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Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet.

Naganthran K, Nazar R, Pop I - Sci Rep (2016)

Bottom Line: The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab.Dual solutions exist for both cases of stretching and shrinking sheet.Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, Faculty of Science &Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.

ABSTRACT
In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

No MeSH data available.


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Physical model and coordinate system.
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f1: Physical model and coordinate system.

Mentions: Consider the unsteady stagnation-point flow and heat transfer of a third grade fluid in the region y > 0 driven by an impulsively started stretching/shrinking surface, as shown in Fig. 1, where x and y are Cartesian coordinates measured along the surface and normal to it, respectively. It is assumed that at time t = 0 the surface starts to move with the velocity Uw(x, t) = λuw(x, t) in an external free stream of velocity ue(x, t), where λ is a dimensionless constant with λ > 0 for a stretching surface and λ < 0 for a shrinking surface, respectively. It is also assumed that the mass flux velocity is vw(t) and the uniform temperature of the surface is Tw, while that of the ambient fluid is T∞, where we consider that Tw > T∞ (heated surface). For third grade fluids, physical considerations were taken into account by Fosdick and Rajagopal1 in order to obtain the following form for the constitutive law


Unsteady stagnation-point flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet.

Naganthran K, Nazar R, Pop I - Sci Rep (2016)

Physical model and coordinate system.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4835756&req=5

f1: Physical model and coordinate system.
Mentions: Consider the unsteady stagnation-point flow and heat transfer of a third grade fluid in the region y > 0 driven by an impulsively started stretching/shrinking surface, as shown in Fig. 1, where x and y are Cartesian coordinates measured along the surface and normal to it, respectively. It is assumed that at time t = 0 the surface starts to move with the velocity Uw(x, t) = λuw(x, t) in an external free stream of velocity ue(x, t), where λ is a dimensionless constant with λ > 0 for a stretching surface and λ < 0 for a shrinking surface, respectively. It is also assumed that the mass flux velocity is vw(t) and the uniform temperature of the surface is Tw, while that of the ambient fluid is T∞, where we consider that Tw > T∞ (heated surface). For third grade fluids, physical considerations were taken into account by Fosdick and Rajagopal1 in order to obtain the following form for the constitutive law

Bottom Line: The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab.Dual solutions exist for both cases of stretching and shrinking sheet.Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, Faculty of Science &Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia.

ABSTRACT
In this paper, the unsteady stagnation-point boundary layer flow and heat transfer of a special third grade fluid past a permeable stretching/shrinking sheet has been studied. Similarity transformation is used to transform the system of boundary layer equations which is in the form of partial differential equations into a system of ordinary differential equations. The system of similarity equations is then reduced to a system of first order differential equations and has been solved numerically by using the bvp4c function in Matlab. The numerical solutions for the skin friction coefficient and heat transfer coefficient as well as the velocity and temperature profiles are presented in the forms of tables and graphs. Dual solutions exist for both cases of stretching and shrinking sheet. Stability analysis is performed to determine which solution is stable and valid physically. Results from the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

No MeSH data available.


Related in: MedlinePlus