2026 ASEE Annual Conference & Exposition

Undergraduate engineering instruction in the thermal-fluid sciences has long relied on forward problem-solving: students are given a scenario and tasked with deriving a solution from governing equations such as the conservation of energy. Widely adopted textbooks in thermal-fluid courses reinforce this approach by providing structured procedures that scaffold student analysis. The forward problem-solving approach aligns well with problem-based learning and has proven effective in building procedural knowledge. However, this approach may limit opportunities for deeper conceptual understanding. Students frequently struggle to connect physical systems to the corresponding symbolic equations that govern system behavior in thermal-fluid courses.

To address this gap, this paper introduces a reverse problem-solving framework implemented across three mechanical engineering courses: thermodynamics, fluid mechanics, and heat transfer. In this approach, students are presented with a final symbolic equation and asked to construct a plausible problem statement with a description of the physical system, schematic, and set of simplifying assumptions that would lead to the provided equation. This inversion of the traditional process draws on the Concrete-Representational-Abstract (CRA) model, rooted in Bruner’s theory of cognitive development, to strengthen connections between physical phenomena (concrete), system schematics (representational), and governing equations (abstract).

Reverse problem-solving encourages students to critically examine boundary conditions, assumptions, and system behavior, promoting systems-level thinking and conceptual integration. It also supports the development of metacognitive skills by shifting the instructional focus from solution execution to problem formulation. This paper includes samples for implementing reverse problem-solving in thermal-fluid courses and initial findings. Future work will further assess the impact of reverse problem-solving on student learning outcomes.