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ABSTRACT
In this paper, an enthalpic lattice Boltzmann method formulation for 3D unsteady convection–diffusion heat transfer problems is used to overcome discontinuity issues in heterogeneous media. The new formulation is based on the appearance of a source term added to the collision step. The major achievement of the proposed enthalpic LB formulation is avoiding any interface treatments or geometry considerations even when dealing with complex geometries. The performance of the present method is tested for several three-dimensional convection–diffusion problems. Comparisons are made with the control volume method, and numerical results show excellent agreements.
Nomenclature
| a, b | = | constants in analytical velocity profile |
| A, B | = | length and high of the inner square duct |
| c | = | lattice streaming speed |
| Cp | = | heat capacity(J/kg · K) |
| cs | = | speed of sound |
| ek | = | propagation velocity in the kth direction in a lattice |
| fk | = | particle distribution function in the k direction |
| = | equilibrium particle distribution function in the k direction | |
| Fk | = | source term in the kth direction in a lattice |
| h | = | enthalpy |
| H | = | characteristic height (m) |
| L | = | characteristic length (m) |
| n | = | normal to the interface |
| Nx, Ny | = | grid mesh size |
| = | effective pressure | |
| Pe | = | Peclet number |
| rc1 | = | radius of inner cylinder |
| rc2 | = | radius of outer cylinder |
| r0 | = | pipe radius |
| S | = | source term |
| t | = | time |
| T | = | temperature |
| U | = | velocity vector |
| u, v | = | velocity components |
| wk | = | weight factor in the k direction |
| Δt | = | time step |
| Δx | = | lattice size |
| x, y | = | axial coordinates |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2/s) |
| λ | = | thermal conductivity (W/m · K) |
| ν | = | viscosity of the fluid (m2/s) |
| ρ | = | density (kg/m3) |
| τ | = | relaxation time |
| = | angular velocity | |
| Superscripts | = | |
| eq | = | equilibrium |
| Subscripts | = | |
| i, j | = | grid nodes indices |
| k | = | direction k in a lattice |
| l | = | layer suffix |
Nomenclature
| a, b | = | constants in analytical velocity profile |
| A, B | = | length and high of the inner square duct |
| c | = | lattice streaming speed |
| Cp | = | heat capacity(J/kg · K) |
| cs | = | speed of sound |
| ek | = | propagation velocity in the kth direction in a lattice |
| fk | = | particle distribution function in the k direction |
| = | equilibrium particle distribution function in the k direction | |
| Fk | = | source term in the kth direction in a lattice |
| h | = | enthalpy |
| H | = | characteristic height (m) |
| L | = | characteristic length (m) |
| n | = | normal to the interface |
| Nx, Ny | = | grid mesh size |
| = | effective pressure | |
| Pe | = | Peclet number |
| rc1 | = | radius of inner cylinder |
| rc2 | = | radius of outer cylinder |
| r0 | = | pipe radius |
| S | = | source term |
| t | = | time |
| T | = | temperature |
| U | = | velocity vector |
| u, v | = | velocity components |
| wk | = | weight factor in the k direction |
| Δt | = | time step |
| Δx | = | lattice size |
| x, y | = | axial coordinates |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2/s) |
| λ | = | thermal conductivity (W/m · K) |
| ν | = | viscosity of the fluid (m2/s) |
| ρ | = | density (kg/m3) |
| τ | = | relaxation time |
| = | angular velocity | |
| Superscripts | = | |
| eq | = | equilibrium |
| Subscripts | = | |
| i, j | = | grid nodes indices |
| k | = | direction k in a lattice |
| l | = | layer suffix |