Stinfinitesimal Simulation Method on Baking Sheet

The main purpose of this paper is to solve the heat distribution on the pan and find a better pan type by optimizing the weighted average of heat distribution and pan number. For the heat distribution problem, we first work out and solve a differential equation for pans´ heat distribution and products´ temperature rise based on laws of thermodynamics. After discretizing governing equation, we perform numerical simulation and compute the heat distributions and effective areas of different pan shapes. Subsequently, we calculate temperature´s variance of different pan shapes to show uneven distributions of heat. After analyzing the sensitivity and stability of our model, we validate that our model is robust. Concludingly, we observe the relationship between the heat concentration at the corner and pan´s shape.