Optimization Design of Baking Pan to Save Energy

摘要

Inspired by certain simulation experiments, we choose round-corner rectangles (RCR) as the shape of our brownie pans. A model based on the heat balance equation and the mechanisms of heat transfer (convection and radiation) is established to show the distribution of heat across the outer edge of a pan for pans of different shapes -rectangular to circular, with the round-corner rectangular a merger of both. To solve this model, we developed a numerical program in MATLAB and provided its flowchart. A multi-objective optimization model is proposed to design our ultimate brownie pans, and a numerical algorithm is designed to solve it. This model attempts to select the best shape which balances properly between pan numbers placed in oven and even heat distribution at the edge of pans. Finally, the efficiency and performance of the RCR pan are analyzed.