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ABSTRACT
A finite element solution has been performed in this work to solve unsteady governing equations of natural convection in a carbon nanotube–water-filled cavity with inclined heater. The temperature of ceiling and left vertical walls is lower than that of the heater while the other walls are adiabatic. The main governing parameters are nanofluid volume fraction and Rayleigh number (Ra). It is found that the heat transfer rate shows different trends based on Rayleigh number and it increases with increase in nanoparticle volume fraction. It has been estimated that average Nusselt number (Nu) is dependent onRa through power regression models with strong positive linear correlation between ln (Nu) and ln (Ra). In particular, for the maximum time, when the solid volume fraction is varied from 0 to 0.1 the dependence between average Nu and linear Ra, on a logarithmic scale, is very high.
Nomenclature
| cp | = | specific heat (J kg−1 k−1) |
| g | = | gravitational acceleration (ms−2) |
| Gr | = | Grashof number |
| H | = | enclosure height (m) |
| k | = | thermal conductivity (Wm−1 k−1) |
| Nu | = | Nusselt number |
| p | = | dimensional pressure (kg m−1 s−2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q | = | heat flux (Wm−2) |
| Ra | = | Rayleigh number |
| Sδ | = | source term in Eq. (1) |
| T | = | fluid temperature (K) |
| t | = | dimensional time (s) |
| u | = | horizontal velocity component (ms−1) |
| U | = | dimensionless horizontal velocity component |
| v | = | vertical velocity component (ms−1) |
| V | = | dimensionless vertical velocity component |
| x | = | horizontal coordinate (m) |
| X | = | dimensionless horizontal coordinate |
| y | = | vertical coordínate(m) |
| Y | = | dimensionless vertical coordinate |
| α | = | thermal diffusivity (m2 s−1) |
| β | = | thermal expansion coefficient (K−1) |
| δ | = | dependent variables |
| Γδ | = | diffusion term in Eq. (1) |
| ϕ | = | solid volume fraction |
| μ | = | dynamic viscosity (kg m−1 s−1) |
| ν | = | kinematic viscosity (m2 s−1) |
| τ | = | dimensionless time |
| θ | = | non-dimensional temperature |
| ρ | = | density (kg m−3) |
| ψ | = | stream function |
| Subscripts | = | |
| av | = | average |
| h | = | heat source |
| c | = | cold |
| f | = | fluid |
| nf | = | nanofluid |
| s | = | solid nanoparticle |
| max | = | maximum |
| min | = | minimum |
Nomenclature
| cp | = | specific heat (J kg−1 k−1) |
| g | = | gravitational acceleration (ms−2) |
| Gr | = | Grashof number |
| H | = | enclosure height (m) |
| k | = | thermal conductivity (Wm−1 k−1) |
| Nu | = | Nusselt number |
| p | = | dimensional pressure (kg m−1 s−2) |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| q | = | heat flux (Wm−2) |
| Ra | = | Rayleigh number |
| Sδ | = | source term in Eq. (1) |
| T | = | fluid temperature (K) |
| t | = | dimensional time (s) |
| u | = | horizontal velocity component (ms−1) |
| U | = | dimensionless horizontal velocity component |
| v | = | vertical velocity component (ms−1) |
| V | = | dimensionless vertical velocity component |
| x | = | horizontal coordinate (m) |
| X | = | dimensionless horizontal coordinate |
| y | = | vertical coordínate(m) |
| Y | = | dimensionless vertical coordinate |
| α | = | thermal diffusivity (m2 s−1) |
| β | = | thermal expansion coefficient (K−1) |
| δ | = | dependent variables |
| Γδ | = | diffusion term in Eq. (1) |
| ϕ | = | solid volume fraction |
| μ | = | dynamic viscosity (kg m−1 s−1) |
| ν | = | kinematic viscosity (m2 s−1) |
| τ | = | dimensionless time |
| θ | = | non-dimensional temperature |
| ρ | = | density (kg m−3) |
| ψ | = | stream function |
| Subscripts | = | |
| av | = | average |
| h | = | heat source |
| c | = | cold |
| f | = | fluid |
| nf | = | nanofluid |
| s | = | solid nanoparticle |
| max | = | maximum |
| min | = | minimum |