Effect of Sierpinski carpet geometry on the distribution of the convection heat transfer coefficient in cooling fins*

Different approaches have been studied to improve the heat exchange capacity of the fins. One of these, involves manufacturing windows in rectangular fins according to the fractal Sierpinski carpet. In this research field the main efforts have been focused on the global heat transfer per unit of mass of the fin, showing promising results. The present work is aimed to study the effect of window patterns on the local heat transfer coefficient. Each fin consists of a copper-squared plate of 10 cm per side and 3.14 mm of thickness. The window patterns were manufactured on the fins according to the first, second and third step of the Sierpinski carpet respectively. A fourth fin with no windows was used as a benchmark case. The inverse heat transfer problem was used to compute the local heat transfer coefficients. This method requires the temperature distribution on the fin surface as a reference data set, which was measured using an infrared camera. Computations of the tridimensional heat conduction problem for each fin were performed using ANSYS and applying similar boundary conditions of the experiments. The local heat transfer coefficient was estimated using the steepest descent method. Results shown the local heat transfer is strongly affected by the windows, mainly in its tip.