Evolutionary Design of Novel Coolant Passages for Cooling a Square Substrate by Single Stream

摘要

Different designs of novel coolant (i.e., water) circuits have been proposed using a well-established constructal law to cool a square substrate made up of aluminum oxide and subjected to a uniform wall heat flux (i.e., q" = 200 W/m~2) at its top. Five different flow-path topologies: case-1 (umbrella-shaped), case-2 (dumbbell-shaped), case-3 (hexagonal-shaped), case-4 (down-arrow-shaped), and case-5 (up-arrow-shaped) are evolved from a single pipe embedded in the heated substrate. The best cooling pathway has been anticipated by comparing the thermo-fluid characteristics of all the designs. A numerical route, via ANSYS R 16, has been implemented to solve the transport equations for continuity, momentum, and energy along with relevant boundary conditions. To access a better design, the nondimensional temperature and pressure drop for these cases have been quantified and compared, by varying the length and Reynolds number in the range of 2 ≤ L_c/L ≤ 3 and 100 ≤ Re ≤ 2000, respectively. We observe a decrease in the temperature and an increase in the pressure drop with Reynolds number for all the considered pathways. When Re ≤ 500, a rapid fall in the nondimensional temperature has been noticed; and thereafter, it looks like a plateau for all cases. For case-4, a minimum temperature is obtained at the nondimensional pipe length of 2.5. At L_c/L ≤ 2.5, we observe that the case-4 provides better cooling to the substrate among all other designs. Also, the pressure drop for case-4 is not too high as compared to other designs.