Putting proof back in the engineering curriculum
Chemical engineers rely on a wide range of modeling and simulation methods to make some sense of an otherwise messy physical world. While these methods continue to be taught to students, they are often presented in an already simplified format, without formal proofs and perhaps even altogether embedded in the complex code of end-user software.
Simant Upreti, Chair of Ryerson University’s Department of Chemical Engineering, feared that if the full scope of these powerful methods continued to be kept out of sight, they might eventually fall out of mind. That could represent a loss to the entire profession, which relies on a full understanding of these tools to take on the most challenging problems in process design.
He has therefore spent the last few years researching and writing a textbook to support just an understanding. Process Modeling and Simulation for Chemical Engineers, published in April by Wiley, takes students from the first principles of defining a system or a process and then develops the mathematical capabilities to engage with real world cases, such as nicotine delivery from the patch, heat loss from a tapered fin, or the dynamics inside a microchannel reactor.
Upreti was also eager to expose his readers to the proofs of various standard equations, some of which have not been documented in textbooks for decades.
“To find a proof of the general transport theorem, you wouldn’t believe how many old texts I had to consult,” he says, referring specifically to a long hard search for the proof of one of his favorites, the Buckingham Pi Theorem. “With a simple symbolic equation we can easily interrelate process variables, such as gravity, and the length and time period of an oscillating pendulum. This is based on the Pi theorem but where’s the proof of it?”
One of Upreti’s overriding goals was to give students the knowledge and the confidence to simplify these methods for themselves, as the situation demands, rather than addressing any given problem with an already simplified version.
“I felt a need to help students get a solid grasp of ‘under-the-hood’ mathematical results, so that they could then be more effective in their work,” he concludes.