Abstract
There is a rising interest in application of nanofluids in porous media. As such, this paper is aimed at numerically investigating convective boundary layer flow over a plate embedded in a porous medium filled with nanofluid. Influence of multifarious boundary layers’ applications namely concentration boundary layer of nanoparticles and thermal ones on thermal conductivity and dynamic viscosity of the nanofluid is studied. A new enhanced boundary condition, zero mass flux of nanoparticles through the surface, is adopted to calculate the volume fraction of nanoparticles on the surface. Furthermore, the effect of different practical non-dimensional parameters such as Brownian motion, thermophoresis, Lewis number, and buoyancy ratio on the hydrodynamic, thermal, and concentration boundary layers is investigated. It is revealed that an increase in buoyancy ratio culminates in temperature rise and velocity reduction. The results also show that as the dimensionless Lewis number increases, the fraction of nanoparticles at the sheet soars; on the other hand, the variation of Lewis number does not have considerable effect on the thermal and hydrodynamic boundary layers. Moreover, introducing an enhancement ratio as a criterion to examine the variation of thermal convective coefficient reveals that this value is a decreasing function of buoyancy ratio parameter. In some cases, the value of enhancement ratio becomes less than unity as the buoyancy ratio gets stronger.
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Abbreviations
- \(D_\mathrm{B}\) :
-
Brownian diffusion coefficient (\(\mathrm{m}^{2}/\mathrm{s}\))
- \(D_\mathrm{T}\) :
-
Thermophoretic diffusion coefficient (\(\mathrm{m}^{2}/\mathrm{s}\))
- F :
-
Rescaled nanoparticles volume fraction, nanoparticles concentration
- g :
-
Gravitational acceleration vector
- h :
-
Convective heat transfer coefficient (\(\mathrm{J}/\mathrm{m}^{2})\)
- \(k_\mathrm{eff}\) :
-
Effective thermal conductivity of the porous medium (W/m K)
- K :
-
Permeability of porous medium
- Le :
-
Lewis number
- \(N_\mathrm{b}\) :
-
Brownian motion parameter
- \(\mathrm{NC}_\mathrm{f}\) :
-
Thermal conductivity concentration coefficient
- \(\mathrm{NC}_\mathrm{T}\) :
-
Thermal conductivity temperature coefficient
- \(N_\mathrm{r}\) :
-
Buoyancy ratio
- \(\mathrm{NV}_\mathrm{f}\) :
-
Viscosity concentration coefficient
- \(\mathrm{NV}_\mathrm{T}\) :
-
Thermal viscosity coefficient
- \(N_\mathrm{t}\) :
-
Thermophoresis parameter
- p :
-
Pressure (Pa)
- \(Ra_{x}\) :
-
Local Rayleigh number
- S :
-
Dimensionless stream function
- T :
-
temperature (K)
- \(\bar{{u}},\,\bar{{v}}\) :
-
Darcy velocity components along x and y directions (m/s)
- \((x,\,y)\) :
-
Cartesian coordinates
- \(\alpha \) :
-
Thermal diffusivity (\(\mathrm{m}^{2}/\mathrm{s}\))
- \(\beta \) :
-
Volumetric expansion coefficient of fluid
- \(\varepsilon \) :
-
Porosity
- \(\eta \) :
-
Dimensionless distance
- \(\theta \) :
-
Dimensionless temperature
- \(\mu _\mathrm{eff}\) :
-
Viscosity of fluid (Pa s)
- \(\nu _\mathrm{eff}\) :
-
Cinematic viscosity
- \(\rho \) :
-
Density (\(\mathrm{kg}/\mathrm{m}^{3})\)
- \(\rho _\mathrm{c}\) :
-
Heat capacity (\(\mathrm{J}/\mathrm{m}^{3}\,\mathrm{K}\))
- \(\tau \) :
-
Parameter defined by Eq. (5)
- \(\varphi \) :
-
Dimensionless nanoparticles volume fraction
- \(\psi \) :
-
Stream function
- \(\infty \) :
-
Free stream
- m:
-
Porous medium
- bf:
-
The base fluid
- drift-flux:
-
The drift flux model
- nf:
-
Nanofluid
- p:
-
Nanoparticles
- w:
-
Sheet, wall, surface
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Acknowledgments
The authors would like to thank the very competent Reviewers for the valuable comments and suggestions. The first author is grateful to Shahid Chamran University of Ahvaz for its support. Noghrehabadi, Zargartalebi and Ghalambaz acknowledge the Iran Nanotechnology Initiative Council (INIC) for financial support.
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Zargartalebi, H., Noghrehabadi, A., Ghalambaz, M. et al. Natural Convection Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid: Case of Variable Thermophysical Properties. Transp Porous Med 107, 153–170 (2015). https://doi.org/10.1007/s11242-014-0430-4
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DOI: https://doi.org/10.1007/s11242-014-0430-4