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ABSTRACT
In the present study, a new method for simulation of the conjugate heat transfer conditions at the curved interface of two media with different thermal properties is proposed based on the ghost fluid lattice Boltzmann method (GF-LBM). The proposed method significantly benefits from the inherent feature of the GF-LBM in availability of the temperature gradient normal to the interface. To test the accuracy of the presented method, three different case studies are simulated. The results revealed the second-order accuracy of the proposed conjugate heat transfer formulation. Furthermore, when compared to the available analytical solutions, the results of this study showed better agreement compared to the results of the other available methods.
Nomenclature
| c | = | lattice streaming speed |
| Cd | = | drag coefficient |
| cs | = | speed of sound |
| d | = | cylinder diameter, (m) |
| ei | = | discrete velocity |
| FD | = | drag force per unite length of cylinder, (kg m/s2) |
| fi | = | density distribution functions |
| = | equilibrium distribution functions | |
| = | postcollision distribution functions | |
| gi | = | internal energy distribution functions |
| = | internal energy equilibrium distribution functions | |
| H | = | half channel height, (m) |
| k | = | thermal conductivity, (W/mK) |
| n | = | normal coordinate |
| Pr | = | Prandtl Number |
| q″ | = | heat flux vector, (W/m2) |
| q″′ | = | volumetric heat generation |
| r | = | radios,(m) |
| Re | = | Reynolds Number |
| T | = | temperature, (K) |
| Tw | = | solid obstacle temperature, (k) |
| u | = | macroscopic velocity vector, (m/s) |
| = | average velocity, (m/s) | |
| Umax | = | maximum velocity at the center of the channel, (m/s) |
| wi | = | equilibrium distribution weight |
| x, y | = | x- and y-coordinate directions, (m) |
| Greek symbols | = | |
| α | = | thermal diffusivity, (m2/s) |
| β | = | blockage ratio (β = d/2H) |
| Γ | = | interface of two media |
| γ | = | gap ratio |
| δ | = | gap between the channel wall and the cylinder, (m) |
| Δℓ | = | distance between the GP and the related IP, (m) |
| δt | = | time step |
| δx | = | lattice step |
| υ | = | kinematic viscosity, (m2/s) |
| ρ | = | density, (kg/m3) |
| τg | = | dimensionless internal energy relaxation time |
| τυ | = | dimensionless momentum relaxation time |
| φ | = | general macroscopic variables |
| ωi | = | angular velocity, (rad/s) |
| Superscripts | = | |
| eq | = | equilibrium |
| neq | = | nonequilibrium |
| Subscripts | = | |
| int | = | interface of two media |
| IP | = | image point |
| BI | = | boundary intersection point |
| GP | = | ghost point |
| Γ | = | interface boundary |
| Ω1 | = | domain 1 |
| Ω2 | = | domain 2 |
Nomenclature
| c | = | lattice streaming speed |
| Cd | = | drag coefficient |
| cs | = | speed of sound |
| d | = | cylinder diameter, (m) |
| ei | = | discrete velocity |
| FD | = | drag force per unite length of cylinder, (kg m/s2) |
| fi | = | density distribution functions |
| = | equilibrium distribution functions | |
| = | postcollision distribution functions | |
| gi | = | internal energy distribution functions |
| = | internal energy equilibrium distribution functions | |
| H | = | half channel height, (m) |
| k | = | thermal conductivity, (W/mK) |
| n | = | normal coordinate |
| Pr | = | Prandtl Number |
| q″ | = | heat flux vector, (W/m2) |
| q″′ | = | volumetric heat generation |
| r | = | radios,(m) |
| Re | = | Reynolds Number |
| T | = | temperature, (K) |
| Tw | = | solid obstacle temperature, (k) |
| u | = | macroscopic velocity vector, (m/s) |
| = | average velocity, (m/s) | |
| Umax | = | maximum velocity at the center of the channel, (m/s) |
| wi | = | equilibrium distribution weight |
| x, y | = | x- and y-coordinate directions, (m) |
| Greek symbols | = | |
| α | = | thermal diffusivity, (m2/s) |
| β | = | blockage ratio (β = d/2H) |
| Γ | = | interface of two media |
| γ | = | gap ratio |
| δ | = | gap between the channel wall and the cylinder, (m) |
| Δℓ | = | distance between the GP and the related IP, (m) |
| δt | = | time step |
| δx | = | lattice step |
| υ | = | kinematic viscosity, (m2/s) |
| ρ | = | density, (kg/m3) |
| τg | = | dimensionless internal energy relaxation time |
| τυ | = | dimensionless momentum relaxation time |
| φ | = | general macroscopic variables |
| ωi | = | angular velocity, (rad/s) |
| Superscripts | = | |
| eq | = | equilibrium |
| neq | = | nonequilibrium |
| Subscripts | = | |
| int | = | interface of two media |
| IP | = | image point |
| BI | = | boundary intersection point |
| GP | = | ghost point |
| Γ | = | interface boundary |
| Ω1 | = | domain 1 |
| Ω2 | = | domain 2 |