The Axisymmetric Motion of a Liquid Film on an Unsteady Stretching Surface
01 Mar 1995-Journal of Fluids Engineering-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 117, Iss: 1, pp 81-85
TL;DR: The axisymmetric motion of a fluid caused by an unsteady stretching surface that has relevance in extrusion process and bioengineering has been investigated in this paper, where asymptotic and numerical solutions are obtained and they could be used in the testing of computer codes or analytical models of more realistic engineering systems.
Abstract: The axisymmetric motion of a fluid caused by an unsteady stretching surface that has relevance in extrusion process and bioengineering has been investigated. It has been shown that if the unsteady stretching velocity is prescribed by rb/(1 − αt), then the problem admits a similarity solution which gives much insight to the character of solutions. The asymptotic and numerical solutions are obtained and they could be used in the testing of computer codes or analytical models of more realistic engineering systems. The results are governed by a nondimensional unsteady parameter S and it has been observed that no similarity solutions exist for S > 4
Citations
More filters
TL;DR: In this paper, an analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation.
Abstract: An analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.
31 citations
Cites methods from "The Axisymmetric Motion of a Liquid..."
...An axisymmetric motion of a fluid caused by an unsteady stretching surface was investigated by Usha and Sridharan [4]....
[...]
TL;DR: The Pade techniques, which have the advantage in turning the polynomial approximation into a rational function, are applied to the series solution of the governing nonlinear problem to improve the accuracy and enlarge the convergence domain.
Abstract: In this study, we investigate the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet by employing the homotopy perturbation method (HPM) and Pade approximation. The series solution of the governing nonlinear problem is developed. Generally, the truncated series solution is adequate only in a small region when the exact solution is not reached. We overcame this limitation by using the Pade techniques, which have the advantage in turning the polynomial approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.
25 citations
06 May 2019
TL;DR: In this paper, the boundary-layer equations for mass and heat energy transfer with entropy generation are analyzed for the two-dimensional viscoelastic second-grade nanofluid thin film flow in the presence of a uniform magnetic field (MHD) over a vertical stretching sheet.
Abstract: The boundary-layer equations for mass and heat energy transfer with entropy generation are analyzed for the two-dimensional viscoelastic second-grade nanofluid thin film flow in the presence of a uniform magnetic field (MHD) over a vertical stretching sheet. Different factors, such as the thermophoresis effect, Brownian motion, and concentration gradients, are considered in the nanofluid model. The basic time-dependent equations of the nanofluid flow are modeled and transformed to the ordinary differential equations system by using similarity variables. Then the reduced system of equations is treated with the Homotopy Analysis Method to achieve the desire goal. The convergence of the method is prescribed by a numerical survey. The results obtained are more efficient than the available results for the boundary-layer equations, which is the beauty of the Homotopy Analysis Method, and shows the consistency, reliability, and accuracy of our obtained results. The effects of various parameters, such as Nusselt number, skin friction, and Sherwood number, on nanoliquid film flow are examined. Tables are displayed for skin friction, Sherwood number, and Nusselt number, which analyze the sheet surface in interaction with the nanofluid flow and other informative characteristics regarding this flow of the nanofluids. The behavior of the local Nusselt number and the entropy generation is examined numerically with the variations in the non-dimensional numbers. These results are shown with the help of graphs and briefly explained in the discussion. An analytical exploration is described for the unsteadiness parameter on the thin film. The larger values of the unsteadiness parameter increase the velocity profile. The nanofluid film velocity shows decline due the increasing values of the magnetic parameter. Moreover, a survey on the physical embedded parameters is given by graphs and discussed in detail.
24 citations
TL;DR: In this article, the governing boundary layer equations are written into a dimensionless form by similarity transformations, and the transformed coupled nonlinear ordinary difierential equations are numerically solved by using an advanced numeric technique.
Abstract: This work is concerned with magnetohydrodynamic viscous ∞ow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary difierential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. numerical results for the dimensionless velocity, temperature and concentration proflles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
22 citations
Additional excerpts
...…( Bhattacharyya and Gupta, 1985, Brady and Acrivos, 1981, Crane, 1970, Gupta and Gupta, 1977, Jensen, Einset, and Fotiadis, 1991, troy et al., 1987, Usha and Sridharan, 1995, Wang, 1984, Wang, 1988, Wang, 1990, Hakiem, Mohammadeian, Kaheir and Gorla, 1999, Kuo, 2005, Cheng and Lin, 2002, Apelblat,…...
