Request for heat transfer calculation to heat the water in the external coil stirred tank using hot water

First, we need to calculate the energy required to heat the water from 40°C to 75°C. The following formula can be used: \ Where: – \( m \) is the mass of water in kilograms – \( c \) is the specific heat capacity of water, approximately 4.186 kJ/kg·K – \( \Delta T \) is the temperature difference, that is, 75℃ – 40℃ = 35K. The density of water is approximately 1000 kg/m³; therefore, the mass of 10 m³ of water is 10,000 kg. \ Next, considering the supply and demand for hot water, it is necessary to calculate the flow rate of hot water based on the temperature difference between the inlet and outlet temperatures. Assuming the temperature of the hot water outlet is 80°C, the temperature difference \( \Delta T_w \) is 85°C - 80°C = 5K. Use the formula to calculate the energy transfer efficiency of hot water: \ where \( m_w \) is the mass flow rate of hot water (kg/s). Set the preheating time to 1 hour, which is 3600 seconds. \ \ The solution gives \, which is the mass of hot water required per hour. Convert it to flow rate (assuming the density of hot water is 980 kg/m³): \ Up to this point, we have determined the flow rate requirement for the hot water. You need to ensure that the hot water system can supply hot water at 85°C at a flow rate of 0.021 m?/s, and that the return temperature is kept around 80°C. At the same time, it is also necessary to ensure that the design of the reactor meets the requirements for heat exchange safety and efficiency. .

Three aspects need to be considered for heat: 1. The heat required to raise the temperature of the water in the tank； 2. Heat required to raise the temperature of the water in the outer coil and circulation pipes ； 3. Heat required to raise the temperature of the reactor vessel itself