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ABSTRACT
A method is proposed for the evaluation of the interfacial conduction heat transfer coefficient in two-temperature macroscopic models of homogeneous fluid-saturated porous media. It is based on the numerical solutions of a microscopic model of unsteady conduction heat transfer in periodic unit cells, with different uniform initial temperatures of the fluid and solid. A novel formulation of the microscopic model in the fully developed regime is also proposed. Results for the variation of interfacial conduction Nusselt number with porosity, fluid–solid thermal conductivity ratio, and fluid–solid thermal diffusivity ratio are presented and discussed for four two-dimensional and two three-dimensional cases.
Nomenclature
| asf | = | interfacial area per unit volume |
| Asf | = | interfacial area between the solid and fluid regions within a periodic unit cell |
| h | = | interfacial conduction heat transfer coefficient |
| H | = | characteristic length |
| kr | = | thermal conductivity ratio, ks/kf |
| ks, kf | = | thermal conductivities of the solid and fluid phases, respectively |
| kss, ksf, kfs, kff | = | thermal cross conductivities in the volume-averaged equations |
| ks,eff, kf,eff | = | effective thermal conductivities of the solid and fluid phases, respectively |
| L | = | characteristic spacing |
| = | unit normal to the interface between the phases, pointing into the fluid phase | |
| Nuf | = | interfacial conduction Nusselt number |
| = | interfacial heat transfer rate per unit volume | |
| rh,pore | = | hydraulic radius of a pore |
| t | = | time |
| Ts, Tf | = | solid and fluid temperatures, respectively |
| = | intrinsic phase-average values of Ts and Tf, respectively | |
| V | = | representative elementary volume |
| Vcell | = | volume of a periodic unit cell |
| Vs, Vf | = | volume occupied by the solid and fluid phases, respectively, within either V or Vcell |
| αr | = | thermal diffusivity ratio, αs/αf |
| αs, αf | = | thermal diffusivity of the solid and fluid phases, respectively |
| ε | = | porosity |
| (ρc)s, (ρc)f | = | volumetric heat capacity of the solid and fluid phases, respectively |
| τ | = | dimensionless time |
| θs, θs | = | solid and fluid dimensionless temperatures, respectively |
| = | intrinsic phase-average values of θs and θs, respectively | |
| ϕs, ϕf | = | solid and fluid dimensionless temperatures in the fully developed regime |
| = | intrinsic phase average values of ϕs and ϕf, respectively |
Nomenclature
| asf | = | interfacial area per unit volume |
| Asf | = | interfacial area between the solid and fluid regions within a periodic unit cell |
| h | = | interfacial conduction heat transfer coefficient |
| H | = | characteristic length |
| kr | = | thermal conductivity ratio, ks/kf |
| ks, kf | = | thermal conductivities of the solid and fluid phases, respectively |
| kss, ksf, kfs, kff | = | thermal cross conductivities in the volume-averaged equations |
| ks,eff, kf,eff | = | effective thermal conductivities of the solid and fluid phases, respectively |
| L | = | characteristic spacing |
| = | unit normal to the interface between the phases, pointing into the fluid phase | |
| Nuf | = | interfacial conduction Nusselt number |
| = | interfacial heat transfer rate per unit volume | |
| rh,pore | = | hydraulic radius of a pore |
| t | = | time |
| Ts, Tf | = | solid and fluid temperatures, respectively |
| = | intrinsic phase-average values of Ts and Tf, respectively | |
| V | = | representative elementary volume |
| Vcell | = | volume of a periodic unit cell |
| Vs, Vf | = | volume occupied by the solid and fluid phases, respectively, within either V or Vcell |
| αr | = | thermal diffusivity ratio, αs/αf |
| αs, αf | = | thermal diffusivity of the solid and fluid phases, respectively |
| ε | = | porosity |
| (ρc)s, (ρc)f | = | volumetric heat capacity of the solid and fluid phases, respectively |
| τ | = | dimensionless time |
| θs, θs | = | solid and fluid dimensionless temperatures, respectively |
| = | intrinsic phase-average values of θs and θs, respectively | |
| ϕs, ϕf | = | solid and fluid dimensionless temperatures in the fully developed regime |
| = | intrinsic phase average values of ϕs and ϕf, respectively |