We developed two models in this study: one to show the distribution of heat for pans of different shapes, and the other to select the best type of pan to maximize the number of pans that can fit in the oven and to maximize even heat distribution in the pans. We constructed a model of heat distribution. The uneven distribution of heat is mainly caused by heat conduction. We established a differential equation for heat conduction according to Fourier’s law. The finite-difference method and Gauss-Seidel iteration were used to solve the equation, and MATLAB was used to draw the corresponding heat-distribution chart. We built a quantitative model of the shape optimization with an evaluation equation. Using the permutation and combination method, we calculated the maximum number of pans and the utilization rate of area. Finally, we determined that the optimal pan type is a round square, which achieved the best state.

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