Introduction:
The economiser is an important component used in boilers to increase their thermal efficiency. It functions by recovering heat from the exhaust flue gases and transferring it to the incoming feedwater. This process helps to reduce fuel consumption and improve the overall efficiency of the boiler system.

Explanation:
The economiser plays a crucial role in the functioning of a boiler. It is a heat exchanger that is typically installed in the flue gas path of the boiler system. The flue gases, which are hot and contain a significant amount of heat energy, pass through the economiser before being discharged into the atmosphere.

1. Increase thermal efficiency of the boiler:
The primary purpose of the economiser is to increase the thermal efficiency of the boiler. It achieves this by recovering the waste heat from the flue gases and transferring it to the incoming feedwater. This preheated feedwater requires less energy to reach the desired steam temperature, resulting in fuel savings and improved efficiency.

2. Economize on fuel:
By recovering and utilizing the waste heat from the flue gases, the economiser helps to economize on fuel consumption. The heat energy that would have otherwise been wasted is now used to preheat the feedwater, reducing the amount of fuel required to raise its temperature. This leads to significant fuel savings and lower operating costs for the boiler system.

3. Extract heat from the exhaust flue gases:
The economiser extracts heat from the exhaust flue gases before they are discharged into the atmosphere. It utilizes the temperature difference between the flue gases and the feedwater to facilitate heat transfer. The flue gases lose heat as they pass through the economiser, while the feedwater gains heat, resulting in improved energy efficiency.

4. Increase flue gas temperature:
The statement "increase flue gas temperature" mentioned in option 'D' is incorrect. The purpose of the economiser is to extract heat from the flue gases, not to increase their temperature. The extracted heat is transferred to the feedwater, raising its temperature and reducing the energy required to produce steam.

Conclusion:
The economiser is a vital component in boilers, primarily used to increase their thermal efficiency. By recovering waste heat from the flue gases and transferring it to the feedwater, the economiser helps to economize on fuel consumption and improve energy efficiency. It plays a crucial role in reducing operating costs and promoting sustainable energy practices in boiler systems.