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ABSTRACT
The present study numerically investigates the two-dimensional laminar natural convection in a differently heated rectangular enclosure with an insulated square block, in the presence of a uniform magnetic field applied in the horizontal direction. Numerical simulations were performed for the conditions of different Rayleigh and Hartmann numbers with a fixed Prandtl number. The heat transfer rate decreases with the increase in the intensity of the magnetic field. It was found that the insertion of an insulated block contributes to the enhancement of the heat transfer rate in certain ranges of the block size and the Hartmann number.
Nomenclature
| AR | = | area ratio of block and enclosure |
| B | = | magnitude of the magnetic field flux (kg/s2 A) |
| Cp | = | specific heat at constant pressure (J/kg K) |
| g | = | gravitational acceleration (m/s2) |
| Ha | = | Hartmann number |
| k | = | thermal conductivity (W/m K) |
| L | = | length of enclosure (m) |
| p | = | dimensionless pressure |
| P | = | pressure (N/m2) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | time (s) |
| T | = | temperature (K) |
| u, v | = | velocity components in the x-direction and the y-direction (m/s) |
| U, V | = | dimensionless velocity components in the X-direction and the Y-direction |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| θ | = | dimensionless temperature |
| µ | = | dynamic viscosity (kg/m s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density of fluid (kg/m3) |
| σ | = | electrical conductivity of fluid (S/m) |
| τ | = | dimensionless time scale |
| Subscripts | = | |
| C | = | cold |
| H | = | hot |
Nomenclature
| AR | = | area ratio of block and enclosure |
| B | = | magnitude of the magnetic field flux (kg/s2 A) |
| Cp | = | specific heat at constant pressure (J/kg K) |
| g | = | gravitational acceleration (m/s2) |
| Ha | = | Hartmann number |
| k | = | thermal conductivity (W/m K) |
| L | = | length of enclosure (m) |
| p | = | dimensionless pressure |
| P | = | pressure (N/m2) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | time (s) |
| T | = | temperature (K) |
| u, v | = | velocity components in the x-direction and the y-direction (m/s) |
| U, V | = | dimensionless velocity components in the X-direction and the Y-direction |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| θ | = | dimensionless temperature |
| µ | = | dynamic viscosity (kg/m s) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density of fluid (kg/m3) |
| σ | = | electrical conductivity of fluid (S/m) |
| τ | = | dimensionless time scale |
| Subscripts | = | |
| C | = | cold |
| H | = | hot |