This study introduces innovative water-based coolant circuit designs, developed in accordance with the well-established Constructal law, to enhance the cooling performance of a solid square substrate. The top surface of the substrate is subjected to a uniform heat flux of 200 W \(\:/\) m². Five distinct flow-path configurations have been investigated: (i) elliptical-shaped, (ii) hexagonal-shaped, (iii) pentagonal-shaped (iv) trapezoidal-shaped, and (v) inverted-trapezoidal-shaped. These configurations originated from a single embedded pipe within the heated square solid substrate. To identify the most effective cooling design, the thermo-fluid performance of each configuration has been thoroughly analyzed. A numerical approach using ANSYS Fluent 24.0, has been employed to solve the transport governing equations for continuity, momentum, and energy, along with appropriate boundary conditions. The study evaluates the non-dimensional temperature and pressure drop across different designs by varying the length, Reynolds number, and fillet ratio within the ranges of \(\:2\le\:\:{L}_{p}/L\le\:\) 3, \(\:100\le\:\:Re\le\:2000\) , and \(\:0\le\:\:{F}_{r}\le\:2,\:\) respectively. The results indicate that as the Reynolds number increases, the non-dimensional temperature decreases, while the pressure drop increases across all cases. A notable reduction in non-dimensional temperature is observed at \(\:Re\approx\:500\) , beyond which only minimal changes in temperature are observed for each configuration. Out of all tested configurations, case-III (i.e., Pentagonal-shaped) demonstrates superior cooling efficiency at a non-dimensional length (i.e., \(\:{L}_{p}/L\) = 3), with a relatively moderate pressure drop compared to other designs. This novel finding holds significant potential for various engineering applications, including solar energy systems, thermal collectors, electronic cooling systems, battery thermal management and heat exchangers.
