Effects Of Boundary Conditions And Layered Filling On The Flow And Heat Transfer In A Porous Channel Under Local Thermal Non-equilibrium Condition

The effects of boundary conditions and layered filling on the flow and heat transfer in a porous channel under local thermal non-equilibrium condition are analyzed in the work. For the research on the effect of boundary conditions, two approaches for an adiabatic boundary condition at the wall of a porous channel are analyzed in this work: the sum of the heat flux through the solid phase and the heat flux through the liquid phase is 0(Model A); the heat flux through the solid phase and the heat flux through the liquid phase are both 0(Model B). The micro-channel is modeled as a porous channel, Darcy- Brinkman is employed for the flow and local thermal non-equilibrium is employed for the heat transfer, the analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived, the analytical solutions for the heat flux distribution at the channel wall and the overall Nusselt number are also derived. The influence of pertinent parameters, Darcy number, Da, and effective thermal conductivity ratio, k, on the fluid and solid phase temperature distributions, the heat flux distribution and the overall Nusselt number are discussed. The applicability of the models A and B are discussed, model A is applicable when the ratio ofthe thermal conductivity of the cover plate to the thermal conductivity of the solid, C, is relatively large and model B is applicable when C is small and close to 0.For the research on the flow and heat transfer in a layered porous channel, the symmetry computational domain of the porous channel is chosen as the object of the study, there are two different regions, in which the porosity, permeability, thermal conductivity are different, in the domain, i.e., region 1(near the heated wall) and region 2(away from the heated wall). Darcy- Brinkman is employed for the flow and local thermal non-equilibrium is employed for the heat transfer in this work, the analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived, the analytical solutions for the overall Nusselt number are also derived. The influence of pertinent parameters, Darcy number, the dimensionless height of region 1, Biot number, the ratio of the effective thermal conductivity of fluid of the two regions to the effective thermal conductivity of solid of region 1, the ratio of the effective thermal conductivity of solid of the two regions to the effective thermal conductivity of solid of region 1 on the velocity distribution, the fluid and solid phase temperature distributions and the overall Nusselt number are discussed. It is found that the Nusselt number of the porous channel which consists of two layers can be larger than the porous channel which consists of one layer when Da1?Da2 and k1?k2, and there is a dimensionless height of region 1,?1, maximizing the Nusselt number for the certain parameters.