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ABSTRACT
This article reports a fundamental numerical study made to understand the effects of aspect ratio and thermal radiation in a porous cavity filled with nanofluid. The vertical walls of the cavity are insulated while the bottom and top horizontal walls are maintained at constant but different temperatures. The governing equations are solved by using a finite volume method (FVM) on a uniformly staggered grid system. The effects of the pertinent parameters, namely, Richardson number, aspect ratio, radiation parameter, Darcy number, and solid volume fraction are investigated in detail. The computational results are presented in the form of isotherm, streamline, midplane velocity, and Nusselt numbers. The effects of solid volume fraction and thermal radiation are not significant for and 0.5. In general, the results indicate that the convective mechanism is suppressed by radiation, which causes a reduction in the overall heat transfer rate. It is also found that the overall heat transfer rate increases with an increase of Darcy number and solid volume fraction in the presence of thermal radiation effect.
Disclosure statement
No potential conflict of interest was reported by the authors.
Nomenclature
| g | = | gravitational acceleration |
| = | specific heat | |
| Gr | = | Grashof number |
| R | = | thermal radiation |
| H | = | enclosure height |
| L | = | enclosure length |
| = | thickness of nano-layer | |
| K | = | permeability |
| k | = | thermal conductivity |
| = | mean absorption coefficient | |
| = | radiative heat flux | |
| = | average Nusselt number | |
| = | local Nusselt number | |
| p | = | fluid pressure |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| = | radius of nanoparticles | |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| = | temperature | |
| T | = | dimensionless temperature |
| u | = | velocity vector |
| U,V | = | dimensionless velocities in X- and Y-direction, respectively |
| = | lid velocity | |
| = | velocities in x- and y-direction, respectively | |
| X,Y | = | dimensionless Cartesian coordinates |
| x,y | = | Cartesian coordinates |
| = | temperature difference | |
| Da | = | Darcy number |
| = | average particle size | |
| F | = | Forchheimer coefficient |
| ϵ | = | porosity |
| = | thermal diffusivity | |
| = | thermal expansion coefficient | |
| = | dynamic viscosity | |
| = | kinematic viscosity | |
| = | density | |
| = | solid volume fraction | |
| = | ratio of thermal conductivity of nano-layers | |
| = | ratio of the thickness of nano-layer | |
| = | electrical conductivity | |
| = | Stefan–Boltzmann constant | |
| Ar | = | aspect ratio ( |
| Subscripts | = | |
| avg | = | average |
| c | = | cold wall |
| eff | = | effective |
| eq | = | equivalent |
| f | = | fluid |
| h | = | hot wall |
| nf | = | nanofluid |
| nl | = | nano-layer |
| s | = | solid |