[...]
References
More filters
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
Book•
01 Jan 1974
TL;DR: In this paper, the authors define the notion of groups of transformations and prove that a one-parameter group essentially contains only one infinitesimal transformation and is determined by it.
Abstract: 1. Ordinary Differential Equations.- 1.0. Ordinary Differential Equations.- 1.1. Example: Global Similarity Transformation, Invariance and Reduction to Quadrature.- 1.2. Simple Examples of Groups of Transformations Abstract Definition.- 1.3. One-Parameter Group in the Plane.- 1.4. Proof That a One-Parameter Group Essentially Contains Only One Infinitesimal Transformation and Is Determined by It.- 1.5. Transformations Symbol of the Infinitesimal Transformation U.- 1.6. Invariant Functions and Curves.- 1.7. Important Classes of Transformations.- 1.8. Applications to Differential Equations Invariant Families of Curves.- 1.9. First-Order Differential Equations Which Admit a Group Integrating Factor Commutator.- 1.10. Geometric Interpretation of the Integrating Factor.- 1.11. Determination of First-Order Equations Which Admit a Given Group.- 1.12. One-Parameter Group in Three Variables More Variables.- 1.13. Extended Transformation in the Plane.- 1.14. A Second Criterion That a First-Order Differential Equation Admits a Group.- 1.15. Construction of All Differential Equations of First-Order Which Admit a Given Group.- 1.16. Criterion That a Second-Order Differential Equation Admits a Group.- 1.17. Construction of All Differential Equations of Second-Order Which Admit a Given Group.- 1.18. Examples of Application of the Method.- 2. Partial Differential Equations.- 2.0. Partial Differential Equations.- 2.1. Formulation of Invariance for the Special Case of One dependent and Two Independent Variables.- 2.2. Formulation of Invariance in General.- 2.3. Fundamental Solution of the Heat Equation Dimensional Analysis.- 2.4. Fundamental Solutions of Heat Equation Global Affinity.- 2.5. The Relationship Between the Use of Dimensional Analysis and Stretching Groups to Reduce the Number of Variables of a Partial Differential Equation.- 2.6. Use of Group Invariance to Obtain New Solutions from Given Solutions.- 2.7. The General Similarity Solution of the Heat Equation.- 2.8. Applications of the General Similarity Solution of the Heat Equation,.- 2.9. -Axially-Symmetric Wave Equation.- 2.10. Similarity Solutions of the One-Dimensional Fokker-Planck Equation.- 2.11. The Green's Function for an Instantaneous Line Particle Source Diffusing in a Gravitational Field and Under the Influence of a Linear Shear Wind - An Example of a P.D.E. in Three Variables Invariant Under a Two-Parameter Group.- 2.12. Infinite Parameter Groups - Derivation of the Poisson Kernel.- 2.13. Far Field of Transonic Flow.- 2.14. Nonlinear and Other Examples.- 2.15. Construction of Partial Differential Equations Invariant Under a Given Multi-parameter Group.- Appendix. Solution of Quasilinear First-Order Partial Differential Equations.- Bibliography. Part 1.- Bibliography. Part 2.
1,037 citations
TL;DR: An exact similarity solution of the Navier-Stokes equations is found in this article, where the solution represents the three-dimensional fluid motion caused by the stretching of a flat boundary.
Abstract: An exact similarity solution of the Navier–Stokes equations is found. The solution represents the three‐dimensional fluid motion caused by the stretching of a flat boundary.
563 citations
TL;DR: In this article, a similarity transform was used to reduce the Navier-Stokes equations to a nonlinear ordinary differential equation governed by a non-dimensional unsteady parameter.
Abstract: A fluid film lies on an accelerating stretching surface. A similarity transform reduces the unsteady Navier-Stokes equations to a nonlinear ordinary differential equation governed by a nondimensional unsteady parameter. Asymptotic and numerical solutions are found. The results represent rare exact similarity solutions of the unsteady Navier-Stokes equations
493 citations
TL;DR: In this paper, the fluid flow outside of a stretching cylinder is studied, governed by a third-order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier-Stokes equations.
Abstract: The fluid flow outside of a stretching cylinder is studied. The problem is governed by a third‐order nonlinear ordinary differential equation that leads to exact similarity solutions of the Navier–Stokes equations. Because of algebraic decay, an exponential transform is used to facilitate numerical integration. Asymptotic solutions for large Reynolds numbers compare well with numerical results. The heat transfer is determined.
248 citations