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Velocity and temperature slip effects on squeezing flow of nanofluid between parallel disks in the presence of mixed convection

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Abstract

Velocity and temperature slip effects on squeezing flow of nanofluid between parallel disks in the presence of mixed convection is considered. Equations that govern the flow are transformed into a set of differential equations with the help of transformations. For the purpose of solution, homotopy analysis method is used. The BVPh2.0 package is utilized for the said purpose. Deviations in the velocity, temperature and the concentration profiles are depicted graphically. Mathematical expressions for skin friction coefficient, Nusselt and the Sherwood numbers are derived and the variations in these numbers are portrayed graphically. From the results obtained, we observed that the coefficient of skin friction increases with increase in Hartmann number M for the suction flow (A > 0), while in the blowing flow (A < 0) a fall is seen with increasing M. However, for rising values of velocity parameter β the effect of skin friction coefficient is opposite to that accounted for M. Variations in thermophoresis parameter N T and thermal slip parameter γ give rise in Nusselt number for both the suction and injection at wall. For both the suction and injection at wall, Sherwood number gets a rise with growing values of Brownian motion parameter N B, while a drop is seen in Sherwood number for increasing values of thermophoresis parameter N T. For the sake of comparison, the same problem is also solved by employing a numerical scheme called Runge–Kutta–Fehlberg (RKF) method. Results thus obtained are compared with existing ones and are found to be in agreement.

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Abbreviations

A :

Suction/injection parameter

B 0 :

Strength of the magnetic field (kg s−2 A−1)

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over C}}_{w}\) :

Nanoparticle concentration at lower disk

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over C}}_{h}\) :

Nanoparticle concentration at upper disk

C p :

Specific heat at constant pressure

D B :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion coefficient

M :

Magnetic field parameter

C fr :

Skin friction coefficient

Nu :

Local Nusselt number

Pr :

Prandtl number

Sh :

Local Sherwood number

S :

Squeeze number

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over T}}\) :

Temperature variable K

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over T}}_{w}\) :

Constant temperature at lower disk

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over T}}_{h}\) :

Constant temperature at upper disk

\({\mathord{\buildrel{\hbox{$\smash{\scriptscriptstyle\smile}$ } } \!\!\!\over C}}\) :

Concentration variable

\(\hat{u},\hat{w}\) :

Radial and axial velocities (m s−1)

β :

Velocity slip parameter

γ :

Thermal slip parameter

ζ :

Similarity variable

f :

Dimensionless velocity

θ :

Dimensionless temperature

ν :

Kinematic viscosity

τ :

Ratio between effective heat capacity of the nanoparticle and the fluid

ϕ :

Dimensionless nanoparticle concentration

Le :

Lewis number

N B :

Brownian motion parameter

Nt:

Thermophoresis parameter

W :

Condition on the sheet

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Acknowledgments

The authors are highly grateful to the unknown referees for their valuable comments which really improved the quality of manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan

    Syed Tauseef Mohyud-Din & Sheikh Irfanullah Khan

  2. Department of Mathematics, College of Sciences, King Saud University, Riyadh, South Africa

    Bandar Bin-Mohsin

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  1. Syed Tauseef Mohyud-Din
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  2. Sheikh Irfanullah Khan
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  3. Bandar Bin-Mohsin
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Correspondence to Syed Tauseef Mohyud-Din.

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Mohyud-Din, S.T., Khan, S.I. & Bin-Mohsin, B. Velocity and temperature slip effects on squeezing flow of nanofluid between parallel disks in the presence of mixed convection. Neural Comput & Applic 28 (Suppl 1), 169–182 (2017). https://doi.org/10.1007/s00521-016-2329-1

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