Analytical optimization of constructal channels used for cooling a ring shaped body based on minimum flow and thermal resistances

Constructal theory is invoked to optimize a dendritic path flow structure for minimizing overall flow and thermal resistances. Convective cooling of a ring-shaped body is the aim of this investigation. The construct of flow paths is Y-tree shaped; while the body has heat generation over the area, uniformly. Cooling is done by a single-phase coolant entering through ports located equidistantly along the internal perimeter or enters through the center (when internal radius of convoluted disc-shaped body is zero), and exits through ports located equidistantly along the external perimeter. The regime of fluid flow is laminar and fully developed. The degrees of freedom are the ratio diameters and lengths of ducts. The constraints are the disc size (external radius is fixed) and the total volume of ducts devised in disc. The aim of design is to obtain the best construct, so that two resistances i.e. flow resistance and thermal resistance are minimized. Results show that the mass flow rate has the greatest effect on thermal resistance, but the effect of mass flow rate on flow resistance is negligible. Moreover, it is seen that at high values of pumping power, increasing complexity (more levels of pairing) results in reducing the thermal resistance.