URGENT !!!! WILL DO UPVOTE

\\\\\\\\\\\\\ Justified assumptions can be made with reasons provided \\\\\\

Note:

Any data that will be crucial in solving the problem may be assumed or taken from any authentic source with reasonable justifications.

The resource name and link whatever available should be provided from where the values are being taken. i.e from where the specific heat capacities, thermal conductivity data has been obtained.

The values given in the text should be checked for validity.

Problem

The production of urea, a widely used nitrogen fertilizer, involves various chemical processes that require careful consideration and optimization to ensure efficiency and safety. One such process is the solidification of liquid urea solution into stable prills using a prilling tower. A critical aspect of this process is the cooling system, which must be designed to maintain the required temperature and shape of the prills while minimizing the risk of fouling and scaling. This complex engineering problem aims to address these challenges by performing a thermal balance analysis of the prilling tower cooling system to calculate multiple variables and parameters involved such as inlet and outlet gas temperatures, heat transfer rate to the liquid urea. The problem also involves the calculations to study different ways of enhancing heat transfer rate by maximizing the contact area between ammonia gas and liquid urea as well as proposing measures to enhance its efficiency and reliability. Prilling towers are widely used in the chemical and fertilizer industry to solidify liquid materials into small, uniform spheres. They are also utilized in the food and pharmaceutical industries to produce small particles of food additives and drugs, respectively. Additionally, prilling towers can be used in environmental applications for producing slow-release fertilizers and encapsulating hazardous waste materials.

In a urea manufacturing process, the prilling tower plays a crucial role in solidifying a liquid urea solution with the aid of a cooling system comprising ammonia, In a specific situation, the prilling tower with a height of 35 meters and a diameter of 9 meters is utilized for solidifying a liquid urea solution. Ammonia gas enters the prilling tower at the bottom with an inlet flow rate of 2000 L/min at a temperature range of 20-30C, which cools the liquid urea solution entering the tower from top and is sprayed through a fine distributor in form of spray droplets. Feed rate of liquid urea is 1000 kg/hr at 135C. The inlet feed stream of liquid urea has a purity of 98.83%, while the outlet urea prills purity is 98.96%. The heat transfer coefficient for the system ranges between 300-400 W/mK, and the specific heat capacity of the urea solution is 2.11 kJ/kgC.

The objectives of this complex engineering problem are listed below:

1. List out all the required data and physical properties required. Make reasonable realistic assumptions wherever required for clear understanding of the problem.

2. Determine the heat transfer rate from the liquid urea solution to the cooling ammonia by applying the heat balances. Take into consideration all the three modes of heat exchange.

3. Propose methods for enhancing the contact area between the liquid urea and the upward moving ammonia to improve the system's efficiency.

4. Determine the optimal inlet and outlet temperatures of the cooling ammonia considering the tower dimensions, heat transfer coefficient, and specific heat capacity of the urea solution.

5. Evaluate the potential fouling and scaling of the cooling system and propose suitable measures to ensure the prilling tower's longevity and reliability