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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 k2 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k1 = 0.5.
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pone.0126698.g012: Effect of non-Newtonian parameter k2 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k1 = 0.5.

Mentions: Unsteady MHD thin film flow of an Oldroyd-B fluid over an oscillating inclined belt has been examined. The governing partial differential equations for velocity are analytically solved by using OHAM and HPM methods. Both of these results are compared. It is found that these results are in excellent agreement. In tables 1 and 2, we calculated the numerical comparisons of OHAM and HPM. Absolute errors of both methods are also calculated. Fig 1 shows the physical configuration of the problem. The graphical comparison of OHAM and HPM solutions is shown in Fig 2 by taking different values of physical parameters. Figs (3–12) are plotted in order to observe the influence of different parameters on the velocity profiles. All results for the Oldroyd-B fluid near the belt are illustrated in the y-coordinate only for a selected domain yϵ[0,1]. The effect of first three periods, ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1. are used to study the thin layer near the belt as shown in Fig (3). Clearly, due to the no-slip condition, the fluid near the belt oscillates jointly with the belt in the same period. The velocity amplitude raises gradually towards the surface of the fluid layer. The effect of transverse magnetic field on velocity is studied in Fig 4. Transverse magnetic field restricts the shearing and forming a thinner boundary layer near the belt. Due to this reason, the speed of flow increases towards the free surface of the belt. Fig 5 shows an increase in the fluid velocity when gravitational parameter m increases. Actually, it is due to friction which appears greater near the belt and smaller at the surface of the fluid. The effects of k1 (relaxation time parameter) and k2 (retardation time parameter) are shown Figs (7 and 8). Increase in these parameters increases the velocity profile.


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 k2 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k1 = 0.5.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0126698.g012: Effect of non-Newtonian parameter k2 on velocity profiles when ω = 0.2,y = 0.4,M = 0.3,t = 1,k1 = 0.5.
Mentions: Unsteady MHD thin film flow of an Oldroyd-B fluid over an oscillating inclined belt has been examined. The governing partial differential equations for velocity are analytically solved by using OHAM and HPM methods. Both of these results are compared. It is found that these results are in excellent agreement. In tables 1 and 2, we calculated the numerical comparisons of OHAM and HPM. Absolute errors of both methods are also calculated. Fig 1 shows the physical configuration of the problem. The graphical comparison of OHAM and HPM solutions is shown in Fig 2 by taking different values of physical parameters. Figs (3–12) are plotted in order to observe the influence of different parameters on the velocity profiles. All results for the Oldroyd-B fluid near the belt are illustrated in the y-coordinate only for a selected domain yϵ[0,1]. The effect of first three periods, ω = 0.2,y = 0.4,M = 0.3,t = 1,k2 = 0.1. are used to study the thin layer near the belt as shown in Fig (3). Clearly, due to the no-slip condition, the fluid near the belt oscillates jointly with the belt in the same period. The velocity amplitude raises gradually towards the surface of the fluid layer. The effect of transverse magnetic field on velocity is studied in Fig 4. Transverse magnetic field restricts the shearing and forming a thinner boundary layer near the belt. Due to this reason, the speed of flow increases towards the free surface of the belt. Fig 5 shows an increase in the fluid velocity when gravitational parameter m increases. Actually, it is due to friction which appears greater near the belt and smaller at the surface of the fluid. The effects of k1 (relaxation time parameter) and k2 (retardation time parameter) are shown Figs (7 and 8). Increase in these parameters increases the velocity profile.

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