(382c) A Systematic and Integrative Sequence Approach (SISA) for Computing Velocity Profiles

Viscous flows are a fundamental part of fluid mechanics and momentum transfer in any engineering degree; and most would agree that they bring a very challenging task to students. Textbooks commonly used to teach these subjects, do not offer students a logical and detailed approach to derive a plausible solution, either integrative connections with previous knowledge and actual situations simultaneously. Students frequently become frustrated when confronted with a challenging problem because conventional teaching methods incorporate confusing hidden assumptions to drive the calculation, instead of recalling familiar concepts from calculus, mass balance and momentum conservation. This situation is further complicated when students cannot, for example, identify a proper location for the coordinate system origin, or why one coordinate system is better suited than others.

Here, we describe a systematic, integrative and learning-based sequence for the calculation of fluid velocity profiles; this sequence clearly utilizes the students’ knowledge and assists them in building an effective and efficient path to successfully obtain any velocity profile and its validation. 

Initially, the student following our sequence sets up or distinguishes the geometry of the control domain. Following that step, a convenient coordinate system is chosen and logically anchored to simplify any existing symmetry within the control domain. Once that is complete, all assumptions of the control domain must be identified to then categorize the fluid and state all applicable properties of said fluid.  The next step is to propose the kinematics of the system. The last thing that the student must identify is the type of flow or the driving force of the flow in the control domain, before recalling the Navier-Stokes equation. Up to this point of the analysis, the student has only tapped into the knowledge, comprehension and application categories of Bloom’s taxonomy’s cognitive domain, without any utilization of concepts related to conservation of total mass and momentum. Moving onto the analysis and synthesis categories, the student must recognize the boundary conditions present in the system and reduce the Navier-Stokes equation to only the applicable terms incorporates the information collected during the previous steps. After the differential model is specified and boundary conditions are selected, the final solution is obtained and verified. The authors will discuss details and illustration about the sequence as well as limitations and pedagogical reasons.

Future efforts will include the study of the pedagogical effects on student learning by comparing traditional approaches to the one described in this contribution.