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Transport in Porous Media

, Volume 86, Issue 1, pp 13–22 | Cite as

Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid

  • Ali Chamkha
  • Rama Subba Reddy Gorla
  • Kaustubh Ghodeswar
Article

Abstract

A boundary layer analysis is presented for the natural convection past an isothermal sphere in a Darcy porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter N r, Brownian motion parameter N b, thermophoresis parameter N t, and Lewis number L e. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) on these parameters has been discussed.

Keywords

Natural convection Porous medium Nanofluid 

List of Symbols

DB

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

f

Rescaled nano-particle volume fraction

g

Gravitational acceleration vector

km

Effective thermal conductivity of the porous medium

K

Permeability of porous medium

Le

Lewis number

Nr

Buoyancy Ratio

Nb

Brownian motion parameter

Nt

Thermophoresis parameter

Nu

Nusselt number

P

Pressure

q′′

Wall heat flux

Rax

Local Rayleigh number

S

Dimensionless stream function

T

Temperature

TW

Wall temperature at vertical cone

T

Ambient temperature attained as y tends to infinity

U

Reference velocity

Pr

Prandtl number

Re

Reynolds number

u, v

Darcy velocity components

(x, y)

Cartesian coordinates

Greek Symbols

αm

Thermal diffusivity of porous medium

β

Volumetric expansion coefficient of fluid

\({\varepsilon}\)

Porosity

η

Dimensionless distance

θ

Dimensionless temperature

μ

Viscosity of fluid

ρf

Fluid density

ρp

Nano-particle mass density

(ρc)f

Heat capacity of the fluid

(ρc)m

Effective heat capacity of porous medium

(ρc)p

Effective heat capacity of nano-particle material

τ

Parameter defined by Eq. 5

\({\phi}\)

Nano-particle volume fraction

\({\phi_{\rm W}}\)

Nano-particle volume fraction at vertical cone

\({\phi_{\infty}}\)

Ambient nano-particle volume fraction attained

ψ

Stream function

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References

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Ali Chamkha
    • 1
  • Rama Subba Reddy Gorla
    • 2
  • Kaustubh Ghodeswar
    • 2
  1. 1.Public Authority for Applied Education and TrainingShuweikhKuwait
  2. 2.Cleveland State UniversityClevelandUSA

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