Transient modelling of tubular heat exchanger: 1st order, exponential temperature profile assumption

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 22:42

*Enlace a Spanish version

Summary:

This video models a tubular heat exchanger element with a heating resistor alognside it.

Intentionally, we seek a first-order dynamics as a simplification compared to dealing with the “true” partial differential equations arising in a more detailed modelling (see video [termedpEN] for PDE modelling and [termedpsolEN] for the Laplace transform solution).

A first approach to a simplified model was addressed in video [term1eEN], under the assumptions of short and perfectly-stirred fluid in the heat exchanger.

Nevertheless, given that the heat exchanger PDE have a well-known stationary solution with exponential terms in the spatial coordinate, this video proposes using such exponential profile when computing the “mean” temperature used in the energy balance, while keeping first order temporal dynamics.

With this exponential spatial profile the match of our simplified setup with the steady-state outlet temperature predictions of the PDE will be better than with other simpler approximations such as the “uniform” interior temperature which was discussed in the video [term1eEN]. In fact, the said result will be the“very long” limit case of the present model; also, the “very short” model will end up being that obtained under assumption of a linear (in space) temperature profile (this model is briefly reviewed here, too).

The relationship of the approach to the firmly established LMTD (Logarithmic mean temperature difference) formulae is briefly outlined; we are a bit more general as we incorporate time transients and the possibility of internal heating.

As a result, transport delay physical phenomena appear as non-minimum-phase components in the transfer function associated to increments of inlet temperature.

Of course, if the accuracy of a 1st-order model were not deemed enough for a particular application, then the actual PDE or finite-element approximations of it would need to be used.

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