Applied Mathematics and Mechanics

, Volume 39, Issue 9, pp 1311–1326 | Cite as

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

  • P. B. Sampath Kumar
  • B. Mahanthesh
  • B. J. GireeshaEmail author
  • S. A. Shehzad


A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.

Key words

nonlinear convection Jeffrey liquid nanoliquid convective condition thermophoretic Brownian motion 



(, )

velocity components along x- and y- axes (m·s−1)


coordinates (m)


Biot numbers


Brownian diffusion coefficient (m2 · s−1)


thermophoretic diffusion coefficient


acceleration due to gravity (m·s−1)


local Grashof number


heat transfer coefficient (W·m−2·K−1)


mass transfer coefficient


Lewis number


dimensionless velocity variable

fluid temperature (K)


temperature of fluid near wall (K)


ambient temperature (K)

volumetric coefficient


volume fraction of fluid near wall


concentration far away from surface


specific heat capacity (J·kg−1·K−1)


thermal conductivity (W·m−1·K−1)


mean absorption coefficient (m−1)


= aX̅, stretching sheet velocity (m·s−1)


constant (s−1)


skin friction coefficient


buoyancy parameter


Brownian motion parameter


thermophoretic parameter


local Nusselt number


local Sherwood number


surface heat flux


surface mass flux


local Reynolds number


radiation parameter


Prandtl number

Greek symbols


density of fluid (kg·m−3)


dynamic viscosity (kg·m−1·s−1)


kinematic viscosity of fluid (m2 · s−1)


Stefan-Boltzman constant (W·m−2·K−4)

α1, a2

nonlinear convection parameters


= k/(ρcp), thermal diffusivity (m2·s−1)


Deborah number


linear volumetric thermal expansion coefficient


nonlinear volumetric thermal expansion coefficient


linear volumetric solute expansion coefficient


nonlinear volumetric solute expansion coefficient


dimensionless temperature


temperature ratio parameter


nanoparticle volume fraction


local mixed convection parameter


ratio of relaxation/retardation time


retardation time


relaxation time of heat flux


relaxation time of mass flux


wall shear stress


thermophoretic parameter


dimensionless similarity variable


derivative with respect to η



fluid properties at wall

fluid properties at ambient conditions

Chinese Library Classification


2010 Mathematics Subject Classification

76A05 76Bxx 76Sxx 


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One of the authors P. B. SAMPATH KUMAR is thankful to University Grant Commission (UGC), New Delhi, for their financial support under National Fellowship for Higher Education (NFHE) of ST students to pursue M. Phil/PhD Degree (F117.1/201516/NFST201517STKAR2228/(SAIII/Website) Dated: 06-April-2016). Also, the author B. MAHANTHESH is thankful to the Management of Christ University, Bengaluru, India, for the support through Major Research Project to accomplish this research work.


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • P. B. Sampath Kumar
    • 1
  • B. Mahanthesh
    • 2
  • B. J. Gireesha
    • 1
    Email author
  • S. A. Shehzad
    • 3
  1. 1.Department of Studies and Research in MathematicsKuvempu UniversityShimogaIndia
  2. 2.Department of MathematicsChrist UniversityBangaloreIndia
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologySahiwalPakistan

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