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ABSTRACT
There is growing interest in application of inclined fins to a cavity wall. As such, this paper focuses on the numerical investigation of laminar free convection flow and heat transfer in an enclosure with an inclined thin local thermal non-equilibrium porous fin and saturated by a nanofluid. The porous medium is assumed to be isotropic and homogenous, the cavity walls are assumed to be impermeable to the nanoparticles, and there is a no-slip boundary condition on the enclosure boundaries. The vertical walls are isothermal and the horizontal ones are adiabatic. Moreover, the influence of indispensable parameters regarding heat and mass transfer, such as Rayleigh number, Darcy number, Prandtl number, porosity, thermophoresis and Brownian parameters, fin length, fin position, and the fin angle on the average Nusselt number, are taken into account. Generally, it is found that the average Nusselt number is an increasing function of Ra, Pr, Da, and porosity (ε). Furthermore, increasing either fin position (Sp) or thermal conductivity ratio (η) produces corresponding decreases in average Nusselt number. Finally, heat transfer shows a different behavior for different values of fin angles and lengths.
Nomenclature
| Latin symbols | = | |
| C | = | dimensional nanoparticle volume fraction |
| C0 | = | dimensional ambient nanoparticle volume fraction |
| Da | = | Darcy number |
| DB | = | Brownian diffusion coefficient |
| DT | = | thermophoretic diffusion coefficient |
| g | = | gravitational acceleration vector |
| hfs | = | interface heat transfer coefficient between the fluid/solid matrix phases |
| K | = | permeability of the porous medium |
| k | = | thermal conductivity |
| L | = | cavity size |
| L1 | = | distance between bottom of fin and bottom of cavity |
| L2 | = | distance between top of fin and bottom of cavity |
| Le | = | Lewis number |
| Lp | = | fin length |
| Nb | = | Brownian motion parameter |
| Nhs | = | Nield number for the fluid/solid matrix interface (fluid/solid matrix interface parameter) |
| Nr | = | buoyancy ratio parameter |
| Nt | = | thermophoresis parameter |
| = | average Nusselt number | |
| p | = | pressure |
| Pr | = | Prandtl number |
| Ra | = | thermal Rayleigh number |
| Sp | = | fin position |
| = | average Sherwood number | |
| Ss | = | a special dimensionless coordinate along the walls with its origin at X = 0 and Y = 1 (defined in [Citation10]) |
| T | = | nanofluid temperature |
| Tc | = | temperature at the right wall |
| Th | = | temperature at the left wall |
| x, y | = | Cartesian coordinates |
| u, v | = | the velocity components along x, y directions |
| Greek symbols | = | |
| α | = | effective thermal diffusivity |
| β | = | thermal expansion coefficient |
| γs | = | modified porous solid matrix thermal conductivity |
| ε | = | porosity |
| θ | = | non-dimensional temperature |
| μ | = | dynamic viscosity |
| ρ | = | fluid density |
| (ρc) | = | effective heat capacity |
| η | = | parameter defined by η = ks/knf |
| ϕ | = | relative nanoparticle volume fraction |
| ψ | = | fin angle |
| ζ | = | non-dimensional parameter defined in Eq. (14) |
| Subscripts | = | |
| 0 | = | the ambient property |
| nf | = | nanofluid phase |
| p | = | porous medium |
| s | = | solid matrix phase in porous medium |
Nomenclature
| Latin symbols | = | |
| C | = | dimensional nanoparticle volume fraction |
| C0 | = | dimensional ambient nanoparticle volume fraction |
| Da | = | Darcy number |
| DB | = | Brownian diffusion coefficient |
| DT | = | thermophoretic diffusion coefficient |
| g | = | gravitational acceleration vector |
| hfs | = | interface heat transfer coefficient between the fluid/solid matrix phases |
| K | = | permeability of the porous medium |
| k | = | thermal conductivity |
| L | = | cavity size |
| L1 | = | distance between bottom of fin and bottom of cavity |
| L2 | = | distance between top of fin and bottom of cavity |
| Le | = | Lewis number |
| Lp | = | fin length |
| Nb | = | Brownian motion parameter |
| Nhs | = | Nield number for the fluid/solid matrix interface (fluid/solid matrix interface parameter) |
| Nr | = | buoyancy ratio parameter |
| Nt | = | thermophoresis parameter |
| = | average Nusselt number | |
| p | = | pressure |
| Pr | = | Prandtl number |
| Ra | = | thermal Rayleigh number |
| Sp | = | fin position |
| = | average Sherwood number | |
| Ss | = | a special dimensionless coordinate along the walls with its origin at X = 0 and Y = 1 (defined in [Citation10]) |
| T | = | nanofluid temperature |
| Tc | = | temperature at the right wall |
| Th | = | temperature at the left wall |
| x, y | = | Cartesian coordinates |
| u, v | = | the velocity components along x, y directions |
| Greek symbols | = | |
| α | = | effective thermal diffusivity |
| β | = | thermal expansion coefficient |
| γs | = | modified porous solid matrix thermal conductivity |
| ε | = | porosity |
| θ | = | non-dimensional temperature |
| μ | = | dynamic viscosity |
| ρ | = | fluid density |
| (ρc) | = | effective heat capacity |
| η | = | parameter defined by η = ks/knf |
| ϕ | = | relative nanoparticle volume fraction |
| ψ | = | fin angle |
| ζ | = | non-dimensional parameter defined in Eq. (14) |
| Subscripts | = | |
| 0 | = | the ambient property |
| nf | = | nanofluid phase |
| p | = | porous medium |
| s | = | solid matrix phase in porous medium |
Acknowledgments
The first and second authors acknowledge the financial support of Dezful Branch, Islamic Azad University, Dezful, Iran. The first, second, and third authors are grateful to Iran Nanotechnology Initiative Council (INIC) for financial support of the present study. The authors gratefully acknowledge the Sheikh Bahaei National High Performance Computing Center (SBNHPCC) for providing computing facilities and time. SBNHPCC is supported by the Scientific and Technological Department of the Presidential Office and Isfahan University of Technology (IUT).