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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
Article

Abstract

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 

Nomenclature

Nomenclature

(, )

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

,

coordinates (m)

Bi1,Bi2

Biot numbers

DB

Brownian diffusion coefficient (m2 · s−1)

DT

thermophoretic diffusion coefficient

g

acceleration due to gravity (m·s−1)

Grx

local Grashof number

h1

heat transfer coefficient (W·m−2·K−1)

h2

mass transfer coefficient

Le

Lewis number

f

dimensionless velocity variable

fluid temperature (K)

Tf

temperature of fluid near wall (K)

T

ambient temperature (K)

volumetric coefficient

Cw

volume fraction of fluid near wall

C

concentration far away from surface

cp

specific heat capacity (J·kg−1·K−1)

k

thermal conductivity (W·m−1·K−1)

k*

mean absorption coefficient (m−1)

Uw

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

a

constant (s−1)

Cf

skin friction coefficient

N

buoyancy parameter

NB

Brownian motion parameter

NT

thermophoretic parameter

Nux

local Nusselt number

Shx

local Sherwood number

qw

surface heat flux

qm

surface mass flux

Rex

local Reynolds number

R

radiation parameter

Pr

Prandtl number

Greek symbols

ρ

density of fluid (kg·m−3)

μ

dynamic viscosity (kg·m−1·s−1)

ν

kinematic viscosity of fluid (m2 · s−1)

σ*

Stefan-Boltzman constant (W·m−2·K−4)

α1, a2

nonlinear convection parameters

αm

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

β

Deborah number

β0

linear volumetric thermal expansion coefficient

β1

nonlinear volumetric thermal expansion coefficient

β2

linear volumetric solute expansion coefficient

β3

nonlinear volumetric solute expansion coefficient

θ

dimensionless temperature

θw

temperature ratio parameter

ϕ

nanoparticle volume fraction

λ

local mixed convection parameter

λ1

ratio of relaxation/retardation time

λ2

retardation time

λE

relaxation time of heat flux

λC

relaxation time of mass flux

τw

wall shear stress

τ

thermophoretic parameter

η

dimensionless similarity variable

Superscript

derivative with respect to η

Subscripts

f

fluid properties at wall

fluid properties at ambient conditions

Chinese Library Classification

O361 

2010 Mathematics Subject Classification

76A05 76Bxx 76Sxx 

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Notes

Acknowledgements

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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