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Thermal Transport of Hybrid Liquid over Thin Needle with Heat Sink/Source and Darcy–Forchheimer Porous Medium Aspects

  • Research Article-Mechanical Engineering
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Abstract

The structure of needle is mostly similar as paraboloid of upset parallel to flow possesses and has huge applications in building and modern procedures including microstructure electronic gadgets and microscale cooling gadgets for thermal evacuation application. Based on these applications, an axisymmetric Darcy–Forchheimer flow and energy transport of hybrid nanoliquid over a slender moving needle is considered. Impact of heat sink/source and Newtonian heating is inspected. The dimensional nonlinear administering partial differential equations (PDEs) are modified to dimensionless nonlinear ordinary differential equations (ODEs) with assistance of similarity technique which is then explained numerically utilizing Runge–Kutta–Fehlberg scheme from Dsolve code MAPLE. It ought to be noticed that approval of results shows a decent concurrence with previously existing reports. It is noticed that the enhancing Forchheimer number and porosity parameter increase the temperature.

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Abbreviations

\(Bi\) :

Newtonian heating parameter

\(c\) :

Size of needle

C f :

Skin friction

f :

Velocity

\(F\) :

Non-uniform inertia coefficient

\(h_{f}\) :

Heat transfer coefficient

\(k^{*}\) :

Permeability of porous space

\(k_{f}\) :

Thermal conductivity \(({\text{W}}/{\text{m}}\,{\text{K}})\)

\(n\) :

Shaped factor of nanoparticles

\(Nu\) :

Nusselt number

\(\Pr\) :

Prandtl number

\(\text{R} (x)\) :

Axisymmetric body surface shape

\(T\) :

Hybrid nanofluid temperature \((K)\)

\(T_{w}\) :

Constant temperature \((K)\)

\(T_{\infty }\) :

Constant ambient surface temperature \((K)\)

\(r,x\) :

Cylindrical coordinates which are in the radial \((u)\) and axial \((v)\) directions \(\left( {{\text{m}}/{\text{s}}} \right)\)

\(U\) :

Composite velocity

\(U_{w}\) :

Constant velocity

\(U_{\infty }\) :

Free stream velocity

\(\nu\) :

Kinematic viscosity \(({\text{m}}^{2} /{\text{s}})\)

\(\mu\) :

Dynamic viscosity \(({\text{N}}\,{\text{s}}/{\text{m}}^{2} )\)

\(\rho\) :

Density \(({\text{kg}}/{\text{m}}^{3} )\)

\(\alpha\) :

Thermal diffusivity \(({\text{m}}^{2} /{\text{s}})\)

\(\lambda\) :

Velocity ratio

\(\psi\) :

Stream function

\(\phi_{1} ,\phi_{2}\) :

Solid volume fraction \(\left( {{\text{kg}}/{\text{m}}^{3} } \right)\)

\(\theta\) :

Dimensionless temperature

\(s_{1}\) :

Solid nanoparticles of Al2O3

\(s_{2}\) :

Solid nanoparticles of Cu

nf:

Nanofluid

\({\text{hnf}}\) :

Hybrid nanofluid

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Authors and Affiliations

  1. Department of Mathematics, K.L.E. Society’s J.T. College, Gadag, Karnataka, 582101, India

    G. K. Ramesh

  2. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    S. A. Shehzad

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Mohsen Izadi

  4. Faculty of Electrical – Electronic Engineering, Duy Tan University, Da Nang, 550000, Vietnam

    Mohsen Izadi

  5. Mechanical Engineering Department, Faculty of Engineering, Lorestan University, Khorramabad, Iran

    Mohsen Izadi

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  1. G. K. Ramesh
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  3. Mohsen Izadi
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Correspondence to S. A. Shehzad.

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Ramesh, G.K., Shehzad, S.A. & Izadi, M. Thermal Transport of Hybrid Liquid over Thin Needle with Heat Sink/Source and Darcy–Forchheimer Porous Medium Aspects. Arab J Sci Eng 45, 9569–9578 (2020). https://doi.org/10.1007/s13369-020-04853-4

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  • DOI: https://doi.org/10.1007/s13369-020-04853-4

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