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.
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Abbreviations
- (U̅, V̅):
-
velocity components along x- and y- axes (m·s−1)
- X̅, Y̅ :
-
coordinates (m)
- Bi 1,Bi 2 :
-
Biot numbers
- D B :
-
Brownian diffusion coefficient (m2 · s−1)
- D T :
-
thermophoretic diffusion coefficient
- g :
-
acceleration due to gravity (m·s−1)
- Gr x :
-
local Grashof number
- h 1 :
-
heat transfer coefficient (W·m−2·K−1)
- h 2 :
-
mass transfer coefficient
- Le :
-
Lewis number
- f :
-
dimensionless velocity variable
- T̅ :
-
fluid temperature (K)
- T f :
-
temperature of fluid near wall (K)
- T ∞ :
-
ambient temperature (K)
- C̅ :
-
volumetric coefficient
- C w :
-
volume fraction of fluid near wall
- C ∞ :
-
concentration far away from surface
- c p :
-
specific heat capacity (J·kg−1·K−1)
- k :
-
thermal conductivity (W·m−1·K−1)
- k*:
-
mean absorption coefficient (m−1)
- U w :
-
= aX̅, stretching sheet velocity (m·s−1)
- a :
-
constant (s−1)
- C f :
-
skin friction coefficient
- N :
-
buoyancy parameter
- N B :
-
Brownian motion parameter
- N T :
-
thermophoretic parameter
- Nu x :
-
local Nusselt number
- Sh x :
-
local Sherwood number
- q w :
-
surface heat flux
- q m :
-
surface mass flux
- Re x :
-
local Reynolds number
- R :
-
radiation parameter
- Pr :
-
Prandtl number
- 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, a 2 :
-
nonlinear convection parameters
- αm :
-
= k/(ρcp), thermal diffusivity (m2·s−1)
- β :
-
Deborah number
- β 0 :
-
linear volumetric thermal expansion coefficient
- β 1 :
-
nonlinear volumetric thermal expansion coefficient
- β 2 :
-
linear volumetric solute expansion coefficient
- β 3 :
-
nonlinear volumetric solute expansion coefficient
- θ :
-
dimensionless temperature
- θ w :
-
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
- τ w :
-
wall shear stress
- τ :
-
thermophoretic parameter
- η :
-
dimensionless similarity variable
- ′:
-
derivative with respect to η
- f:
-
fluid properties at wall
- ∞:
-
fluid properties at ambient conditions
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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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Sampath Kumar, P.B., Mahanthesh, B., Gireesha, B.J. et al. Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion. Appl. Math. Mech.-Engl. Ed. 39, 1311–1326 (2018). https://doi.org/10.1007/s10483-018-2362-9
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DOI: https://doi.org/10.1007/s10483-018-2362-9