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
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27 Jan 2017
TL;DR: In this article, the influence of surface tension on the laminar flow of a thin film of a non-Newtonian nano liquid over an unsteady stretching sheet is considered.
Abstract: The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nano liquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with tem ...
6 citations
TL;DR: In this paper, the mass transfer in a time varying thin liquid film over a stretching heated plate having variable temperature and concentration is analyzed and a new similarity is found using group-theoretic analysis which renders the exact similar governing equations amenable to analytical solution using perturbation method.
Abstract: In this paper, the mass transfer in a time varying thin liquid film over a stretching heated plate having variable temperature and concentration is analyzed. The analytical solution for the unsteady Navier- Stokes, energy and diffusion equations are obtained. A new similarity is found using group-theoretic analysis which renders the exact similar governing equations amenable to analytical solution using perturbation method. Numerical solution of the problem is also obtained showing good agreement with analytical results. Graphs of velocity, temperature, concentration, skin-friction, Nusselt number and Sherwood number are displayed for various values of pertinent parameters.
Key words: Thin film, mass transfer, group-theoretic analysis, perturbation solution.
6 citations
TL;DR: In this paper, the finite element method was used to solve the system of ordinary differential equatio-... problems, and the method introduced in this paper is based on the method described in the paper.
Abstract: The method introduced in this paper is based on the finite element method. As an application for this efficient numerical method, we employ it in solving the system of ordinary differential equatio...
5 citations
01 Jan 2014
TL;DR: In this paper, the governing equations are transformed to a system of ordinary differential equations and then solved numerically for various values of the parameters, and the dual solution exists for velocity and temperature for certain values of velocity ratio parameter.
Abstract: Oblique stagnation point flow and heat transfer towards a stretching sheet of a viscous fluid is investigated. The governing equations are transformed to a system of ordinary differential equations and then solved numerically for various values of the parameters. It is observed that the dual solution exists for velocity and temperature for certain values of velocity ratio parameter.
5 citations
TL;DR: In this article, the Navier-Stokes (NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically for both two-dimensional and axisymmetric flow configurations.
Abstract: In this paper, the liquid film flow over an unsteady moving surface is investigated by considering a new surface moving velocity Uw = Ax/t With this prescribed surface velocity, the governing Navier-Stokes (NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically for both two-dimensional and axisymmetric flow configurations The results are an exact solution to the full NS equations The flow characteristics are controlled by a wall moving parameter, namely, A It is found that solutions only exist for a certain range of the wall moving parameter, ie, A ≥ −1/2 for the two dimensional case and A ≥ −1/4 for the axisymmetric case The dimensionless liquid film thickness (β) first increases with the increase in A in the solution domain, and then, it reaches a peak of βm = 13864 at A = 090 for the two-dimensional case and βm = 15836 at A = 053 for the axisymmetric case For both flow configurations, the liquid film thickness increases with time and there exists flow reversal for a positive value of A These new solutions can not only provide an exact solution to the NS equations but also be used to explain the liquid film flow occurring in practical applications
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
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