What is the significance of axial sampling for a finished cement mill ?

The principle of axial testing is to crash stop the mill, then go inside and take samples at 1m intervals along the axis of the mill. You need to dig down into the media to take the samples as the mill ventilation fan will pull some of the cement off the top of the media while the mill cools sufficiently for you to enter. The size distribution of the samples are then measured in the laboratory. You are looking for progressively finer material along the axis of the mill, reaching the desired fineness at the outlet diaphragm.

I want to make a complete evaluation of the cement lines in my plant by doing a mass and heat balance, how do recommend for me to do and how to start, I'm still new in the field and don't have much experience.

Your idea is a good one to understand the process and construct the mass and heat balances. First you need to measure every flow into and out of the process. The raw feed and fuel should be metered and therefore easy. The dust loss from the top of the preheater is more difficult and requires that you use dilution techniques. The preheater exhaust gas flow is comprised of the combustion products from the fuel, plus the CO₂ from calcination of the limestone, plus the excess air drawn into the kiln. Hopefully the air flow into cooler grate is measured, you can estimate the excess air from the changing oxygen contents through the process. The excess of the cooler air over the combustion and excess air is then the cooler exhaust. It is always worth cross-checking this by measuring the flow of the cooler exhaust. Having balanced the mass flow in this way you then need to calculate the energy flow associated with each of these mass flows and also the energy loss through the shell of the preheater, kiln and cooler. The difference in the balance is then the heat of clinker formation which will be in the order of 1700 kJ/kg clinker.