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Numerical investigation of boundary layer flow past a thin heated needle immersed in hybrid nanofluid

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Abstract

The heat transfer in flow past thin needle has applications in instruments like hot wire anemometers. The objective of this article is to study the influence of hybrid nanoparticles on heat transfer distribution of the boundary layer flow over a parabolically shaped thin hot needle. The Sakiadis and Blasius 2-D flow scenarios have been analyzed by implementing a mathematical model with the Navier–Stokes and the energy equations. The resulting equations are solved numerically by using a similarity solution technique. This technique results in a differential equation in terms of a single variable, representing the curves parallel to the needle surface. The results show that using distinct nanoparticles allows us to control the heat transfer rate apart from the physical parameters, such as, needle size or velocity ratio parameter. A comparative analysis of Nusselt number, frictional drag, temperature, and velocity profiles for Ag–water nanofluid, Ag–CuO/water hybrid nanofluid, and CuO–water nanofluid has been carried out for different flow conditions, including Sakiadis and Blasius flow. The addition of nanoparticles hikes the heat transfer rate by 27–28% in Blasius flow and 6–8% in Sakiadis flow.

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Abbreviations

\( T_{w} \) :

Temperature at the needle surface (K)

\( u_{w} \) :

Needle velocity (m s−1)

\( T_{\infty } \) :

Temperature of the ambient fluid (K)

\( u_{\infty } \) :

Velocity of the ambient fluid (m s−1)

\( \kappa \) :

Thermal conductivity (W m−1 K−1)

\( \mu \) :

Dynamic viscosity (kg m−1 s−1)

\( \nu \) :

Kinematic viscosity (m2 s−1)

\( \rho \) :

Density (kg m−3)

Pr:

Prandtl number \( \left( { = \frac{{\mu \left( {c_{p} } \right)_{\text{f}} }}{\kappa }} \right) \)

\( c \) :

Needle size

\( \eta \) :

Non-dimensional space variable

\( \theta \) :

Non-dimensional temperature

\( \phi_{1} \) :

Volume fraction of copper oxide nanoparticles

\( \phi_{2} \) :

Volume fraction of silver nanoparticles

\( \lambda \) :

Flow parameter

u,v :

Velocities in x and r direction, respectively (m s−1)

\( \infty \) :

For Ambient fluid

\( w \) :

For needle surface

hnf:

For hybrid nanofluid

nf:

For nanofluid

f:

For base fluid

\( s1 \) :

For copper oxide nanoparticles

\( s2 \) :

For silver nanoparticles

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Acknowledgments

The authors owe their deep sense of gratitude to the honorable Vice-Chancellor of Defence Institute of Advanced Technology (Deemed University) for constant encouragement and support in the current research. Also, Miss Preeti is thankful to the Defence Research and Development Organization (DRDO), Government of India, for supporting this work under the Senior Research Fellowship (F-16-52-08).

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Authors and Affiliations

  1. Department of Applied Mathematics, Defence Institute of Advanced Technology (Deemed to be University), Pune, 411025, India

    Preeti Prashar, Odelu Ojjela & Samir Kumar Das

  2. Department of Mathematics, Vellore Institute of Technology, Chennai, Tamil Nadu, 600127, India

    Pravin Kashyap Kambhatla

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  1. Preeti Prashar
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  2. Odelu Ojjela
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Correspondence to Odelu Ojjela.

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Prashar, P., Ojjela, O., Kambhatla, P.K. et al. Numerical investigation of boundary layer flow past a thin heated needle immersed in hybrid nanofluid. Indian J Phys 96, 137–150 (2022). https://doi.org/10.1007/s12648-020-01944-8

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