![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
The present work deals with the numerical simulation of contact melting using a cell-splitting enthalpy method, which is an improvement over the conventional enthalpy-porosity method. It is demonstrated that such a method is far superior to the enthalpy-porosity method which not only is unable to capture the interface precisely but is also unable to capture the melt rates, unless the coefficients are back-fitted with the experimental data. In contact melting, the contact layer is thin and hence to resolve the flow, fine grids have to be used. A novel integral model is proposed where a single control volume is used in the contact layer. A parametric study is performed for contact melting in a square geometry and a correlation is evolved for the melt rates. The shapes of the solid during contact and noncontact melting are discussed and the physical mechanisms that decide the evolution are articulated.
Nomenclature
| Ar | = | Archimedes number |
| CP | = | specific heat (J/kg K) |
| FBody | = | body force on the solid (N) |
| FSurface | = | surface force on the solid (N) |
| f | = | liquid fraction |
| g | = | acceleration due to gravity (m/s2) |
| = | unit vector along the acceleration due to gravity vector | |
| h | = | enthalpy (J/kg) |
| k | = | thermal conductivity (W/m K) |
| L | = | characteristic length (m) |
| = | unit normal | |
| P | = | pressure (N/m2) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| St | = | Stefan number |
| T | = | temperature (K) |
| TM | = | melting temperature (K) |
| t | = | time (s) |
| u,v | = | velocity components (m/s) |
| V | = | volume (m3) |
| V | = | velocity vector (m/s) |
| x,y | = | coordinate directions (m) |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| γ | = | diffusion coefficient of a generic transport variable |
| δ | = | thickness of the contact layer (m) |
| ΔHM | = | latent heat of melting (J/kg) |
| θ | = | nondimensional temperature |
| μ | = | dynamic viscosity (N s/m2) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| τ | = | nondimensional time |
| ϕ | = | generic transport variable |
| Subscripts | = | |
| g | = | grid |
| I | = | solid–liquid interface |
| L | = | liquid |
| M | = | evaluated at melting temperature |
| S | = | solid |
| W | = | wall |
| Superscript | = | |
| * | = | nondimensional variables |
Nomenclature
| Ar | = | Archimedes number |
| CP | = | specific heat (J/kg K) |
| FBody | = | body force on the solid (N) |
| FSurface | = | surface force on the solid (N) |
| f | = | liquid fraction |
| g | = | acceleration due to gravity (m/s2) |
| = | unit vector along the acceleration due to gravity vector | |
| h | = | enthalpy (J/kg) |
| k | = | thermal conductivity (W/m K) |
| L | = | characteristic length (m) |
| = | unit normal | |
| P | = | pressure (N/m2) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| St | = | Stefan number |
| T | = | temperature (K) |
| TM | = | melting temperature (K) |
| t | = | time (s) |
| u,v | = | velocity components (m/s) |
| V | = | volume (m3) |
| V | = | velocity vector (m/s) |
| x,y | = | coordinate directions (m) |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| γ | = | diffusion coefficient of a generic transport variable |
| δ | = | thickness of the contact layer (m) |
| ΔHM | = | latent heat of melting (J/kg) |
| θ | = | nondimensional temperature |
| μ | = | dynamic viscosity (N s/m2) |
| ν | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| τ | = | nondimensional time |
| ϕ | = | generic transport variable |
| Subscripts | = | |
| g | = | grid |
| I | = | solid–liquid interface |
| L | = | liquid |
| M | = | evaluated at melting temperature |
| S | = | solid |
| W | = | wall |
| Superscript | = | |
| * | = | nondimensional variables |