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Stability analysis for model-based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip

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Abstract

This article aims to present the nanofluid flow over an exponentially porous shrinking sheet in the presence of velocity slip and thermal slip. Single-phase fluid model for nanofluid has been used. In this investigation, the effects of silver (Ag) nanoparticle in two different types of base fluids (water and kerosene oil) are investigated. Using similarity transformations, the governing boundary-layer equations and the boundary conditions are reduced to the system of coupled nonlinear ordinary differential equations and then solved numerically with the help of shooting method. Dual solutions exist for some particular range of values of the governing parameters. A stability analysis has been performed to find out the stable solution. A comparison is made between the boundary-layer flow of Ag–water and Ag–kerosene. Impacts of various parameters on velocity, temperature profiles, skin friction coefficient, and Nusselt number are computed and presented in graphs and tables. The fluid velocity and temperature both increase with the increasing nanoparticle volume fraction.

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Abbreviations

\(x,y\) :

Cartesian coordinate system (m)

\(u,v\) :

Velocity components along the \(x,y\) directions, respectively (m/s)

\(\mu_{\text{nf}}\) :

Viscosity of the nanofluid (kg/m s)

\(\mu_{f}\) :

Viscosity of the base fluid (kg/m s)

\(v_{\text{nf}}\) :

Kinematic viscosity of the nanofluid (m2/s)

\(v_{f}\) :

Kinematic viscosity of the base fluid (m2/s)

\((\rho c_{p} )_{\text{nf}}\) :

Specific heat capacitance of the nanofluid (J/kg K)

\((\rho c_{p} )_{f}\) :

Heat capability of foundation liquid (J/kg K)

\((\rho c_{p} )_{s}\) :

Heat capability of solid nanoparticle (J/kg K)

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

Density of the nanofluid (kg/m3)

\(\rho_{f}\) :

Density of the base fluid (kg/m3)

\(\rho_{s}\) :

Density of the solid nanoparticle (kg/m3)

\(f\) :

Dimensionless velocity fields

\(\kappa_{\text{nf}}\) :

Thermal conductivity of the nanofluid (m2/s)

\(\kappa_{f}\) :

Thermal conductivity of the base fluid (m2/s)

\(\kappa_{s}\) :

Thermal conductivity of the solid nanoparticle (m2/s)

\(T\) :

Temperature K (°C)

\(T_{w}\) :

Variable temperature at the sheet K (°C)

\(T_{\infty }\) :

Free-stream temperature K (°C)

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless nanoparticle volume fraction

Pr :

Prandtl number

\(C_{f}\) :

Local skin resistance coefficient

\(Nu_{x}\) :

Local Nusselt number

\(Sh_{x}\) :

Local Sherwood number

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Acknowledgements

Thanks are indeed due to the learned reviewers for their constructive suggestions which helped a lot for the improvement of the quality of the paper. S. Ghosh (SRF, CSIR) is thankful to CSIR, New Delhi, India, for the financial assistance. S. Mukhopadhyay is thankful to SERB, New Delhi, India, for financial support received through Young Scientist Project (YSS/2014/000681).

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  1. Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, 713104, India

    Sudipta Ghosh & Swati Mukhopadhyay

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  1. Sudipta Ghosh
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Correspondence to Swati Mukhopadhyay.

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Ghosh, S., Mukhopadhyay, S. Stability analysis for model-based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip. Neural Comput & Applic 32, 7201–7211 (2020). https://doi.org/10.1007/s00521-019-04221-w

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