Transient analysis of forced convective incompressible flows through porous media

The study under investigation aims at exploring the thermal response of a packed bed under transient condition. The analysis is made for an incompressible fluid flow through a two-dimensional bed, which consists of spherical beads that are packed randomly. In addition, the generalized momentum equation was employed that takes into account the non-Darcian terms, such as the inertial and viscous effects. Moreover, the porosity variation in the bed was simulated using the decaying exponential function. The energy transport process was modeled using separate energy equations that account for the local fluid and the solid temperatures. The convective energy mode between the fluid and solid phases, which emerges when using the two-equation model, was formulated using a documented experimental correlation. Furthermore, the thermal dispersion phenomenon due to mixing and recirculation of local fluid streams was incorporated in the modeling of the fluid phase energy equation.; The choice of three non-dimensional parameters was found to depict most of the mechanisms associated with the energy transport process over abroad range of thermophysical properties. These parameters are the particle Reynolds number (Re{dollar}rmsb{lcub}p{rcub}),{dollar} the Darcy number (Da) and the solid-to-fluid thermal diffusivity ratio {dollar}rm(alphasb{lcub}s{rcub}/alphasb{lcub}f{rcub}).{dollar} Next, the implication of the non-Darcian terms was found to have a profound impact on modeling the dynamic response and, as a result, the thermal response in a packed bed. In addition, the incorporation of thermal dispersion effect was found to greatly enhance the heat transfer coefficient. Unlike the transverse dispersion, the axial dispersion was found to have very limited contribution to the overall increase in thermal capability. The effect of the non-Darcian and thermal dispersion terms was presented in integrated forms using error maps, which estimate the percentage error in neglecting any of the non-Darcian terms or the thermal dispersion effects.; The assessment of local thermal equilibrium LTE condition and the one-dimensional approach in simulating the energy transport was performed. The study yields that the LTE condition is plausible only when the ratio of thermal conductivity of the fluid and the solid are close to unity. Also, the one-dimensional can be justified for solid-to-fluid thermal diffusivity ratios of the order of unity.