Needs help in thermo problem

Hi all

I'm a newbie here and it's long time since I finished my physics classes so I need some help.

I have a wood fireplace in my home and an under-floor heating operated on a gas burner.

I wants to place a copper pipe in the fireplace and connect it in serial and before to the gas burner so it will heat the water of the under-floor pipes. Of course I will add some pressure/temp relief valve, and make sure that the water will not exceed the 80'C limit.

I need to calculate what should be the length of the copper pipe placed inside the fireplace.

The parameters:

The fireplace temperature is about 1000'C (to be on the safe side)

The copper pipe inner radius is 5.5mm and outer radius 6.5mm.

The water enter the pipe in about 25'C and should exit in about 55'C.

The water flow speed in the pipe is about 2500 liter/hour.

Can anyone help me to calculate the copper pipe length?

I tried to calculate with what I remembered and it yield a 157m copper pipe, could it be right? does it means that the fireplace can't do the job?

Tnx

Ilan