Field synergy analysis on thermal-hydraulic behavior of phase change slurry in porous microchannel heat sink with graded porosity configuration

In this study, a novel design of porous microchannel heat sink (MCHS) with graded porosity configuration is proposed in the hope of attaining lower flow and thermal resistances than constant porosity (CP) configuration. The efficacy of new scheme is validated by utilizing a three-dimensional solid-fluid conjugate model based on the finite volume method, which considers the flow and heat transfer of microencapsulated phase change material slurry (MPCMS) inside the porous fins. It is reported that the thermal performance of porous MCHS with constant and graded porosity configurations is significantly better than that of non-porous MCHS. The feasibility of new design is verified by comparing the hydrothermal behavior of multiple graded porosity MCHSs and CP configuration for different fin designs (involving the number of graded equidistant fins N, graded length ratio R, and fin-to-pitch width ratio β) and operating conditions (including Reynolds number Re, mass fraction cm, and inlet velocity uin). The comprehensive performance improvement mechanism of MPCMS in graded porosity microchannels is discussed through the analysis of flow and thermal details, field synergy angle (θ) and field synergy number (Fc), and the overall performance of new design is evaluated by performance evaluation factor (PEF). Results indicate that the six types of porous MCHS with stepwise varying porosity exhibit lower thermal resistance than CP mode, and better thermal behavior and larger PEF can be obtained at N = 2 and β = 0.7. Smaller and larger R should be chosen for stepwise increasing porosity (SIP) and stepwise decreasing porosity (SDP) modes, respectively, to achieve higher heat transfer enhancement while avoiding greater friction losses. The Fc value of porous MCHS with various porosity configurations is about two orders of magnitude less than 1 and shows a monotonically reducing trend with Re, and the synergistic effect deteriorates at high Re. Compared to the CP mode, a low-θ “drift” toward the low porosity region of porous fin occurs within the graded porosity MCHS, which decreases and increases in the downstream and upstream directions of the “drift”, respectively. Among the novel MCHS designs, the z-directional SIP mode acquires the best overall performance due to the excellent synergy between the velocity and temperature fields, and its PEF consistently exceeds 1.13 and reaches up to 1.33. Generally speaking, the fin porosity of graded porosity MCHS near the channel cavity, channel top, and channel inlet should be greater for superior comprehensive performance.