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Numerical Analysis of the Nanofluids Flow Near the Stagnation Point over a Permeable Stretching/Shrinking Wall: A New Modeling

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Abstract

The stagnation-point flow towards a permeable linearly stretching/shrinking wall immersed in copper/water nanofluids is treated numerically using Runge–Kutta–Fehlberg Method (RKF45). A realistic contemporary nanofluids model is employed to modify the involved thermo-physical properties including viscosity and thermal conductivity. This new model enables us to specifically explore the effects of nano particles size and heat transfer direction (say cooling or heating) on the evolution of velocity and temperature profiles as well as on the main quantities of engineering interest. In this respect, it is shown how these effects play significant roles in the evolution of skin friction coefficient and convective heat transfer coefficient. It should be pointed out that these effects are obscure respecting the classic modeling of nanofluids. It is also found that dual solutions (say upper and lower) appear and a stability analysis revealed that the solutions associated with the lower branch are not likely to reside in the actual physics.

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Abbreviations

\( \rho \) :

Density

\( \phi \) :

Volumetric concentration

\( C_{\text{p}} \) :

Specific heat capacity

\( k \) :

Thermal conductivity

Pr:

Prandtl number

T :

Temperature

\( N_{\text{A}} \) :

Avogadro number

\( T_{\text{fr}} \) :

The freeing point temperature

\( k_{\text{Bo}} \) :

Boltzmann constant

\( \mu \) :

Dynamic viscosity

d :

Diameter

M :

Molecular weight

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

Density of the base fluid

\( \upsilon \) :

Kinematic viscosity

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  1. Tehran, Iran

    Amin Jafarimoghaddam

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  1. Amin Jafarimoghaddam
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Correspondence to Amin Jafarimoghaddam.

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Previously at the Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran.

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Jafarimoghaddam, A. Numerical Analysis of the Nanofluids Flow Near the Stagnation Point over a Permeable Stretching/Shrinking Wall: A New Modeling. Arab J Sci Eng 45, 1001–1015 (2020). https://doi.org/10.1007/s13369-019-04205-x

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