Engineering Optimization Problem (maximum no. of equidistant circles fitting)

Hi folks,

I'm an engineer from the UK and I was wondering if any one of you smart lads might be able to help me out with the following problem:

I'm designing a heat exchanger that needs to fit into a tube of 20in diameter. I would like to have maximum surface area, yet minimal volume in a way, that the heat exchanger tubes (Ds), that are cylindrical, occupy the 20in diameter equidistant from each other (and 0.5 Ds distance from one another), and they cannot be smaller than 1in.

Any help is appreciated,

Cheers

Re: Engineering Optimization Problem (maximum no. of equidistant circles fitting)

If you consider the heat exchanger tubes and half the required distance between them as a single object, you are just asking how many circles of diameter 1.25 can be fit in a circle of diameter 20.

Your question does not have a provable answer. This website:

The best known packings of equal circles in a circle

has packings sorted by number of circles, and since your radius is 1.25/20 = 0.625, it looks like the maximum number is 213. It also looks like you might be able to download a file that shows you the pattern for 213.

- Hollywood