(581g) Enhancing Undergraduate Heat and Mass Transfer Education with Computational Tools

There is no denying that Transport or its sub-disciplines lean heavily on classic mathematics to reduce generalized balance equations to useful outcomes. The mathematics required for entry-level problems should lie within the scope of an undergraduate engineering curriculum and students are expected to retain their foundational engineering math courses knowledge to apply analytical solution techniques to differential and partial differential equation techniques. In the heat and mass transfer courses, the key objectives are teaching students the transport phenomena concepts so that they can translate “word descriptions” of real systems to “mathematical models” and able to interpret these models.

Many curricula have separated fluid dynamics from heat and mass transfer to allow more curricular time for each. Nevertheless, the time budget of a semester-long course does seem adequate to expand on both problems set-up and on the mathematical steps used to reduce initial equations to a working result. Even less time is afforded to interpreting and generalizing on results. Too often, the lifelong skills we wish students to develop take a back seat to mechanics of solution that very few will use after graduation.

This work describes the total integration of MATLAB, Symbolic Math Toolbox and Partial Differential Equation Toolbox as a vehicle for problem solving in lecture notes, homework assignments, exams, and design projects for the Heat & Mass Transfer course at NJIT. Before the Fall 2023 offering, all lecture slides were recreated from “pen and ink” solutions to an equivalent form solved using MATLAB’s Symbolic Math Toolbox. All lecture scripts were posted to the learning management system and homework assignments were heavily templated to coach proper technique by example. Exams were given as MATLAB Live Scripts, and although students could revert to paper and pen solutions, everyone in a class of 35 opted to work in the scripting environment. Similarly, open ended design projects – one each in heat transfer and mass transfer – were created in the Live Script environment and students wrote their project reports in that form as well.

The approach was piloted in Fall 2023 and has been repeated with the Spring 2024 cohort and will be repeated in Fall 2024. The results have been strongly encouraging. From an instructional viewpoint, the transformation permitted changes in depth and breadth. The fraction of class time devoted to problem definition, road-mapping the solution, and analyzing the results increased by as much as 25% over previous iterations of the course. In the past, due to time pressure mass transfer took a back seat to heat transfer – as little as 3-4 lectures in a 14-week semester. The increased efficiency afforded by the MATLAB-based approach freed up enough time to expand mass transfer to 8 lectures and an ability to dive into that topic with fewer preliminaries and greater use of an analogy between similar problems in heat and mass transfer. The approach also affords a seamless migration to more complicated problems, such as transient, multi-dimensional problems that can be solved with MATLAB’s Partial Differential Equation Toolbox. Without getting mired in the solutions steps, one can show that the relationships and dependencies derived from analytic solutions provide meaningful guidance to the behavior in more complex settings as well as validation of the quantitative application of simple models.

From a student performance perspective, the response and outcomes have been equally encouraging. After expected grumbling and resistance to change the students quickly took to the new format. The most notable outcome during the semester was the performance on exams. The quality of answers – even when incorrect – was demonstrably better. The coding environment encouraged more orderly approaches to problem-solving. Unit conversion and substitution errors were eliminated providing real-time feedback on the correctness of the solution. Answers with inconsistent units gave clear evidence that the solution was incorrect, and numerical values out of the bounds of reality also triggered reinspection of the solution.

Finally, the student response after the course has reaffirmed the value of the experience. They report using the techniques on their own to solve problems in subsequent courses like Reaction Kinetics and Separations. Several have reported a new-found interest in applied computing.

The opportunities to build on this foundation seem unlimited. MATLAB Grader, automated grading tool for MATLAB assignments, has the capacity to provide instant feedback and evaluation to increase the value of homework assignments. Integration of advanced equipment simulations is possible to better connect classroom models to practical application. MATLAB’s inherent capability to handle data acquisition, process control, and advanced data analytics suggests an abundance of opportunities to enhance the core content with examples and applications relevant across the spectrum of process industries.