Analysis of Non-Newtonian Fluid Boundary Layer Flows Due to Surface Tension Gradient
The paper considers non-Newtonian power-law fluid flow driven by the convection of surface tension gradient in the presence of transverse magnetic field along a free-surface. The aim is to examine the effects of temperature and solute-dependent surface te
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Analysis of Non-Newtonian Fluid Boundary Layer Flows Due to Surface Tension Gradient Azhani Mohd Razali and Seripah Awang Kechil
Abstract The paper considers non-Newtonian power-law fluid flow driven by the convection of surface tension gradient in the presence of transverse magnetic field along a free-surface. The aim is to examine the effects of temperature and solute-dependent surface tension and magnetic field on the boundary layer flow of non-Newtonian fluids. The governing partial differential equations are reduced to a set of ordinary differential equations using similarity transformations. The coupled nonlinear system of equations is solved using a numerical approach known as the fourth-order finite difference scheme with shooting method. The numerical calculations were carried out for various values of fluid physical properties: power-law index, thermosolutal Marangoni number, and magnetic parameter. The results indicate that the free-surface velocity decreases with the increasing number of power-law index. As the thermosolutal Marangoni number increases, the thickness of thermal boundary layer decreases, while the surface temperature and concentration gradients increases. The magnetic field modifies the flow patterns of the non-Newtonian power-law fluid by reducing the fluid velocity at the surface.
Keywords Non-Newtonian fluid Power-law model Surface tension Marangoni convection Finite difference Shooting method
Nomenclature A B rT rC
Surface temperature variation Surface concentration variation Temperature coefficient of surface tension Concentration coefficient of surface tension
A.M. Razali (&) Plant Assessment Technology Group, Industrial Technology Division Malaysian Nuclear Agency, Bangi, 43000 Kajang, Malaysia e-mail: [email protected] S.A. Kechil Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 A.-R. Ahmad et al. (eds.), Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), DOI 10.1007/978-981-10-2772-7_21
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r0 u v K f ðgÞ hðgÞ /ðgÞ T T0 q n cm a D g w C C0
21.1
A.M. Razali and S.A. Kechil
Surface tension at origin Velocity components along x direction Velocity components along y direction Consistency coefficient Dimensionless stream function Dimensionless temperature function Dimensionless concentration function Temperature Surface temperature Density of fluid Power-law index Electrical conductivity Thermal diffusivity of fluid Mass diffusivity of fluid Similarity variable Stream function Concentration Surface concentration
Introduction
With the increasingly fast growing technology, many industrial processes, especially in manufacturing, involve the flows of non-Newtonian fluids. Many new products also exhibit non-Newtonian behaviour. Examples of industrial non-Newtonian fluids are multiphase mixtures, pharmaceutical formulations, molten plastics, cosmetics, toiletries, synthetic
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