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Impact of Thermal Radiation on an Unsteady Casson Nanofluid Flow Over a Stretching Surface

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Abstract

This article employs the analytical approach to examine the heat and mass transfer characteristics on an unsteady flow of Casson nanofluid past an elongated surface with thermal radiation effect. A perturbation technique is adopted to solve the governing equations of the flow. Copper, Silver and Ferrous nanoparticles are suspended in water based nanofluid. Impacts of physical parameters like nanoparticle volume fraction, thermal radiation, magnetic field, stretching parameter, heat source/sink, a chemical reaction on velocity, thermal and concentration attributes along with wall friction, heat, and mass transfer rates are demonstrated with the aid of graphs and tables. Dual nature is witnessed for Newtonian and non-Newtonian fluid cases. Obtained results demonstrate the volumetric size, shape and conductive property of the nanoparticle play an important role in enriching the effectiveness of convection heat transfer of nanofluids. Also, Casson nanofluid has a tendency to reduce the velocity of the fluid due to its higher viscidness.

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Abbreviations

x, y :

Cartesian coordinates (m)

\( u,v \) :

Velocity component at x, y direction respectively (m s−1)

t :

Time (s)

\( B_{o} \) :

Magnetic field strength

\( R \) :

Thermal radiation

\( U_{w} \) :

Sheet velocity

\( T_{s} \) :

Surface temperature (K)

\( T_{0} \) :

Free stream temperature (K)

\( M \) :

Magnetic field

\( S \) :

Stretching parameter

\( R \) :

Radiation parameter

\( \Pr \) :

Prandtl number

\( C_{f} \) :

Skin friction coefficient

\( k^{*} \) :

Mean absorption coefficient

\( q_{w} \) :

Heat flux from the flux (J m−2 s−1)

\( Nu_{x} \) :

Local Nusselt number

\( \text{Re}_{x} \) :

Local Reynolds number

\( \sigma^{*} \) :

Stefan–Boltzman constant

\( \xi \) :

Casson fluid parameter

\( \mu_{nf} \) :

Viscosity (kg m−1 s−2)

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

Heat capacitance (J m−3 K−1)

\( k_{nf} ,k_{f} \) :

Thermal conductivity

\( \rho_{f} ,\rho_{s} ,\rho_{nf} \) :

Density (kg m−3)

\( \phi \) :

Volume fraction

\( \upsilon_{f} \) :

Kinematic viscosity (m2 s−1)

nf :

Nanofluid

f :

Base fluid

s :

Solid

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Authors and Affiliations

  1. Department of Mathematics, Gulbarga University, Kalaburagi, 585106, India

    S. P. Samrat & C. Sulochana

  2. Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Ballari, 583105, India

    G. P. Ashwinkumar

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  1. S. P. Samrat
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  2. C. Sulochana
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  3. G. P. Ashwinkumar
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Correspondence to C. Sulochana.

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Appendix

Appendix

$$ \begin{aligned} & r_{1} = \frac{{SS_{c} + \sqrt {(SS_{c} )^{2} + 4KrS_{c} } }}{2},\quad r_{2} = \frac{{SS_{c} + \sqrt {(SS_{c} )^{2} + 4(iw + Kr)S_{c} } }}{2}, \\ & r_{3} = \frac{{\Pr CS + \sqrt {(\Pr CS)^{2} + 4H} Q}}{2H},\quad r_{4} = \frac{{\Pr CS + \sqrt {(\Pr CS)^{2} + 4H(iwC + Q)} }}{2H}, \\ & r_{5} = \frac{{AS + \sqrt {(AS)^{2} + 4aD(M + {1 \mathord{\left/ {\vphantom {1 K}} \right. \kern-0pt} K}} )}}{2aD},\quad r_{6} = \frac{{AS + \sqrt {(AS)^{2} + 4aD(M + {1 \mathord{\left/ {\vphantom {1 K}} \right. \kern-0pt} K}} - iw)}}{2aD}, \\ & m_{1} = \frac{{ - r_{1}^{2} Du}}{{r_{1}^{2} H - r_{1} \Pr CS + Q}},\quad m_{2} = \frac{{ - Dur_{1}^{2} }}{{r_{2}^{2} H - r_{2} \Pr CS + (Q + \Pr Ciw)}}, \\ & m_{3} = \frac{ - BGr}{{Dar_{3}^{2} - ASr_{3} - (M + {1 \mathord{\left/ {\vphantom {1 {K)}}} \right. \kern-0pt} {K)}}}},\quad m_{4} = \frac{ - BGm}{{Dar_{1}^{2} - ASr_{1} - (M + {1 \mathord{\left/ {\vphantom {1 {K)}}} \right. \kern-0pt} {K)}}}}, \\ & m_{5} = \frac{ - BGm}{{Dar_{2}^{2} - ASr_{2} - (M + ({1 \mathord{\left/ {\vphantom {1 {K) - iw)}}} \right. \kern-0pt} {K) - iw)}}}},\quad m_{6} = \frac{ - BGm}{{Dar_{2}^{2} - ASr_{2} - (M + ({1 \mathord{\left/ {\vphantom {1 {K) - iw)}}} \right. \kern-0pt} {K) - iw)}}}} \\ \end{aligned} $$

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Samrat, S.P., Sulochana, C. & Ashwinkumar, G.P. Impact of Thermal Radiation on an Unsteady Casson Nanofluid Flow Over a Stretching Surface. Int. J. Appl. Comput. Math 5, 31 (2019). https://doi.org/10.1007/s40819-019-0606-2

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