Analytical interpretation of the local thermal non-equilibrium condition of porous media imbedded in tube heat exchangers

Local thermal non-equilibrium (LTNE) effects in the developed region of the forced convection in a circular tube filled with saturated porous medium are analytically studied at the constant wall-temperature boundary condition, as well as at the iso-flux boundary condition. The flow in the pipe is described by the Brinkman-Forchheimer-extended Darcy equation. A two-equation model is used for the energy balance. Profiles describing the velocity field obtained by perturbation techniques are used to find the temperature distributions using the successive approximation method. Moreover, the velocity and temperature fields are simulated numerically to validate the results of the analytical part. A fundamental relation and a new dimensionless number, ΔNE, for the temperature difference between the fluid and solid phases (LTNE intensity) are established based on a perturbation analysis. It is found that the LTNE intensity (ΔNE) is proportional to the product of the normalized velocity and the dimensionless temperature at LTE condition and depends on the conductivity ratio, Darcy number, and the porosity of the medium. Finally, the proposed relation for the LTNE intensity is simple and fundamental for estimation of the importance of LTNE condition.