Well, if you have the required heat transfer (but you did not mention in how much time would you deliver the 2,800,000,000,000,000,000,000,000 cal ;-) I assume that you're building an ice bank or some sort of. If I am correct, most of your problem will reside in calculating the required tube lengh for convection heat transfer to the water, this is supposed to be a strain in the system (the inside of the tube is working in steady conditions, working fluid circulating in the system, with known velocity and temperature, so easy to put into the equations...). Check your books for heat and mass transfer - basics. I remember that the heat transfer by a straight tube under known conditions is a classic exercise that can be found in any one. At the end of the book its usual to have several tables with heat transfer coeficients for different medias. I'd find the worst condition for heat transfer to the water, assume it as a constraint in the system, and calculate all of the other stuff with the lenght found. Optimise the material? Only the lenght, once you stated that you must use 1" tube carbon steel. Good luck with your homework. Besides this forum usually does not help with it.

More information is needed even to start with this problem. 2,800,000 Kcal per hour, per day, or per other time period? What water temperature is required to furnish to the process, and how much much will the temperature rise before the water returns to the chiller? Is the chiller intended as an ice bank (water outside the pipes, ammonia inside); or as a nonfreezing application (in this case the water could be inside the pipes)? Is the water flow known?

Thanks for your response. 2,800,000 kcal per hour. Water temperature required is 4 degrees C. Water into chiller is 30 degrees C. The chiller is actually an ice bank, water outside, with ammonia inside. Water flow is 50,000 liters per hour. Pipe specified to be 1". Agitation of water by compressed air bubbling.

Regards

I am not sure what an ice bank means. To get the area of tube needed one way is this approach.

As a starting point consider the tube temperature to be 0.0 degrees C. Much colder and you risk ice forming on the outside of the tubes in the water insulating the system. To get from 30 deg C to 4 Deg C use a log mean delta T. Also assume the interior of the tube is all boiling ammonia at the same pressure / temperature.

Ln m Delta T = (delta T1 - delta T2)/ Ln(delta T1 / delta T2)

Start with interior tube of 0.0 deg C= 273 K

Delta T1 = 303k-273k= 30K

Delta T2 = 276K-273K=4K

Plug in numbers!

You now have heat duty, and temp diff, you determine the heat transfer Coeff (from tube, turbulence, flow regime and your system size, with patterns, turbulence. Not enough details for me to be much help)

Calculate the area needed. a=h/(u*dT)

Is this homework?