Analysis of Local Thermal Equilibrium Assumption in Transient Forced Convection in a Graphite Foam Channel

In this study, the validity of Local Thermal Equilibrium (LTE) assumption in the transient forced convection of a rectangular channel filled with a block of graphite foam is examined numerically. The governing macroscopic energy conservation equations for solid and gas phases are derived by taking the average of the microscopic one over the averaging volume. Initially, LTE is in existence between the phases and then, the fluid temperature at the channel inlet is suddenly raised. Besides, an appropriate insulation is provided for the wall of the channel. Hence, a transient one-dimensional Local Thermal Non-Equilibrium (LTNE) model is considered in the numerical investigation. Thermo-physical properties of the solid and fluid phases are presumed to be constant. The graphite foam porosity is spatially uniform and constant. The impact of two dimensionless variables such as fluid to solid Nusselt number (Nu(fs)) and Reynolds number (Re) on the LTE assumption is extensively investigated. . It was found that the dimensionless time required to attain LTE between the phases (tau(LTE)) increases with the increasing value of Reynolds number. However, the real-time (sigma(LTE)) corresponding to tau(LTE) was found to be nearly 4 sec over the range of Re numbers studied. Additionally, an increase in the Nu(fs), resulted in a decrease in TLTE for a constant value of Re number and sigma(LTE) varied from 1.5 to 5 sec. As a result, the obtained findings showed that it is reasonable to assume the LTE between the phases under the investigated conditions.