Re: PLANETARY COOLER SURFACE LOSSES

dear sir,

Why I have taken this calculation because the planetry cooler are attached to the hood and some empty part of the kiln, The kiln parts attached to coolers are heated up due to the radiation from the cooler shell.

I may be wrong in that theory

thanks for the concept

chari

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Re: PLANETARY COOLER SURFACE LOSSES

Sorry Chari,

I was somewhat absentminded: I reasoned as if the kiln shell was in the center of the cooler tubes!
Below are pictures showing three possible case.
Without any kiln shell in the middle !!

The exact calculations are not easy.
You can see why on the first picture or on this detail below:

Almost any surface (like S1) on the outer side of a tube views the ambiant as well as a part of the neigbouring tubes (S2). Here you can find more on "view factors", as well as here. You can also find a funny method to estimate the view factors, here.

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Re: PLANETARY COOLER SURFACE LOSSES

dear sir,

Thank you very much for the details with attchment figures. My concept is bit clear now . Can I get the exact calculations any where .

please help.

thanks

chari

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Re: PLANETARY COOLER SURFACE LOSSES

Chari,

A calculation can be attempted using formulas for "radiation view factors". A large database of such formulas can be found on this site:

University of Texas at Austin / A catalog of radiation heat transfer ... 

One of these formulas solves the problem of two cylinders with same diameters. Using this, it is possible to calculate how much each tube absorbs from the radiations of any other tube in a planetary cooler. The remaining part is of course lost to the environment.

I have created an Excel file that does these calculations for any number of tubes and any diameters. See this file: planetaryCoolerViewFactor.zip .

Of course, when the radiation from one tube to another is partly hidden by a third tube, the formula is not applicable. Therefore, in this case, there is still an imprecision in these Excel calculations. My guess is that the error will be lower than a few percent for a normal planetary cooler geometry.

Based on these calculations, the chart here below gives the radiation view factor of a planetary cooler as a function of the number of tubes and the diameter ratio d/D.
(d is the diameter of a tube, D is the diameter of the circle joining all the centers of the tubes)

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