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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TL;DR: In this article, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time, and it is also noticed in this work that improvement in the Marangoni convection process leads to a decline of the fluid's film.
Abstract: In the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered The flow is also exposed to Joule heating and magnetic effects The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM) It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film
13 citations
TL;DR: In this article, the authors presented an efficient analytical approach based on new homotopy perturbation sumudu transform method (HPSTM) to investigate the magnetohydrodynamics (MHD) viscous flow due to a stretching sheet.
13 citations
TL;DR: In this article, the effectiveness of Lorentz force, viscous dissipation and internal heating on the heat and flow characteristics of a non-Newtonian Casson fluid thin film resting on a stretching surface under the influence of a magnetic field was analyzed.
Abstract: The aim of this investigation is to analyze the effectiveness of Lorentz force, viscous dissipation and internal heating on the heat and flow characteristics of a non-Newtonian Casson fluid thin film resting on a stretching surface under the influence of a magnetic field. Employing suitable similarity variables and shooting technique and integrating scheme numerical solutions for velocity and temperature are obtained. The results of this analysis are compared with the published work and are found to be in good agreement. The thickness of the thin film is evaluated and is observed that Lorentz force and the non-Newtonian nature of the fluid have a thinning influence on the film. Velocity and temperature distributions in the thin film are discussed for various flow parameters.
13 citations
Cites methods from "The Axisymmetric Motion of a Liquid..."
...A similar investigation in a liquid film on an unsteady stretching sheet was examined by Usha and Sridharan [5]....
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TL;DR: In this article, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg-Marquardt scheme-based backpropagation technique (NN-BLMS), which is used to find a solution for the nonlinear system obtained from the governing equations of the MHD boundary layer flow over a stretching sheet.
Abstract: In this study, a new computing model is developed using the strength of feed-forward neural networks with the Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It is used to find a solution for the nonlinear system obtained from the governing equations of the magnetohydrodyanmic (MHD) boundary layer flow over a stretching sheet. Moreover, the partial differential equations (PDEs) for the MHD boundary layer flow over a stretching sheet are converting into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated at different scenarios by a variation of various embedding parameters: Deborah number and magnetic parameter (M). The training (TR), testing (TS), and validation (VD) of the NN-BLMS model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics, such as the mean square error (MSE), error histogram (EH), and regression (RG) plots, are utilized for measuring the effectiveness and performance of the NN-BLMS infrastructure model. The experiments showed that comparisons between the results of proposed model and the reference results match in terms of convergence up to E-02 to E-10. This proves the validity of the NN-BLMS model. Furthermore, the results demonstrated that there is a decrease in the thickness of the boundary layer by increasing the Deborah number and magnetic parameter. The importance of the experiment can be seen due to its industrial applications such as MHD power generation, MHD generators, and MHD pumps.
12 citations
TL;DR: In this paper, the authors examined the problem of thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically The sheet is permeable, and there is an injection effect at the surface of the stretching sheet The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c.
Abstract: Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically The sheet is permeable, and there is an injection effect at the surface of the stretching sheet The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process
10 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