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Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid

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Abstract

Viscosity of fluid keeps its leading role in the polymer process, biological fluids, mayonnaise, colloidal suspensions, melt solutions and lubrication models. The Carreau nanofluid viscosity model can explain features of non-Newtonian fluids in the shear-thinning/thickening regions. This article describes the Lorentz force effects with the use of the infinite shear rate of the Carreau viscosity model and thermal radiation along with the influence of non-uniform heat source/sink transportation phenomenon of heat over the surface. The transformations of dimensionless variables are implemented to convert the partial differential equations into nonlinear coupled ordinary differential equations (ODEs). The solution of these ODEs is performed using the Runge–Kutta Fehlberg method along with the shooting scheme. The effects of the We, Pr, M, Nr, β*, β, B*and A*parameters denote the Weissenberg number, Prandtl number, radiation parameter, temperature ratio parameter, viscosity ratio parameter, stretching parameter, coefficients of space and temperature-dependent heat source/sink. For the correctness and exactness of the scheme, a comparison study is also provided based on the present results and the published results.

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Abbreviations

\(n\) :

Carreau fluid index

\(\tau\) :

Cauchy stress tensor

A*:

Coefficients of space

C :

Concentration of fluid

\(\rho\) :

Fluid density

L :

Gradient of velocity

\(q\) :

Heat flux

\(\lambda\) :

Heat sink source parameter

\(h_{f}\) :

Heat transfer coefficient

\(T_{\infty }\) :

Infinite temperature

\(\upsilon\) :

Kinematic viscosity

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

Local Reynold number

\({\text{We}}\) :

Local Weissenberg number

\(k^{*}\) :

Mean absorption coefficient

M :

Ma questions no chick genetic number

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

Nusselt number

\(p\) :

Pressure

\(\Pr\) :

Prandtl number

\(q_{r}\) :

Radiative heat flux

\(A_{1}\) :

Rivlin–Ericksen tensor

\({\text{Rd}}\) :

Radiation parameter

\(\sigma^{*}\) :

Stefan–Boltzmann constant

\(x,y\) :

Space coordinates

\(c_{f}\) :

Skin friction coefficient

\(c_{p}\) :

Specific heat

\(U_{w} \left( {x,t} \right)\) :

Stretching velocity

\(\Omega\) :

Shear rate of strain tensor

\(\alpha\) :

Thermal diffusivity

T :

Temperature of the fluid

B*:

Temperature-dependent heat source/sink

\(\gamma\) :

Thermal Biot number

\(k\) :

Thermal conductivity

\(\theta_{w}\) :

Temperature ratio parameter

\(A\) :

Unsteadiness parameter

\(\beta^{*}\) :

Viscosity ratio

\(u,v\) :

Velocity component

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Hazara University, Mansehra, Pakistan

    Assad Ayub, Zulqurnain Sabir & Syed Zahir Hussain Shah

  2. GRC Department, Faculty of Applied Studies, King Abdulaziz University, Jeddah, Saudi Arabia

    S. R. Mahmoud

  3. Statistics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ali Algarni

  4. Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt

    R. Sadat

  5. Faculty of Engineering and Technology, Future University, Cairo, Egypt

    Mohamed R. Ali

  6. Department of Basic Science, Faculty of Engineering at Benha, Benha University, Benha, 13512, Egypt

    Mohamed R. Ali

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  1. Assad Ayub
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Correspondence to R. Sadat.

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Ayub, A., Sabir, Z., Shah, S.Z.H. et al. Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid. Eur. Phys. J. Plus 137, 247 (2022). https://doi.org/10.1140/epjp/s13360-022-02410-6

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