On the similarity solutions of magnetohydrodynamic flows of power-law fluids over a stretching sheet

A similarity analysis is performed for a steady laminar boundary layer stagnation-point flow of an electrically conducting fluid in a porous medium subject to a transverse non-uniform magnetic field past a non-linear stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third order ordinary differential equation corresponding to the momentum is obtained. We show the existence and uniqueness of convex and concave solutions for the power law exponent, according to the values of magnetic parameter, permeability parameter and velocity ratio parameter.

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Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0211 ◽

2018 ◽

Vol 19 (3-4) ◽

pp. 415-426 ◽

Cited By ~ 1

Author(s):

G.C. Layek ◽

Bidyut Mandal ◽

Krishnendu Bhattacharyya ◽

Astick Banerjee

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Thermal Radiation ◽

Stagnation Point ◽

Power Law ◽

Stretching Sheet ◽

Symmetry Analysis ◽

Flow And Heat Transfer ◽

Power Law Fluids ◽

Self Similar

AbstractA symmetry analysis of steady two-dimensional boundary layer stagnation-point flow and heat transfer of viscous incompressible non-Newtonian power-law fluids over a nonlinearly shrinking/stretching sheet with thermal radiation effect is presented. Lie group of continuous symmetry transformations is employed to the boundary layer flow and heat transfer equations, that gives scaling laws and self-similar equations for a special type of shrinking/stretching velocity ($c{x^{1/3}}$) and free-stream straining velocity ($a{x^{1/3}}$) along the axial direction to the sheet. The self-similar equations are solved numerically using very efficient shooting method. For the above nonlinear velocities, the unique self-similar solution is obtained for straining velocity being always less than the shrinking/stretching velocity for Newtonian and non-Newtonian power-law fluids. The thickness of velocity boundary layer becomes thinner with power-law index for shrinking as well as stretching sheet cases. Also, the thermal boundary layer thickness decreases with increasing values the Prandtl number and the radiation parameter.

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Similarity solutions for the converging or diverging steady flow of non-newtonian elastic power law fluids with wall suction or injection. Part I: Two-dimensional channel flow

AIChE Journal ◽

10.1002/aic.690170525 ◽

1971 ◽

Vol 17 (5) ◽

pp. 1181-1188 ◽

Cited By ~ 11

Author(s):

R. T. Balmer ◽

James J. Kauzlaich

Keyword(s):

Steady Flow ◽

Channel Flow ◽

Power Law ◽

Similarity Solutions ◽

Two Dimensional ◽

Wall Suction ◽

Power Law Fluids ◽

Suction Or Injection

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Coupling Effects of Viscous Sheet and Ambient Fluid on Boundary Layer Flow and Heat Transfer in Power-Law Fluids

Journal of Heat Transfer ◽

10.1115/1.4042774 ◽

2019 ◽

Vol 141 (6) ◽

Cited By ~ 3

Author(s):

Xiaochuan Liu ◽

Liancun Zheng ◽

Goong Chen ◽

Lianxi Ma

Keyword(s):

Heat Transfer ◽

Power Law ◽

Numerical Solutions ◽

Skin Friction Coefficient ◽

Similarity Solutions ◽

Temperature Fields ◽

Ambient Fluid ◽

Local Skin ◽

Flow And Heat Transfer ◽

Power Law Fluids

This paper investigates the flow and heat transfer of power-law fluids over a stretching sheet where the coupling dynamics influence of viscous sheet and ambient fluid is taken into account via the stress balance. A modified Fourier's law is introduced in which the effects of viscous dissipation are taken into account by assuming that the thermal conductivity is to be shear-dependent on the velocity gradient. The conditions for both velocity and thermal boundary layers admitting similarity solutions are found, and numerical solutions are computed by a Bvp4c program. The results show that the viscous sheet and rheological properties of ambient fluids have significantly influences on both velocity and temperature fields characteristics. The formation of sheet varies with the viscosity of fluid and draw ratio, which then strongly affects the relations of the local skin friction coefficient, the local Nusselt number, and the generalized Reynolds number. Moreover, for specified parameters, the flow and heat transfer behaviors are discussed in detail.

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