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Effects of lubrication in the oblique stagnation-point flow of a nanofluid

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Abstract

This study investigates the oblique flow of a nanofluid near a stagnation point past a lubricated plate. A power-law fluid is utilized for lubrication. A suitable set of transformation is utilized to obtain system of dimensionless governing equations. A well-known numerical technique known as Keller-box method is employed to get the similar solution. Influence of emerging parameters on the flow characteristics has been discussed in the presence of lubrication through graphs and numerical data ranging from no slip (\(\beta \to \infty )\) to full slip (\(\beta \to 0)\). Impact of thermophoresis and Brownian motion is further investigated. A comparison in the special cases between the present and published data validates this work.

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Abbreviations

\(Q\) :

Flow rate

\(T_{\text{w}}\) :

Wall temperature

\(T_{\infty }\) :

Free stream temperature

\(T\) :

Fluid temperature

\(\delta\) :

Thickness of lubrication layer

\(C\) :

Concentration of nanoparticles

\(x,y\) :

Rectangular coordinates

\(u,v\) :

Velocity components in \(x\) and \(y\) directions for nanofluid

\(k\) :

Consistency coefficient

\(\rho_{\text{f}}\) :

Density of base fluid

\(D_{\text{B}}\) :

Brownian diffusion coefficient

\(\alpha\) :

Boundary layer displacement

\(\lambda\) :

Free parameter

\(N_{\text{b}}\) :

Brownian motion parameter

\(\eta\) :

Dimensionless independent variable

\(L_{\text{visc}}\) :

Viscous length scale

\(C_{\text{w}}\) :

Concentration at wall

\(u_{e} , v_{e}\) :

Free stream velocities

\(C_{\infty }\) :

Concentration at free stream

\(\beta\) :

Slip (lubrication) parameter

\(\mu_{L}\) :

Apparent viscosity

\(D_{\text{T}}\) :

Thermophoresis diffusion coefficient

\(N_{\text{t}}\) :

Thermophoresis parameter

\(U,V\) :

Velocity components in \(x\) and \(y\) directions for a power-law fluid

\(n\) :

Flow behavior index

\(\rho_{\text{p}}\) :

Density of nanoparticles

\(\nu\) :

Kinematic viscosity

\(\alpha^{*}\) :

Thermal diffusivity

\(\gamma\) :

Shear at free stream

\(\phi\) :

Dimensionless concentration

\(Pr\) :

Prandtl number

\(\theta\) :

Dimensionless temperature

\(f,g\) :

Dimensionless velocities

\(L_{\text{lub}}\) :

Lubrication length scale

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    K. Mahmood, M. Sajid & N. Ali

  2. Department of Basic Sciences, Riphah International University, Islamabad, 44000, Pakistan

    A. Arshad & M. A. Rana

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  1. K. Mahmood
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  2. M. Sajid
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Correspondence to K. Mahmood.

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Mahmood, K., Sajid, M., Ali, N. et al. Effects of lubrication in the oblique stagnation-point flow of a nanofluid. Microfluid Nanofluid 21, 100 (2017). https://doi.org/10.1007/s10404-017-1934-3

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