Abstract
An electrically directing viscous fluid’s boundary layer flow on a curved shrinking sheet with magnetic field is considered. Curvilinear coordinates system is used for mathematical modeling of the flow equations. By making use of similarity variables, the developed partial differential equations are reduced into sets of differential equations. Then, the attained differential equations describing the flow phenomena are resolved numerically through employing shooting scheme. The impacts of different pertinent factors, namely curvature, magnetic and suction parameters on velocity and pressure distribution, are shown graphically and are observed that dual-type solutions occur on a specific range of physical parameters. It is also noticed from these results that the flow velocity and the pressure within the boundary layer region are considerably affected by the shrinking and the mass transfer parameter since the pressure is no more constant in curved shrinking surface, as noticeable from the flat shrinking surface. Comparison of the numerical solution for the dual solution between the present studies with the existing solution is noticed in excellent agreement.
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Abbreviations
- b :
-
Constant
- \(B_0 \) :
-
Applied magnetic field
- f :
-
Dimensionless fluid velocity in r-directions
- \({f}'\) :
-
Dimensionless fluid velocity in s-directions
- p :
-
Pressure of the fluid
- P :
-
Dimensionless pressure of the fluid
- M :
-
Dimensionless magnetic parameter
- \(v_w\) :
-
Suction velocity
- R :
-
Radius of the semicircle
- S :
-
Dimensionless suction parameter
- \(S_c\) :
-
Critical values of the suction parameter
- \(U_w\) :
-
Uniform velocity
- u :
-
Velocity component in the s-direction
- v :
-
Velocity component in the r-direction
- \(\alpha \) :
-
Constant
- \(\beta \) :
-
Shrinking parameter
- \(\rho \) :
-
Density of the fluid
- \(\mu \) :
-
Viscosity of the fluid
- \(\nu \) :
-
Kinematics viscosity
- \(\eta \) :
-
Dimensionless variable
- \(\sigma \) :
-
Electrical conductivity
- \(\kappa \) :
-
Dimensionless radius of curvature
- \(\tau _{rs}\) :
-
Shear stress at the surface
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Naveed, M., Abbas, Z., Sajid, M. et al. Dual Solutions in Hydromagnetic Viscous Fluid Flow Past a Shrinking Curved Surface. Arab J Sci Eng 43, 1189–1194 (2018). https://doi.org/10.1007/s13369-017-2772-z
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DOI: https://doi.org/10.1007/s13369-017-2772-z