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Chemical Reaction Effects on Nano Carreau Liquid Flow Past a Cone and a Wedge with Cattaneo-Christov Heat Flux Model

R.V.M.S.S. Kiran Kumar , C.S.K Raju , B Mahanthesh , B.J Gireesha EMAIL logo and S.V.K Varma

Abstract

Chemical reaction aspect is utilized for heat mass transfer analysis of nano non-Newtonian liquid flow past a cone and a wedge. Flow is steady, laminar and two dimensional created due to a cone and a wedge. The Carreau liquid and Cattaneo-Christov heat flux models are utilized. The magneto-nano Carreau liquid material occupies the porous space. The relevant PDEs are rendered into coupled non-linear ODEs via appropriate transformations before treated them numerically through Runge-Kutta and Newton’s method. The computed results are plotted for employing the various values of physical constraints on the profiles of velocity, temperature and nanoparticle volume fraction. Moreover, vitiation of the friction factor, Nusselt number and Sherwood number against physical parameters are presented numerically. It is figured out that convective heating and Brownian motion effects are constructive for thermal boundary layer growth. Aspect of chemical reaction is significant to control the solute layer growth and mass transfer rate.

List of symbols

u,v

Velocity components in xandydirections respectively (m/s)

x

Distance along the surface (m)

y

Distance normal to the surface(m)

r

radius of the cone(m)

Tw

temperature near the surface(K)

Cw

concentration near the surface(Moles/Kg)

T

ambient temperature (K)

Greek symbols
n

power law index

k0

porosity parameter

B0

applied magnetic field strength

hf

heat transfer coefficient

g

acceleration due to gravity(m/s2)

k

thermal conductivity(W/mK)

DB

Brownian motion coefficient(m2/s)

f

Dimensionless velocity

DT

thermophoresis coefficient

kl

chemical reaction parameter

l

characteristic length(m)

cp,cs

Specific heat capacity at constant pressure (J/KgK)

ρcp

Effective heat capacity of the nanoparticle medium (Kg/m3K)

We

local Weissenberg number

M

magnetic field parameter

K

porosity parameter

Gc

mass Grashof number

Gr

Grashof number

Pr

Prandtl number

Le

Lewis number

Kr

chemical reaction parameter

Bi

Biot number

Nt

Thermophoresis parameter

Nb

Brownian motion parameter

Cf

shear stress

Nu

local Nusselt number

Sh

local Sherwood number

Cf

dimensional wall shear stress

T

ambient temperature (K)

γ

cone or wedge half angle

Ω

wedge full angle

υ

kinematic viscosity(m2/s)

Γ

material time constant

σ

electrical conductivity(S/m)

ρ

density of the fluid(Kg/m3)

βT

volumetric thermal expansion coefficients

βc

concentration expansion coefficients

β1

heat flux relaxation time

τ

ratio of the effective heat capacity of the nanoparticle to that of an ordinary fluid

(ρc)s

Heat capacity of the fluid (Kg/m3K)

ρcp

Effective heat capacity of the nanoparticle medium (Kg/m3K)

ζ

Similarity variable

δ

thermal relaxation parameter

Subscript:
w

Condition at the wall

Condition at the free stream

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Received: 2017-6-17
Accepted: 2017-10-9
Published Online: 2017-10-25

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