Cooking with Chem-E: Analysis of Sensitivities of Assumptions in Multilayered Beef Wellington Comsol Model

The analysis of what makes a complex simulation “good,” or accurate, is highly relevant in chemical engineering. Assumptions are constantly being made with engineering design aspects, and the hope is to illustrate this significant chemical engineering concept with a model that people can resonate with: the example of food. A model of the cook time of beef wellington, the popular British dish, takes around 40-45 minutes to cook at 425ºF. The goal of the research was to create a transport-based model that would predict cooking time based on different assumptions and compare it to actuality.

Principles of heat and mass transport coupled with the equations of energy and appropriate boundary conditions were used to provide the mathematical model regarding the beef wellington. Like the traditional dish, the steak fillet was at the center, followed by a cream-based mushroom sauce, and ending with a puff pastry wrapped around the entire piece of steak. This dish is normally served rare, or about 48ºC at the center. The computational model was developed via COMSOL Multiphysics software, version 6.1. The material and temperature properties of these layers were included in the COMSOL Multiphysics model. For the purposes of the model, the beef wellington was considered a multi-layered cylinder with constant volume. One of the many assumptions that were implemented in the model was that there was that moisture transport by diffusion was neglected, so the equations of continuity were not used in the first case of the model.

This “base case” model with its relevant assumptions, differential equations, and boundary conditions, predicted cook time of 40.2 minutes. When determining the sensitivity of the model to thermal conductivity of the meat, the cook time increased to 45.8 minutes when thermal conductivity decreased by forty percent and decreased to 34.6 minutes when thermal conductivity increased by forty percent. In accord with physical expectations, cooking time decreased as the thermal conductivity increased, further validating the model. The next phase of research will address the impacts of the addition of moisture transport will truly affect the predictions by measuring cook time at different levels of doneness: rare, medium, and well-done.