysis is presented for the unsteady boundary layer flow and heat transfer of power law fluid model over a radially stretching sheet. A uniform magnetic field is applied perpendicular to the direction of the flow. With the aid of new similarity transformations, the governing time dependent nonlinear boundary layer equations are converted into nonlinear ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM) and numerically by shooting method. The influence of different parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, and generalized Prandtl number Pr on velocity and temperature profiles are presented graphically and discussed. It is found that the velocity and the thermal boundary layer thickness are the decreasing function of unsteadiness parameter. The impact of the local skin friction coefficient and local Nusselt number is presented in tabular form. (C) 2016 Published by Elsevier B.V.

关键词： axisymmetric flow Power law fluid Unsteady stretching

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axisymmetric flow and heat transfer to modified second grade fluid over a radially stretching sheet

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RESULTS IN PHYSICS 2017年 7卷 878-889页

作者： Khan, Masood Rahman, Masood ur Manzur, Mehwish Quaid I Azam Univ Dept Math Islamabad 44000 Pakistan

In the present work, an analysis is made to the two-dimensional axisymmetric flow and heat transfer of a modified second grade fluid over an isothermal non-linear radially stretching sheet. The momentum and energy equations are modelled and the boundary layer equations are derived. The governing equations for velocity and temperature are turned down into a system of ordinary differential equations by invoking appropriate transformations which are then solved numerically via fourth and fifth order Runge-Kutta Fehlberg method. Moreover, the influence of the pertinent parameters namely the generalized second grade parameter, stretching parameter, the power-law index and the generalized Prandtl number is graphically portrayed. It is inferred that the generalized second grade parameter uplifted the momentum boundary layer while lessened the thermal boundary layer. Furthermore, the impact of stretching parameter is more pronounced for the second grade fluid (m = 0) in contrast with the power-law fluid (k = 0). For some special cases, comparisons are made with previously reported results and an excellent agreement is established. (C) 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.

关键词： Modified second grade fluid axisymmetric flow Heat transfer Non-linear stretching sheet

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Non swirling axisymmetric flow of the ω-D fluid

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RHEOLOGICA ACTA 1998年第6期37卷 566-572页

作者： Brunn, PO Ryssel, E Univ Erlangen Nurnberg Lehrstuhl Stromungsmech D-91058 Erlangen Germany

In this paper a constitutive equation for the extra stress tensor tau is considered, which can be used for steady axisymmetric flows when mu(phi)=0 (non-swirling). It is explicit with coefficients which, in case of incompressibility, depend only upon three invariants. As such it should prove useful in numerical calculations, especially so if used in its simplest form, namely the quasi-Newtonian fluid Here, a purely viscous code can be used. The constitutive equation is self-consistent and receives additional justification from the fact that any constitutive equation is bound to result in the form proposed if the flow is a constant stretch history flow.

关键词： axisymmetric flow relative vorticity invariants of D constitutive equation quasi-Newtonian fluid

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MHD axisymmetric flow of third grade fluid between stretching sheets with heat transfer

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COMPUTERS & FLUIDS 2013年 86卷 103-108页

作者： Hayat, T. Shafiq, A. Alsaedi, A. Awais, M. Quaid I Azam Univ 45320 Dept Math Islamabad 44000 Pakistan King Abdulaziz Univ Fac Sci Nonlinear Anal & Appl Math NAAM Res Grp Jeddah 21589 Saudi Arabia

This investigation looks at the heat transfer effects in magnetohydrodynamic (MHD) axisymmetric flow of third-grade fluid between the stretching sheets. Viscous and Joule heating effects are given due attention. The resulting nonlinear problem is computed for velocity and temperature fields. Expressions of skin friction coefficient and local Nusselt number are calculated. Dimensionless results of velocity and temperature fields are examined for various parameters of interest. Numerical values of skin friction coefficient and Nusselt number are obtained and analyzed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Viscous dissipation axisymmetric flow Third grade fluid Joule heating

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