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Importance of entropy generation and infinite shear rate viscosity for non-Newtonian nanofluid

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Abstract

This study addresses the novel characteristics of infinite shear rate viscosity and entropy generation in magneto-mixed convective flow of cross-nanomaterial toward a stretched surface. Moreover, analysis of current research work has been prepared for Brownian moment and thermophoresis deposition. Radiation and viscous dissipation aspects are accounted. More specifically, roles of activation energy and Lorentz force on nanofluids transportation are examined. ODEs are acquired from PDEs via implementation of suitable transformations. Numerical algorithm is implemented to tackle the nonlinear system for numerical results. Discussion on rheological parameters involved in current research work is presented through graphs. Results demonstrate the significant rise in temperature and nanoparticles concentration with the intensification of Brownian moment aspects. More specially, we perceived that entropy rate is significantly affected by radiation parameter and Brinkman number. Intensification in entropy rate is observed for rising values of magnetic parameter, radiation parameter and Brinkman number.

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Abbreviations

u, v :

Velocity components

x, y :

Space coordinates

\(\rho\) :

Density of fluid

\(\nu\) :

Kinematic viscosity

\(\mu\) :

Dynamic viscosity

\(n\) :

Power law index

\(B_{0}\) :

Uniform magnetic field strength

\(\left( {\rho c} \right)_{\text{f}}\) :

Heat capacity of fluid

\(T\) :

Ratio of heat capacity

\(\left( {\rho c} \right)_{p}\) :

Effective heat capacity

\(\alpha\) :

Thermal diffusivity

\(\sigma^{**}\) :

Stefan–Boltzmann constant

\(D_{\text{T}}\) :

Thermophoresis effect

\(k_{f}\) :

Thermal conductivity

\(c_{p}\) :

Specific heat capacity

\(m^{*}\) :

Mean absorption coefficient

\(D_{\text{B}}\) :

Brownian motion

T :

Temperature

\(T_{\infty }\) :

Ambient temperature

\(C_{\infty }\) :

Ambient concentration

\(T_{w}\) :

Surface temperature

\(C_{w}\) :

Surface concentration

\(k_{\text{r}}^{2}\) :

Reaction rate

\(E_{\text{a}}\) :

Activation energy

\(\varGamma\) :

Time material constant

\(\beta^{*}\) :

Ratio of viscosities

C:

Concentration

\(m\) :

Fitted rate constant

\(c\) :

Dimensional constant

\(U_{w}\) :

Stretching velocity

\(\eta\) :

Dimensionless variable

We :

Weissenberg number

Pr :

Prandtl number

M :

Magnetic parameter

Nr :

Buoyancy ratio parameter

\(\lambda\) :

Mixed convection parameter

R :

Thermal radiation parameter

\(Nb\) :

Brownian motion parameter

\(Nt\) :

Thermophoresis parameter

\(Ec\) :

Eckert number

Sc :

Schmidt number

\(\sigma\) :

Dimensionless reaction rate

E :

Dimensionless activation energy

\(\delta\) :

Temperature difference parameter

\(\tau_{\text{w}}\) :

Wall shear stress

\(q_{\text{w}}\) :

Wall heat flux

\(f\) :

Dimensionless velocities

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

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

Entropy generation rate

\(\alpha_{2}\) :

Dimensionless temperature ratio variable

\(\alpha_{1}\) :

Dimensionless concentration ratio variable

L :

Diffusive variable

Br :

Brinkman number

\(C_{fx}\) :

Skin fraction

\(Nu_{x}\) :

Local Nusselt number

\(Re_{x}\) :

Local Reynolds number

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Acknowledgements

This project was funded by the postdoctoral international exchange program for incoming postdoctoral students, at Beijing Institute of Technology, Beijing, China.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan

    F. Sultan, M. Ali & M. Shahzad

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    W. A. Khan & H. Sun

  3. Department of Mathematics, Mohi-ud-Din Islamic University, 12010, Nerian Sharif, Azad Jammu and Kashmir, Pakistan

    W. A. Khan

  4. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    M. Irfan

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  1. F. Sultan
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  2. W. A. Khan
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  6. M. Irfan
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Correspondence to F. Sultan or W. A. Khan.

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Technical Editor: Cezar Negrao, PhD.

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Sultan, F., Khan, W.A., Ali, M. et al. Importance of entropy generation and infinite shear rate viscosity for non-Newtonian nanofluid. J Braz. Soc. Mech. Sci. Eng. 41, 439 (2019). https://doi.org/10.1007/s40430-019-1950-1

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  • DOI: https://doi.org/10.1007/s40430-019-1950-1

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