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

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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.

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Abbreviations

D B :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion coefficient

f :

Rescaled nano-particle volume fraction

g :

Gravitational acceleration vector

k m :

Effective thermal conductivity of the porous medium

K :

Permeability of porous medium

L e :

Lewis number

N r :

Buoyancy Ratio

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

Nu :

Nusselt number

P :

Pressure

q′′:

Wall heat flux

Ra x :

Local Rayleigh number

S :

Dimensionless stream function

T :

Temperature

T W :

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

α m :

Thermal diffusivity of porous medium

β :

Volumetric expansion coefficient of fluid

\({\varepsilon}\) :

Porosity

η :

Dimensionless distance

θ :

Dimensionless temperature

μ :

Viscosity of fluid

ρ f :

Fluid density

ρ p :

Nano-particle mass density

(ρ c)f :

Heat capacity of the fluid

(ρ c)m :

Effective heat capacity of porous medium

(ρ c)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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Authors and Affiliations

  1. Public Authority for Applied Education and Training, Shuweikh, Kuwait

    Ali Chamkha

  2. Cleveland State University, Cleveland, OH, 44115, USA

    Rama Subba Reddy Gorla & Kaustubh Ghodeswar

Authors
  1. Ali Chamkha
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  2. Rama Subba Reddy Gorla
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  3. Kaustubh Ghodeswar
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Correspondence to Rama Subba Reddy Gorla.

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Chamkha, A., Gorla, R.S.R. & Ghodeswar, K. Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid. Transp Porous Med 86, 13–22 (2011). https://doi.org/10.1007/s11242-010-9601-0

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  • DOI: https://doi.org/10.1007/s11242-010-9601-0

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