Constructal design of cooling channels embedded in a ring-shaped heat-generating body

This study outlines the fundamental problem of design and optimization of a tree-shaped flow structure for minimizing overall flow resistance. The flow paths are designed between many points located equidistantly on an internal circle centered at O and also many points that are located equidistantly on an external circle centered at O. The fluid enters points on internal circle and exits from external circle points. The global volume of channels is constrained. The study is performed on Y-shaped structures with suitable bifurcation. Obtaining the best geometric feature of tree-shaped structures for minimized overall flow resistance is purpose of design and optimization. The influence of several parameters on overall flow resistance is investigated such as number of ducts (n0) that reach the points on the internal circle, number of branching, internal radius of body disc and mass flow rate. It is demonstrated that the increase in complexity or the number of pairing levels leads to increase in overall flow resistance; however, the best performance is obtained by increasing the number of bifurcations or more number of branching levels. Moreover, the results show that the impact of mass flow rate on the global flow resistance is negligible.