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ABSTRACT
In this paper, we propose a direct extension of a previous work presented by Hamila et al. [Citation1] dealing with the simulation of conjugate heat transfer by conduction in heterogeneous media. In [Citation1] a novel enthalpy-based lattice Boltzmann (LB) formulation was successfully simulated in several conjugate heat transfer problems by conduction. We propose testing this enthalpic LB formulation in solving convection-diffusion heat transfer problems in heterogeneous media. The main idea of this formulation is to introduce an extra source term, avoiding any additional treatment of the distribution functions at the interface. Continuity of temperature and normal heat flux at the interface is satisfied automatically. The performance of the present method is successfully validated by comparison to the control volume methods (CVMs) solutions of several heat convection-diffusion problems in heterogeneous media.
Nomenclature
| a, b | = | constants in analytical velocity profile |
| c | = | lattice streaming speed |
| Cp | = | heat capacity (J/KgK) |
| cs | = | speed of sound |
| ek | = | propagation velocity in the kth direction in a lattice |
| fk | = | particle distribution function in the kth direction |
| = | equilibrium particle distribution function in the kth 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 |
| ra | = | radius of the inner cylinder |
| rb | = | radius of the outer cylinder |
| Re | = | Reynolds number |
| Rec | = | critical Reynolds number |
| S | = | source term |
| t | = | time |
| T | = | temperature |
| U | = | velocity vector |
| u, v | = | velocity components |
| up | = | peak velocity |
| wk | = | weight factor in the kth direction |
| Δt | = | time step |
| Δx | = | lattice size |
| x, y | = | axial coordinates |
| Greek | = | |
| α | = | thermal diffusivity (m2/s) |
| λ | = | thermal conductivity (W/mK) |
| ν | = | viscosity of the fluid (m2/s) |
| ρ | = | density (Kg/m3) |
| τ | = | relaxation time |
| ωa | = | angular velocity |
| Subscripts | = | |
| f | = | fluid |
| i, j | = | grid nodes indices |
| k | = | direction k in a lattice |
| l | = | layer suffix |
| s | = | solid |
| Superscripts | = | |
| eq | = | equilibrium |
Nomenclature
| a, b | = | constants in analytical velocity profile |
| c | = | lattice streaming speed |
| Cp | = | heat capacity (J/KgK) |
| cs | = | speed of sound |
| ek | = | propagation velocity in the kth direction in a lattice |
| fk | = | particle distribution function in the kth direction |
| = | equilibrium particle distribution function in the kth 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 |
| ra | = | radius of the inner cylinder |
| rb | = | radius of the outer cylinder |
| Re | = | Reynolds number |
| Rec | = | critical Reynolds number |
| S | = | source term |
| t | = | time |
| T | = | temperature |
| U | = | velocity vector |
| u, v | = | velocity components |
| up | = | peak velocity |
| wk | = | weight factor in the kth direction |
| Δt | = | time step |
| Δx | = | lattice size |
| x, y | = | axial coordinates |
| Greek | = | |
| α | = | thermal diffusivity (m2/s) |
| λ | = | thermal conductivity (W/mK) |
| ν | = | viscosity of the fluid (m2/s) |
| ρ | = | density (Kg/m3) |
| τ | = | relaxation time |
| ωa | = | angular velocity |
| Subscripts | = | |
| f | = | fluid |
| i, j | = | grid nodes indices |
| k | = | direction k in a lattice |
| l | = | layer suffix |
| s | = | solid |
| Superscripts | = | |
| eq | = | equilibrium |