Taylor Number Definition???

[arto]

I'm trying to do rotating cylinder-in-a-cylinder heat transfer design & am finding generally two different definitions for Taylor Number.

One is basically porportional to Reynold No., & the other to Reynolds Number ^squared.

The GE heat transfer book, et al, use:

Ta = [omega*radius*gap/kin.viscosity] * sqrt [gap/radius]

~Re*sqrt(gap/radius)

whereas others {i.e., Becker& Kaye, ASME Jnl H.T. may '62, et al.] use

Ta = [omega^2 * radius * gap^3]/kin.viscosity^2

~Re^2

where omega = rad/sec
These are then used to find the Nusselt No. & thence "h."


Can anybody shed some light/wisdom on this?? [The more I look [articles, internet], the more I find of either one or the other.]
Thanks
Arto

 

[25362]

Although I haven't been involved with heat transfer of rotating fluids, from reading relevant material it seems that the Ta/Re relation depends on the flow r[é]gime.

 

[unclesyd]

arto,
No help, but this a similar problem to one that gave an extra point on a final. A glass wine bottle in a metal Dewar with slush ice. What is the optimum speed to rotate the bottle to get the wine cooled to serving temperature in the quickest possible time.

 

[abeltio]

don't know... maybe this is just an algebra problem?

calling the OP expressions...
Ta. = [omega*radius*gap/kin.viscosity] * sqrt [gap/radius]
Ta.. = [omega^2 * radius * gap^3]/kin.viscosity^2

to make expressions shorter i use the following nomenclature:
w = omega
r = radius
t = gap
n = nu = kinematic viscosity


Ta. = ((w*r*t)/n)*(t/r)^0.5
squaring Ta.
Ta.^2 = (w^2*r^2*t^2/n^2)*(t/r) = Re^2*(t/r)
Ta.^2 = (w^2*r*t^3/n^2)
then,
Ta.^2 = Ta..

so, the last expression should say...

Ta.. = Re^2*(t/r)

which is ~ Re^2 if t~r (t/r ~ 1)

the square of an adimensional number is still adimensional
so may be it has no influence in the end result...

what do you guys think?



saludos.
a.

 

[arto]

except if the Re's ~ 1000, then Re^2 ~ 1000000

 

[abeltio]

agree of course, it is up to the reader to determine if it makes sense or not.

saludos.
a.

 

[25362]

To abeltio, when making H/T calculations for the Nu dependence on Re[sup]n[/sup] the value of n could be, for example, 0.3 and 0.15, or 0.5 and 0.25, depending on which Ta has been selected...

Hasta pronto.