Numerical investigation on the thermal non-equilibrium in low-velocity reacting flow within porous media

This paper addresses the thermal non-equilibrium problem for a low-velocity reacting flow within isotropic porous media. The method of volume-averaging is employed to derive the macroscopic thermal transport equation for the fluid phase inside the porous medium including a heat source due to a homogenous chemical reaction, which is then closed by representing the temperature deviation through a constitutive equation. Theoretical treatment indicates that the contribution of the non-equilibrium due to reaction heat to the macroscopic heat transfer comes up in terms of an additional energy source rather than affecting thermal transport properties. Through dimensional analysis, this term can be interpreted as a convective transport of the reaction heat. Numerical computations are conducted by solving the closure problems at the pore scale for the fluid phase in a spatially periodic representative elementary volume (REV). Simulation results show that the convective coefficient related with the reaction heat is dependent on the Thiele modulus number, and the arrangement of cylinders. For the inline case, when the Péclet number is less than 10, a part of reaction heat will feed back to the upstream due to local conductivity, for Péclet number greater than 10 this part of energy will be transmitted to the downstream. For the staggered case, the same conclusion holds for smaller Péclet number, while the non-equilibrium will gradually decay to zero as the Péclet number increases. In addition, the other effective coefficients, such as effective conductivity, surface convective heat transfer coefficient are calculated with and without inertia.