http://orcid.org/0000-0002-4750-0227
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ABSTRACT
The effect of surface radiation on laminar natural convection in a rotating cavity with a discrete heater has been analyzed numerically. The enclosure is insulated at the bottom and top, heated by a constant temperature from the discrete heater located on the bottom wall, and cooled by a constant temperature from the side walls. Governing equations with corresponding initial and boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The effects of surface emissivity, Rayleigh number, and Taylor number on the fluid flow and heat transfer have been studied. Obtained results have revealed that rotation can be a very good control parameter for heat transfer and fluid flow.
Nomenclature
| Fk−i | = | view factor from kth element to the ith element of the cavity |
| g | = | gravitational acceleration (m s−2) |
| H | = | size of the cavity (m) |
| Jk | = | radiosity for the kth differential element (W m−2) |
| k | = | thermal conductivity (W m−1 K−1) |
| = | radiation number | |
| = | average convective Nusselt number at the heater | |
| = | average radiative Nusselt number at the heater | |
| NS | = | number of surface elements in the cavity |
| p | = | dimensional pressure (Pa) |
| = | Prandtl number | |
| qk | = | irradiance for the kth differential element (W m−2) |
| qrad | = | dimensional radiative heat flux (W m−2) |
| Qrad | = | dimensionless net radiative heat flux |
| = | Rayleigh number | |
| Rk | = | dimensionless radiosity of the kth element of the cavity |
| t | = | dimensional time (s) |
| T | = | dimensional temperature (K) |
| Tc | = | dimensional cooled wall temperature (K) |
| Th | = | dimensional heated wall temperature (K) |
| T0 = (Th + Tc)/2 | = | dimensional mean temperature of heated and cooled walls (K) |
| = | Taylor number | |
| Vx | = | dimensional velocity component in x-direction (m s−1) |
| Vy | = | dimensional velocity component in y-direction (m s−1) |
| u | = | dimensionless velocity component in x-direction |
| v | = | dimensionless velocity component in y-direction |
| = | dimensional Cartesian coordinates (m) | |
| x, y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2 s−1) |
| β | = | thermal expansion coefficient (K−1) |
| = | temperature parameter | |
| ε | = | surface emissivity |
| θ | = | dimensionless temperature |
| μ | = | dynamic viscosity (Pa · s) |
| ν | = | kinematic viscosity (m2 s−1) |
| = | angular velocity (s−1) | |
| ρ | = | density of the fluid (kg m−3) |
| σ | = | Stefan–Boltzmann constant |
| τ | = | dimensionless time |
| ϕ | = | rotation angle |
| = | dimensional stream function (m2 s−1) | |
| ψ | = | dimensionless stream function |
| = | dimensional vorticity (s−1) | |
| ω | = | dimensionless vorticity |
| Subscripts | = | |
| c | = | cooled wall |
| con | = | convective |
| h | = | heated wall |
| max | = | maximum value |
| rad | = | radiative |
Nomenclature
| Fk−i | = | view factor from kth element to the ith element of the cavity |
| g | = | gravitational acceleration (m s−2) |
| H | = | size of the cavity (m) |
| Jk | = | radiosity for the kth differential element (W m−2) |
| k | = | thermal conductivity (W m−1 K−1) |
| = | radiation number | |
| = | average convective Nusselt number at the heater | |
| = | average radiative Nusselt number at the heater | |
| NS | = | number of surface elements in the cavity |
| p | = | dimensional pressure (Pa) |
| = | Prandtl number | |
| qk | = | irradiance for the kth differential element (W m−2) |
| qrad | = | dimensional radiative heat flux (W m−2) |
| Qrad | = | dimensionless net radiative heat flux |
| = | Rayleigh number | |
| Rk | = | dimensionless radiosity of the kth element of the cavity |
| t | = | dimensional time (s) |
| T | = | dimensional temperature (K) |
| Tc | = | dimensional cooled wall temperature (K) |
| Th | = | dimensional heated wall temperature (K) |
| T0 = (Th + Tc)/2 | = | dimensional mean temperature of heated and cooled walls (K) |
| = | Taylor number | |
| Vx | = | dimensional velocity component in x-direction (m s−1) |
| Vy | = | dimensional velocity component in y-direction (m s−1) |
| u | = | dimensionless velocity component in x-direction |
| v | = | dimensionless velocity component in y-direction |
| = | dimensional Cartesian coordinates (m) | |
| x, y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2 s−1) |
| β | = | thermal expansion coefficient (K−1) |
| = | temperature parameter | |
| ε | = | surface emissivity |
| θ | = | dimensionless temperature |
| μ | = | dynamic viscosity (Pa · s) |
| ν | = | kinematic viscosity (m2 s−1) |
| = | angular velocity (s−1) | |
| ρ | = | density of the fluid (kg m−3) |
| σ | = | Stefan–Boltzmann constant |
| τ | = | dimensionless time |
| ϕ | = | rotation angle |
| = | dimensional stream function (m2 s−1) | |
| ψ | = | dimensionless stream function |
| = | dimensional vorticity (s−1) | |
| ω | = | dimensionless vorticity |
| Subscripts | = | |
| c | = | cooled wall |
| con | = | convective |
| h | = | heated wall |
| max | = | maximum value |
| rad | = | radiative |