New approach to the exact solution of viscous flow due to stretching (shrinking) and porous sheet

Ali, Amjad; Marwat, Dil Nawaz Khan; Asghar, S.

doi:10.1016/j.rinp.2017.02.036

Cited by 2 publications

(8 citation statements)

References 18 publications

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“…g 0 (0) is computed from equations ( 6) to ( 8) numerically when m = À 1=2, d = 0, and d 2 = À 1 and compared with f 00 (0) of the previous works. 10,16,17,20,22…”

Section: Comparison Of the Current Model And Its Solutions With Literaturementioning

confidence: 99%

“…f 00 (0) from equations ( 16) to (18) in the work of Magyari and Keller 10 1 ---f 00 (0) from equation (14) in the work of Liao 22 -À0:5 --f 00 (0) from equations ( 9) and ( 13) in the work of Fang et al 20 --À2 -f 00 (0) from equation (10) in the work of Asghar et al 16 ---2 f 00 (0) from equations (10) to (12) in the work of Ali et al 17 ----1 g 0 (0) from equations ( 6) to (8) (Current results) 1…”

Section: Comparison Of the Current Model And Its Solutions With Literaturementioning

confidence: 99%

“…Recently, lot of works have been carried out by many researchers to model and solve the problems of fluid flow related to stretching (shrinking) over a sheet of an arbitrary shape in Newtonian and non-Newtonian fluids. [16][17][18][19][20][21][22][23][24] This section is strengthened by citing latest research work from the literature into it. In these research articles, nano and micropolar fluid models are investigated for both Newtonian and non-Newtonian fluids over a stretching sheet.…”

Section: Introductionmentioning

confidence: 99%

“…The last system has two ordinary differential equations (ODEs) in two unknown functions, which are the representatives of velocity components. The new modeled equations are matched with some of the studies 4,10,16–24 for fixed value of parameters involved in the problem, and details of the comparison are shown in tables and graphs. New exact, numerical, and power series solutions of the modeled problem are attempted.…”

Section: Introductionmentioning

confidence: 99%

“…g 0 (0) is computed from equations (6) to (8) numerically when m = À 1=2, d = 0, and d 2 = À 1 and compared with f 00 (0) of the previous works. 10,16,17,20,22 d 1 , d 3 1, 2 À1=2, 1 À2, 2 À2, À 2 1 , 2 f 00 (0) from equations (16) to (18) in the work of Magyari and Keller 10 1 ---f 00 (0) from equation (14) in the work of Liao 22 -À0:5 --f 00 (0) from equations (9) and (13) in the work of Fang et al 20 --À2 -f 00 (0) from equation (10) in the work of Asghar et al 16 ---2 f 00 (0) from equations (10) to (12) in the work of Ali et al 17 ----1 g 0 (0) from equations (6) to (8) (Current results) 1 À0:5 À2 2 1…”

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confidence: 99%

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Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Alam

Marwat

Asghar

2020

Advances in Mechanical Engineering

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Viscous flow over a porous and stretching (shrinking) surface of an arbitrary shape is investigated in this article. New dimensions of the modeled problem are explored through the existing mathematical analogies in such a way that it generalizes the classical simulations. The latest principles provide a framework for unification, and the consolidated approach modifies the classical formulations. A realistic model is presented with new features in order to explain variety of previous observations on the said problems. As a result, new and upgraded version of the problem is appeared for all such models. A set of new, unusual, and generalized transformations is formed for the velocity components and similarity variables. The modified transformations are equipped with generalized stretching (shrinking), porous velocities, and surface geometry. The boundary layer governing equations are reduced into a set of ordinary differential equations (ODEs) by using the unification procedure and technique. The set of ODEs has two unknown functions f and g. The modeled equations have five different parameters, which help us to reduce the problem into all previous formulations. The problem is solved analytically and numerically. The current simulation and its solutions are also compared with existing models for specific value of the parameters, and excellent agreement is found between the solutions.

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“…g 0 (0) is computed from equations ( 6) to ( 8) numerically when m = À 1=2, d = 0, and d 2 = À 1 and compared with f 00 (0) of the previous works. 10,16,17,20,22…”

Section: Comparison Of the Current Model And Its Solutions With Literaturementioning

confidence: 99%

Section: Comparison Of the Current Model And Its Solutions With Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Alam

Marwat

Asghar

2020

Advances in Mechanical Engineering

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Multiple series solutions of viscous flows over a stretching/shrinking and porous sheet

et al. 2023

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The viscous fluid-flow over a stretching (shrinking) and porous sheets of non-uniform thickness is investigated in this paper. The modeled problem is presented by utilizing the stretching/shrinking and porous velocities and variable thickness of the sheet. Consequently, the new problem reproduces the different available forms of flow motion maintained over a stretching/shrinking and porous sheet of variable thickness in one go. As a result, the governing equations are embedded in several parameters which can be transformed into classical cases of stretched/shrunk flows over porous sheets. A set of general, unusual and new variables is formed in order to simplify the governing PDE and boundary conditions. Three different series solutions of the final ODE are presented. A single analytical solution is not sufficient to predict the exact effects of all parameters on the flow field properties. The problem is solved by a power and two asymptotic series methods. The results are verified by providing a powerful numerical solution the problem. A complete set of solutions is provided and comparison of the solutions with classical models is established for appropriate values of the parameters which is shown in different graphs and tables.

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New approach to the exact solution of viscous flow due to stretching (shrinking) and porous sheet

Cited by 2 publications

References 18 publications

Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Multiple series solutions of viscous flows over a stretching/shrinking and porous sheet

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