An approximate analytical solution is obtained of the steady, laminar three-dimensional flow for an incompressible, viscous fluid past a stretching sheet using the homotopy perturbation method (HPM) proposed by He. The flow is governed by a boundary value problem (BVP) consisting of a pair of non-linear differential equations. The solution is simple yet highly accurate and compares favorably with the exact solutions obtained early in the literature. The methodology presented in the paper is useful for solving the BVPs consisting of more than one differential equation.

The three-dimensional flow past a stretching sheet and the homotopy perturbation method

An analysis is carried out to study the flow characteristics in an elastico-viscous fluid (Walters' liquid-B model) over a stretching sheet with partial slip. The flow is generated due to linear stretching of the sheet. Using suitable similarity transformations on the highly non-linear partial differential equations we derive exact analytical solution with appropriate boundary conditions. The important finding in this communication is the effect of partial slip on the velocity and skin friction coefficient.

The flow of an elastico-viscous fluid past a stretching sheet with partial slip

Two-dimensional stagnation-point flow of viscoelastic fluids is studied theoretically assuming that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary-layer theory is used to simplify the equations of motion which are further reduced to a single non-linear third-order ODE using the concept of stream function coupled with the technique of the similarity solution. The equation so obtained was solved using Chebyshev pseudo-spectral collocation-point method. Based on the results obtained in the present work, it is concluded that the well-established but controversial prediction that in stagnation-point flows of viscoelastic fluids the velocity inside the boundary layer may exceed that outside the layer may just be an artifact of the rheological model used in previous studies (namely, the second-grade model). No such peculiarity is predicted to exist for the Maxwell model. For a UCM fluid, a thickening of the boundary layer and a drop in wall skin friction coefficient is predicted to occur the higher the elasticity number. These predictions are in direct contradiction with those reported in the literature for a second-grade fluid.

Stagnation-point flow of upper-convected Maxwell fluids

The laminar flow of an incompressible, viscous, electrically conducting fluid impinging normal to a plane in the presence of a transverse magnetic field is investigated. Using finite-differences and quasilinearization, an exact numerical solution is presented which takes into account the asymptotic boundary condition. It is demonstrated that iff denotes the dimensionless stream function, the value off″(0) increases monotonically withM, the Hartmann number, where a prime denotes the derivative normal to the plane.

Hiemenz flow in hydromagnetics

The three-dimensional steady, laminar flow due to stretching of a sheet is considered. The governing equations of motion admit a similarity solution. By drawing an analogy with the flow due to a rotating disk it is demonstrated that the resulting boundary value problem admits a solution in terms of series of exponentially decaying functions. The solution is highly efficient and very accurate, as it eliminates the need of replacing numerical infinity in the range of integration by a finite value. Two perturbation solutions are also developed when the primary flow corresponds to the two-dimensional case and the axisymmetric case. In each case the expansion is obtained up to the second degree term of the perturbation parameter. Finally, an approximate solution is derived, which is very simple and highly accurate.

Generalized three‐dimensional flow due to a stretching sheet

SUMMARY A hybrid method for computing the flow of viscoelastic and second-order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear. The method is applied to obtain the solutions to three problems of flow of Walters’ B fluid (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.

A hybrid method for computing the flow of viscoelastic fluids

A technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Two flow problems are considered: (i) three-dimensional flow near a stagnation point and (ii) axisymmetric flow due to stretching of a sheet. Both flows are characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. The exact numerical solutions are obtained using the technique described in the paper. Also, the first-order perturbation solutions (in terms of the viscoelastic fluid parameter) are derived. A comparison of the results shows that the perturbation method is inadequate in predicting some of the vital characteristic features of the flows, which can possibly be revealed only by the exact numerical solution.

Computation of flow of viscoelastic fluids by parameter differentiation

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

P. D. Ariel

Author Tools

Chat about Author

Papers

A hybrid method for computing the flow of viscoelastic fluids

Computation of flow of viscoelastic fluids by parameter differentiation