n to move back and forth continuously. The operating efficiency of a fan can be optimized by carefully adjusting the frequency of alternating current until it is just right for that particular fan. The piezoelectric fans can be made in a wide range of sizes. The Purdue engineers are developing fans small enough to fit on a computer chip: their blades will only be about 100 micrometers long, which is roughly the width of a human hair. Piezoelectric fans were developed during the 1970s. The first versions were considered noisy, but the Purdue group has developed fans that are almost inaudible. The fans are made by attaching a tiny "patch" of piezoelectric ceramic to a metal or Mylar blade. Two factors affecting the performance of the fans are how much the ceramic patch overlaps the blade and how thick the patch is compared with the blade's thickness. Another critical factor is pre- cisely where to attach the blade to the patch. Those factors dictate perform- ance characteristics such as how far the blade moves, how much airflow it produces, and how that flow produces complicated circulation patterns. An improperly designed fan could actually make matters worse by recirculating hot air back onto electronic components, notes Arvind Raman, an assistant professor of mechanical engineering at Purdue. The Purdue researchers have developed mathematical techniques that take these factors into consideration when designing fans for specific purposes. "These fans typically have been novelty items," says Raman. "If you want to COOLING TECHNOLOGIES really be serious about putting them into any practical use, there are SO many things you need to understand about how they work and how to optimize them." Mathematical models developed by Purdue researchers can be used to provide design guidelines for engineers. "What we bring to the table is a knowledge of the modeling of these fans," says Garimella. "How to analyze the design, to figure out how large a patch should be for how long a blade, how thick the patch should be, and what h