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

Experimental based numerical approach for determination of volumetric heat transfer coefficients of modified graphite foams

Graphite-based porous materials are emerging as attractive alternatives to metals for use as heat dissipation elements in thermal management applications. While having several desirable features such as high thermal conductivity and low density, graphite foam heat sinks also tend to have low permeability that can limit transport of working fluid within the component and result in inefficient heat transfer. In order to improve their heat dissipation performance, graphite foams can be modified by channels drilled in various arrangements. However, the heat transfer characteristics of such modified graphite foams are not well characterized. In order to address this problem, we report novel empirical correlations for graphite foams modified in a specific configuration where circular channels with 2 mm diameter are drilled in graphite foam along the flow direction in a staggered arrangement. Then, volumetric heat transfer coefficients between the modified graphite foam and a stream of air are obtained by using transient single-blow technique (TSBT). The transient one-dimensional local thermal nonequilibrium (LTNE) model is employed for determination of the volumetric heat transfer coefficient from experimentally obtained data. Nine different modified graphite foam samples of various L/H ratios are studied in experiments and an empirical correlation of the form Nu(v) = CRea for each sample is derived. Empirical correlations for three different sample lengths (L = 27 mm, 52 mm, 76 mm) at a fixed height are also developed in the form of Nu(v) = CRea(L/H)(b). The novel empirical correlations in question are valid for the Reynolds (Re) number varying from approximately 1000 to 10000. Results show that Nuv generally increases with the increasing value of Re and L at a fixed value of H and the uncertainties associated with Re and Nu(v) are evaluated to be less than 1.3% and 3.6%, respectively. Consequently, we anticipate that the proposed correlations will be useful in reliable design of a new generation of electronic devices