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Laminar Free Convection Over a Vertical Wavy Surface Embedded in a Porous Medium Saturated with a Nanofluid

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Abstract

Numerical analysis is performed to examine laminar free convective of a nanofluid along a vertical wavy surface saturated porous medium. In this pioneering study, we have considered the simplest possible boundary conditions, namely those in which both the temperature and the nanoparticle fraction are constant along the wall. Non-similar transformations are presented for the governing equations and the obtained PDE are then solved numerically employing a fourth order Runge–Kutta method with shooting technique. A detailed parametric study (nanofluid parameters) is performed to access the influence of the various physical parameters on the local Nusselt number and the local Sherwood number. The results of the problem are presented in graphical forms and discussed.

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Abbreviations

a :

Amplitude of the wavy surface

D :

Brownian diffusion coefficient

\({\bar{{D}}}\) :

Thermophoretic diffusion coefficient

F :

Dimensionless stream function

g :

Acceleration due to gravity

k :

Thermal conductivity

K :

Modified permeability of the porous medium

Le :

Lewis number

N b :

The Brownian motion parameter

N r :

The buoyancy ratio

N t :

The thermophoresis parameter

Nu :

Local Nusselt number

P :

Pressure

q w :

Heat transfer rate

q m :

Mass transfer rate

Ra :

Rayleigh number

S :

Rescaled nanoparticle volume fraction

Sh :

Local Sherwood number

T :

Temperature of the fluid

u, υ :

Components of velocity of the fluid

x, y :

Coordinate axes

α :

Thermal diffusivity of porous medium

β :

Volumetric coefficient of thermal expansion of fluid

μ :

Viscosity of the fluid

γ :

The ratio between the effective heat capacity of the nanoparticle material and heat capacity of the fluid

:

The characteristic length of the wavy surface

ρ f :

Fluid density

ρ p :

Nanoparticle mass density

(ρ c)f :

Heat capacity of the fluid

(ρ c)p :

Effective heat capacity of nanoparticle material

ψ :

Stream function

θ :

Dimensionless temperature

\({\phi }\) :

Nanoparticle volume fraction

w:

Conditions at the wall

∞, •:

Conditions in the free stream

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Correspondence to Sameh E. Ahmed.

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Mahdy, A., Ahmed, S.E. Laminar Free Convection Over a Vertical Wavy Surface Embedded in a Porous Medium Saturated with a Nanofluid. Transp Porous Med 91, 423–435 (2012). https://doi.org/10.1007/s11242-011-9852-4

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Keywords

  • Wavy surface
  • Nanofluid
  • Porous medium
  • Natural convection