Numerical Investigation of Constructal Flow Paths for Enhanced Cooling of a Solid Square Substrate

ABSTRACT In this study, innovative designs for water‐based coolant circuits have been developed by applying five evolutionary circular cooling pipe passages to enhance the cooling of a square solid substrate. This substrate is exposed to a constant wall heat flux of 200 Wm² at the top surface. Five distinct flow‐path configurations have been investigated: (i) pen‐tip‐shaped, (ii) boat‐shaped, (iii) elliptical‐shaped, (iv) cordate‐shaped, and (v) star‐shaped. These configurations have grown out of a single embedded pipe within the heated solid square substrate. To determine the most effective cooling design, the thermofluid performance of all configurations has been analyzed. The study evaluates the nondimensional temperature and pressure drop across different designs by varying the nondimensional length (ratio of morphing‐pipe length to substrate length), Reynolds number, and fillet ratio (ratio of fillet radius to morphing‐pipe radius) within the ranges of 3, , and respectively. Results indicate that as the increases, the temperature decreases while the pressure drop rises throughout all cases. A significant drop in nondimensional temperature is observed at . Beyond this point, the nondimensional temperature changes by 36.649%, 25.990%, 17.079%, 36.552%, and 27.801% for the pen‐tip, boat, elliptical, cordate, and star‐shaped configurations, respectively. Among the tested configurations, Case‐iv (i.e., cordate‐shaped) demonstrates superior cooling efficiency at a nondimensional pipe length (i.e., = 3), with a relatively moderate pressure drop compared with other designs.