Limits...
Unsteady MHD Thin Film Flow of an Oldroyd-B Fluid over an Oscillating Inclined Belt.

Gul T, Islam S, Shah RA, Khalid A, Khan I, Shafie S - PLoS ONE (2015)

Bottom Line: Both of these solutions are presented graphically and compared.An excellent agreement is observed.The effects of various physical parameters on velocity have also been studied graphically.

View Article: PubMed Central - PubMed

Affiliation: Mathematics Department, Abdul Wali Khan University, Mardan, KPK Pakistan.

ABSTRACT
This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.

No MeSH data available.


Related in: MedlinePlus

Effect of non-Newtonian parameter k1 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4493037&req=5

pone.0126698.g011: Effect of non-Newtonian parameter k1 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1.

Mentions: In case of oscillation, it can be observed in Fig (9) that the boundary layer thickness is reciprocal to the perpendicular magnetic field and the fluid motion decreases one step towards the surface of the fluid. Due to oscillation of the belt, we observed that the fluid motion is maximum at the surface of the belt and minimum at the surface of the fluid. Also, it is observed that for large values of M, the fluid motion increases quickly as compared to small values. The influence of gravitational parameter can be seen from Fig (10) in the oscillation case. In the presence of friction force, the gravitational effect seems to be smaller near the belt and greater at the fluid surface. By increasing m, the speed of fluid layer increases. The effects of non-Newtonian parameters k1 and k2 on velocity profiles are shown in Figs (11 and 12). It is observed that in the presence of magnetic field, the structure of the thin layer becomes similar with those of Ekman and classical Stokes layers. It is also observed that for all frequencies, the thickness of the hydromagnetic thin layers remain bounded. The reason is that the magnetic field controls the growth of the thin layer thickness at the resonant frequency.


Unsteady MHD Thin Film Flow of an Oldroyd-B Fluid over an Oscillating Inclined Belt.

Gul T, Islam S, Shah RA, Khalid A, Khan I, Shafie S - PLoS ONE (2015)

Effect of non-Newtonian parameter k1 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493037&req=5

pone.0126698.g011: Effect of non-Newtonian parameter k1 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1.
Mentions: In case of oscillation, it can be observed in Fig (9) that the boundary layer thickness is reciprocal to the perpendicular magnetic field and the fluid motion decreases one step towards the surface of the fluid. Due to oscillation of the belt, we observed that the fluid motion is maximum at the surface of the belt and minimum at the surface of the fluid. Also, it is observed that for large values of M, the fluid motion increases quickly as compared to small values. The influence of gravitational parameter can be seen from Fig (10) in the oscillation case. In the presence of friction force, the gravitational effect seems to be smaller near the belt and greater at the fluid surface. By increasing m, the speed of fluid layer increases. The effects of non-Newtonian parameters k1 and k2 on velocity profiles are shown in Figs (11 and 12). It is observed that in the presence of magnetic field, the structure of the thin layer becomes similar with those of Ekman and classical Stokes layers. It is also observed that for all frequencies, the thickness of the hydromagnetic thin layers remain bounded. The reason is that the magnetic field controls the growth of the thin layer thickness at the resonant frequency.

Bottom Line: Both of these solutions are presented graphically and compared.An excellent agreement is observed.The effects of various physical parameters on velocity have also been studied graphically.

View Article: PubMed Central - PubMed

Affiliation: Mathematics Department, Abdul Wali Khan University, Mardan, KPK Pakistan.

ABSTRACT
This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.

No MeSH data available.


Related in: MedlinePlus