, Volume 9, Issue 4, pp 937–951 | Cite as

Time-Dependent Nonlinear Convective Flow and Radiative Heat Transfer of Cu-Al2O3-H2O Hybrid Nanoliquid with Polar Particles Suspension: a Statistical and Exact Analysis

  • Joby Mackolil
  • B. MahantheshEmail author


The statistical and exact analysis of heat transfer rate and skin friction coefficient of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is performed. The heat transport phenomenon includes radiative heat effect. A micropolar fluid model is accounted. Exact solutions to the governing problem are found via Laplace transform method (LTM). The heat transfer rate and skin friction are analysed critically via statistical methods like probable error and regression models. The slope of linear regression of data points for skin friction and Nusselt number is estimated to quantify the increase/decrease. The Nusselt number and thermophysical properties for twenty-four different hybrid nanofluids are presented. A novel idea of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is investigated for the first time. Opposite behaviour of velocity and microrotation profile are established when the physical parameters are varied.


Micropolar fluid; hybrid nanofluid Nonlinear convection Thermal radiation Laplace transform method Regression analysis Probable error 


\( \overrightarrow{V} \)

Fluid velocity vector (m/s)


Temperature (K)

\( \overrightarrow{N} \)

Microrotation vector


Effective specific heat coefficient of fluid (J/kg K)


Acceleration due to gravity (m/s2)


Pressure (kg/m s2)


Thermal conductivity (W/m K)


Rosseland mean absorption coefficient


Body force


Time (s)


Micro-inertia density


Body couple per unit mass


Characteristic velocity


Thermal Grashof number


Thermal radiation parameter


Prandtl number


a1 − a13b1, b2

Symbols denoting the expressions involving constants.

Greek symbols


Thermal expansion coefficient

α, λ

Spin-gradient viscosity coefficient


Kinematic viscosity (m2/s)


Dynamic viscosity (kg/m s)


Nanoparticle volume fraction


Density (kg/m3)


Stefan-Boltzmann constant


Vortex viscosity


Spin-gradient viscosity


Microrotation parameter


Nonlinear convection parameter



Base fluid


Hybrid nanofluid

Cu, Al2O3



Z1 − Z6

Symbols denoting the definition of functions

Mathematics Subject Classification

76Dxx 76Nxx 76Rxx 62Jxx 



We express our sincere thanks to the Management, CHRIST (Deemed to be University), Banglore, India for their support to complete this work. Further, we would like to express our sincere gratitude to the Editors and anonymous Reviewers for their constructive suggestions to enhance the quality of the paper.

Compliance with Ethical Standards

Conflict of Interest

The authors report no conflict of interests.

Research Involving Humans and Animals Statement


Informed Consent


Funding Information



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsCHRIST (Deemed to be University)BangaloreIndia

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