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Convective Poiseuille flow of Al2O3-EG nanofluid in a porous wavy channel with thermal radiation

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Abstract

In current article, convective Poiseuille boundary layer flow of ethylene glycol (C2H6O2)-based nanofluid with suspended aluminum oxide (Al2O3) nanoparticles through a porous wavy channel has been examined. The impact of thermal radiation, Ohmic dissipation, electric field, and magnetic fields are also considered. The flow is due to constant pressure gradient in a wavy frame of reference. The governed momentum and thermal boundary layer equations is system of PDE’s, which are converted to system of ODE’s via suitable similarity transformations. The homotopy analysis method is applied to solve the governed flow problem. Convergence of series solutions is inspected through h-curves and residual errors norm, whereas the optimal value of convergence control parameter is obtained by means of genetic algorithm Nelder–Mead approach. The influence of numerous involving parameters like Hartmann number, Grashof number, Eckert number, electric parameter, radiation parameter, and porosity parameter on flow, heat transfer, skin friction coefficient and Nusselt number are illustrated through graphs and discussed briefly.

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Abbreviations

a :

Wave amplitude (m)

L :

Length of channel (m)

\( H_{1} , \, H_{2} \) :

Lower and upper walls of channel

\( \bar{V} \) :

Dimensional fluid velocity

\( \bar{p} \) :

Pressure (Nm−2)

ρ :

Density parameter \( \left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right) \)

k :

Thermal conductivity \( \left( {{\text{W}}\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} } \right) \)

c p :

Specific heat at constant pressure \( \left( {{\text{kJ}}\;{\text{ kg}}^{ - 1} \;{\text{K}}^{ - 1} } \right) \)

β :

Volumetric volume expansion coefficient (k−1)

K :

Porous medium permeability coefficient

\( T_{1} \) :

Lower wall temperature

\( T^{*} \) :

Mean value of \( T_{1} \) and \( T_{2} \)

E 0 :

Uniform electric field

\( \bar{u}, \, \bar{v} \) :

Dimensional \( \bar{x} \) and \( \bar{y} \) components of velocity (ms−1)

\( u, \, v \) :

Dimensional x and \( y \) components of velocity (ms−1)

\( Re \) :

Local Reynolds number

Pr :

Prandtl number

D a :

Darcy number

Ha :

Hartmann number

α :

Radiation absorption coefficient

Nu :

Nusselt number

u :

Embedding parameter for veocity

d :

Width of channel (m)

λ:

Wavelength

g :

Gravitational acceleration (ms−2)

\( \bar{T} \) :

Dimensional fluid temperature

p :

Dimensionless pressure

μ :

Viscosity parameter \( \left( {{\text{N}}\;{\text{s}}\;{\text{m}}^{ - 2} } \right) \)

σ :

Electrical conductivity

Φ :

Viscous dissipation

ϕ :

Nanoparticle volume fraction

n :

Temperature scale

\( T_{2} \) :

Upper wall temperature

\( \bar{J} \) :

Joule current

B 0 :

Uniform transverse magnetic field

δ :

Dimensionless wave number

θ :

Dimensionless temperature

q r :

Radiative heat flux

Gr :

Grashof number

E c :

Eckert number

E 1 :

Local electromagnetic parameter

N :

Radiation parameter

C f :

Skin friction coefficient

θ :

Embedding parameter for temperature

f:

Fluid

p:

Particle

nf:

Nanofluid

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Correspondence to R. Ellahi.

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Zeeshan, A., Shehzad, N., Ellahi, R. et al. Convective Poiseuille flow of Al2O3-EG nanofluid in a porous wavy channel with thermal radiation. Neural Comput & Applic 30, 3371–3382 (2018). https://doi.org/10.1007/s00521-017-2924-9

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