Mathematically Modeling Engineering Problems

For most of my engineering career, when delving into a new problem for a given project, I would usually find a lack of true understanding within the engineering team of fundamental aspects of solving a problem. What I mean is that if a certain technology was part of the company’s ecosystem, the way it worked was simply accepted and the details were not necessary to understand. At almost every company, this would be the case. I remember at one company, I was creating a mathematical model for determining how long a jug of milk could stay on a counter before it reached an unsafe temperature. This was an ask by the company’s food safety team to settle a particular internal debate. It had been a while since I performed a free convection heat transfer calculation, so I got out my old text and started a model in Mathcad (yes, I still use it). As I was entering the equations, my manager asked me what I was doing. After I had explained, he told me that I didn’t need to do that, and it would be better to “just test it.” The problem with that way of thinking is that while testing would work, the time and resources were limited. After I had completed the model, I could enter any number of conditions like ambient air temperature, amount of milk in the jug, and the starting temperature of the milk to inform a prediction of an array of conditions. If I had chosen a design of experiment for those three said variables which had a low, middle and high value that would have amounted to twenty-seven individual experiments, assuming all combinations. Not only did I reinforce my skill at calculating a free convection problem, but I saved a great deal of time and resources by being able to tell the entire story by a simple pushing of the button for all the possible scenarios. Not only that, but I gained additional insights into the actual physics that were happening.

This philosophy has served me well in my career. I have always started every project by first beginning with the fundamentals and creating a mathematical model of a system. It could be anything from blood flowing through medical tubing, to the pneumatics of a rotary vane compressor, to determining the capacity needed for a bladder tank, and so on. At times, these models would become standard design “calculators” at a given company, which becomes yet another asset for years to come.

Milk Jug Temperature Rise When Taken Out of Refrigerator as a Function of Time