This report discusses the use of micro-fabrication techniques for creating experimental test sections containing trees of micro-finned conducting pathways, also referred to as constructal trees, for cooling a heat generating substrate. These trees are made of copper and contain branches that bifurcate at 90° angles to form constructal patterns. The patterns for the finalized test sections were created using photolithography techniques, and copper was deposited via thermal evaporation onto a 1 cm² substrate to create the trees. Certain test section design parameters were varied including the geometric complexity of the constructal trees, the volume of copper used between tree complexities, choice of material for the substrate, and the height, or thickness, of the trees. Also described in this report is an experimental methodology and testing apparatus designed to assess the cooling performance of the test sections. This methodology includes using controlled uniform heating applied to the bottom of each test section, while cooled nitrogen is impinged on the tip of the constructal tree to create a heat sink. / text

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The heat transfer behavior of phase change material fluid under laminar flow conditions in circular tubes and internally longitudinal finned tubes are presented in this study. Two types of boundary conditions, including uniform axial heat flux with constant peripheral temperature and uniform axial and peripheral temperature, were considered in the case of circular tubes. An effective specific heat technique was used to model the phase change process assuming a hydrodynamically fully-developed flow at the entrance of the tube. Results were also obtained for the phase change process under hydro dynamically and thermally fully developed conditions. In case of a smooth circular tube with phase change material (PCM) fluid, results of Nusselt number were obtained by varying the bulk Stefan number. The Nusselt number results were found to be strongly dependent on the Stefan number. In the case of a finned tube two types of boundary conditions were studied. The first boundary condition had a uniform axial heat flux along the axis of the tube with a variable temperature on the peripheral surface of the tube. The second boundary condition had a constant temperature on the outer surface of the tube. The effective specific heat technique was again implemented to analyze the phase change process under both the boundary conditions. The Nusselt number was determined for a tube with two fins with different fin height ratios and fin thermal conductivity values. It was determined that the Nusselt number was strongly dependent on the Stefan number, fin thermal conductivity value, and height of the fins. It was also observed that for a constant heat axial flux boundary condition with peripherally varying temperature, the phase change slurry with the internally finned tube performed better than the one without fins. A similar trend was observed during the phase change process with internal fins under the constant wall temperature boundary condition.

The heat transfer behavior of phase change material fluid under laminar flow conditions in circular tubes and internally longitudinal finned tubes are presented in this study. Two types of boundary conditions, including uniform axial heat flux with constant peripheral temperature and uniform axial and peripheral temperature, were considered in the case of circular tubes. An effective specific heat technique was used to model the phase change process assuming a hydrodynamically fully-developed flow at the entrance of the tube. Results were also obtained for the phase change process under hydro dynamically and thermally fully developed conditions. In case of a smooth circular tube with phase change material (PCM) fluid, results of Nusselt number were obtained by varying the bulk Stefan number. The Nusselt number results were found to be strongly dependent on the Stefan number. In the case of a finned tube two types of boundary conditions were studied. The first boundary condition had a uniform axial heat flux along the axis of the tube with a variable temperature on the peripheral surface of the tube. The second boundary condition had a constant temperature on the outer surface of the tube. The effective specific heat technique was again implemented to analyze the phase change process under both the boundary conditions. The Nusselt number was determined for a tube with two fins with different fin height ratios and fin thermal conductivity values. It was determined that the Nusselt number was strongly dependent on the Stefan number, fin thermal conductivity value, and height of the fins. It was also observed that for a constant heat axial flux boundary condition with peripherally varying temperature, the phase change slurry with the internally finned tube performed better than the one without fins. A similar trend was observed during the phase change process with internal fins under the constant wall temperature boundary condition.

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