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ABSTRACT
A lattice Boltzmann model is proposed with a newly modified equilibrium distribution function for solving the conservation form of the energy equation to treat the interphase conjugate heat transfer problems under both steady state and unsteady state. The temperature and heat flux continuity conditions at the interface can be inherently satisfied without needing any additional treatments, such as iterative computation, correcting procedure for the incoming distribution function, and the complicated calculation procedure for the source term, to account for the interphase conjugate heat transfer. The implementation of the present LB model, therefore, is more straightforward and more efficient than those in most previous models, especially for problems with complex interfaces. The applicability and accuracy of the proposed LB model were evaluated by some benchmark problems including both simple flat interface and complex interface geometry. The results show excellent agreements with analytical solutions or finite volume results, demonstrating that the present model can serve as a promising numerical technique for dealing with fluid flow and heat transfer in complex heterogeneous systems.
Nomenclature
| Cp | = | heat capacity |
| c | = | lattice speed |
| cs | = | lattice speed of sound |
| ds | = | side length of solid blocks |
| e | = | discrete particle velocity |
| E2 | = | relative L2-norm error |
| fb | = | buoyancy force |
| g | = | acceleration of gravity |
| g | = | distribution function |
| H | = | height |
| J | = | advective–diffusive flux |
| k | = | thermal conductivity |
| L | = | length |
| n | = | normal unit vector |
| Ns | = | number of the solid blocks |
| Nu | = | Nusselt number |
| Pe | = | Péclet number |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| RC | = | heat capacity ratio |
| Rk | = | thermal conductivity ratio |
| Rα | = | thermal diffusivity ratio |
| S | = | source term |
| S | = | relaxation parameter |
| T | = | temperature |
| Tref | = | reference temperature |
| Th | = | hot temperature |
| Tc | = | cold temperature |
| t | = | time |
| u | = | velocity |
| U | = | reference velocity |
| w | = | weighting coefficients |
| α | = | diffusivity |
| β | = | thermal expansion coefficients |
| Γ | = | diffusion coefficient |
| δ | = | boundary layer thickness |
| δx | = | lattice spacing |
| δt | = | time step |
| ε | = | porosity |
| ϕ | = | scalar |
| τg | = | relaxation time |
| ρ | = | density |
| ν | = | kinematic viscosity |
| ζ | = | small parameter |
| Subscripts | = | |
| 0 | = | reference |
| 1, 2, 3 | = | phase component |
| numeric | = | numerical solution |
| exact | = | exact solution |
| s | = | solid |
| l | = | liquid |
| α | = | direction index |
Nomenclature
| Cp | = | heat capacity |
| c | = | lattice speed |
| cs | = | lattice speed of sound |
| ds | = | side length of solid blocks |
| e | = | discrete particle velocity |
| E2 | = | relative L2-norm error |
| fb | = | buoyancy force |
| g | = | acceleration of gravity |
| g | = | distribution function |
| H | = | height |
| J | = | advective–diffusive flux |
| k | = | thermal conductivity |
| L | = | length |
| n | = | normal unit vector |
| Ns | = | number of the solid blocks |
| Nu | = | Nusselt number |
| Pe | = | Péclet number |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| RC | = | heat capacity ratio |
| Rk | = | thermal conductivity ratio |
| Rα | = | thermal diffusivity ratio |
| S | = | source term |
| S | = | relaxation parameter |
| T | = | temperature |
| Tref | = | reference temperature |
| Th | = | hot temperature |
| Tc | = | cold temperature |
| t | = | time |
| u | = | velocity |
| U | = | reference velocity |
| w | = | weighting coefficients |
| α | = | diffusivity |
| β | = | thermal expansion coefficients |
| Γ | = | diffusion coefficient |
| δ | = | boundary layer thickness |
| δx | = | lattice spacing |
| δt | = | time step |
| ε | = | porosity |
| ϕ | = | scalar |
| τg | = | relaxation time |
| ρ | = | density |
| ν | = | kinematic viscosity |
| ζ | = | small parameter |
| Subscripts | = | |
| 0 | = | reference |
| 1, 2, 3 | = | phase component |
| numeric | = | numerical solution |
| exact | = | exact solution |
| s | = | solid |
| l | = | liquid |
| α | = | direction index |