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ABSTRACT
The MHD phase change heat transfer of a phase change substance in the presence of a uniform magnetic field is theoretically studied in a cavity. A fixed grid method associated with the enthalpy–porosity method is utilized. The governing equations are transformed into a non-dimensional form and solved using the finite element method. The impacts of the crucial parameters such as the Hartmann number and the inclination angle on the phase change process are investigated. It is found that any increase in Hartmann number and the inclination angle of the cavity leads to a decrease in the rate of the melting process.
Nomenclature
| Amush | = | mushy-zone constant (Carman–Koseny equation constant) |
| a | = | enclosure inclination angle |
| B0 | = | magnetic induction |
| C | = | specific heat (J/kg K) |
| Cp | = | specific heat in constant pressure (J/kg K) |
| f | = | nondimensional liquid fraction |
| g | = | gravity (m/s2) |
| Ha | = | Hartmann number |
| k | = | thermal conductivity (W/m K) |
| L | = | latent heat of fusion (J/kg) |
| Lx | = | length in x-direction (m) |
| Ly | = | length in y-direction (m) |
| N | = | total number of grid nodes |
| = | average Nusselt number | |
| P | = | pressure (Pa) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| S(T) | = | Carman–Kozeny equation (source term) |
| Ste | = | Stefan number |
| T | = | temperature (K) |
| t | = | time (s) |
| Tf | = | melting temperature (K) |
| u | = | velocity in the x-direction (m/s) |
| v | = | velocity in the y-direction (m/s) |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| ε | = | Carman–Kozeny equation constant |
| γ | = | the ratio of thermal diffusivity |
| φ(T) | = | liquid fraction |
| µ | = | dynamic viscosity (kg/m.s) |
| θ | = | nondimensional temperature |
| ρ | = | density (kg/m3) |
| σ | = | electrical conductivity |
| ν | = | kinematic viscosity (m2/s) |
| ξ(x,y) | = | horizontal and vertical coordinate in a unit square |
| ΔT | = | mushy-zone temperature range (K) |
| Subscripts | = | |
| c | = | cold |
| F | = | fusion |
| h | = | hot |
| p | = | interface position |
| l | = | liquid phase |
| k | = | node number |
| R | = | ratio |
| i | = | residual number |
| s | = | solid phase |
Nomenclature
| Amush | = | mushy-zone constant (Carman–Koseny equation constant) |
| a | = | enclosure inclination angle |
| B0 | = | magnetic induction |
| C | = | specific heat (J/kg K) |
| Cp | = | specific heat in constant pressure (J/kg K) |
| f | = | nondimensional liquid fraction |
| g | = | gravity (m/s2) |
| Ha | = | Hartmann number |
| k | = | thermal conductivity (W/m K) |
| L | = | latent heat of fusion (J/kg) |
| Lx | = | length in x-direction (m) |
| Ly | = | length in y-direction (m) |
| N | = | total number of grid nodes |
| = | average Nusselt number | |
| P | = | pressure (Pa) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| S(T) | = | Carman–Kozeny equation (source term) |
| Ste | = | Stefan number |
| T | = | temperature (K) |
| t | = | time (s) |
| Tf | = | melting temperature (K) |
| u | = | velocity in the x-direction (m/s) |
| v | = | velocity in the y-direction (m/s) |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| ε | = | Carman–Kozeny equation constant |
| γ | = | the ratio of thermal diffusivity |
| φ(T) | = | liquid fraction |
| µ | = | dynamic viscosity (kg/m.s) |
| θ | = | nondimensional temperature |
| ρ | = | density (kg/m3) |
| σ | = | electrical conductivity |
| ν | = | kinematic viscosity (m2/s) |
| ξ(x,y) | = | horizontal and vertical coordinate in a unit square |
| ΔT | = | mushy-zone temperature range (K) |
| Subscripts | = | |
| c | = | cold |
| F | = | fusion |
| h | = | hot |
| p | = | interface position |
| l | = | liquid phase |
| k | = | node number |
| R | = | ratio |
| i | = | residual number |
| s | = | solid phase |