Tubular heater/exchanger: finite element modelling (1)

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 15:06

*Enlace a Spanish version

Summary:

This video addresses the finite element modeling of the tubular heat exchanger/heater discussed in the videos starting with [term1eEN] and continuing in the links/references in the video description.

The first seven minutes review the many models discussed in this case study, ranging from:

• Model as a partial differential equation, PDE, [termedpEN]

• Static (stationary) models derived from said PDE (very common in practice), setting time derivatives to zero

• First-order models based on energy balance (see video [term1expEN]) over a mean temperature.

This review may be of interest in itself, to understand/unify the concepts of all those previous videos.

Next, it is proposed to subdivide the exchanger into $N$ equal pieces (finite elements). Thus, we discuss how to interconnect the elements, both in a block-diagram form and with the state and output equations of each of the elements (which will be assumed first order, as mentioned above), so that they form a model, of order $N$, that approximates the “exact” solution of the PDE (which would be the limit when making the elements infinitesimal). Obviously, forming the $N$ state equations with very large $N$ is done using a loop and the Symbolic Math Toolbox, and explaining the code that does this is the goal of the final part of the video.

Actual simulation of this finite-element models will be discussed in video [tubulFEsim1EN], which will be the next in the case study.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.