# (Chemistry) Dimensionless heat transfer coefficient

I'm trying to reproduce in Matlab the model of a continuous stirred tank reactor (CSTR) that I've gotten for a project.

The model is written in the state space and uses some dimensionless values, including a "heat transfer coefficient" β. Here's the table:

I've been trying to investigate in chemical process books to figure out how to calculate this coefficient (I imagine the numerator is Area times Height, but no idea about the terms in the denominator), but I've found nothing. I think even the order of magnitude of this coefficient would be useful, so I don't mess up when entering the equations. Thanks in advance for your help.

To start, $h$,$\rho$ and $c_p$ are standard symbols for heat transfer coefficient (energy per unit area per unit temperature), density(mass per unit volume), and heat capacity at constant pressure (energy per unit mass per unit temperature).

If you put all these together you get that something in units of volume per unit time equals divided by $F_0$ is equal to $\beta$ (unitless). Therefore $F_0$ must also have units of volume per unit time. So I think that it's safe to say that it's the flow rate into your reactor

$\beta$ is meant to give you a measure of the relative strength between convective losses to the wall (numerator) and the energy associated with the inflow of gas (denominator).

The first would be

$q_{loss} = hA(\Delta T)$: heat loss proportional to surface area, temperature difference and a constant related to the flow

the second would be

$q_{flow} = \rho c_p \Delta T F_0$:

In $\beta$, they've just dropped the $\Delta T$ from the top and bottom.

• Thanks very much for your answer, it was really clarifying information. Best regards – javman1986 Oct 1 '14 at 15:58