Design a heat exchanger for a chemical process that requires the transfer of heat from a hot stream containing molten sodium at 1100°C to a cold stream containing water at 25°C. The hot stream inlet flow rate is 1000 kg/hr, and the cold stream outlet temperature should be limited to a maximum of 70°C. The heat transfer coefficient for the tubeside and shellside is 1000 W/m²K and 500 W/m²K, respectively. The design should minimize the size and cost of the heat exchanger while meeting the thermal requirements of the process.

Question

Design a heat exchanger for a chemical process that requires the transfer of heat from a hot stream containing molten sodium at 1100°C to a cold stream containing water at 25°C. The hot stream inlet flow rate is 1000 kg/hr, and the cold stream outlet temperature should be limited to a maximum of 70°C. The heat transfer coefficient for the tub

Answer 1

To design a heat exchanger for this chemical process, we need to follow these steps:1. Calculate the heat duty.2. Determine the log mean temperature difference  LMTD .3. Calculate the overall heat transfer coefficient  U .4. Determine the required heat transfer area  A .5. Select the type of heat exchanger and finalize the design.Step 1: Calculate the heat dutyFirst, we need to determine the heat duty  Q  required to heat the cold stream  water  from 25C to 70C. We can use the formula:Q = m_c * C_p,c *  T_out,c - T_in,c where m_c is the mass flow rate of the cold stream, C_p,c is the specific heat capacity of the cold stream  water , T_out,c is the outlet temperature of the cold stream, and T_in,c is the inlet temperature of the cold stream.For water, the specific heat capacity  C_p,c  is approximately 4.18 kJ/kgK. We are given the mass flow rate  m_c  as 1000 kg/hr. The inlet and outlet temperatures are 25C and 70C, respectively. Plugging these values into the formula, we get:Q = 1000 kg/hr * 4.18 kJ/kgK *  70C - 25C  = 188,300 kJ/hr = 52.3 kWStep 2: Determine the log mean temperature difference  LMTD Next, we need to calculate the LMTD, which is given by the formula:LMTD =  T_1 - T_2  / ln T_1 / T_2 where T_1 is the temperature difference between the hot and cold streams at one end of the heat exchanger, and T_2 is the temperature difference at the other end.In this case, T_1 = 1100C - 25C = 1075C, and T_2 = 1100C - 70C = 1030C. Plugging these values into the formula, we get:LMTD =  1075C - 1030C  / ln 1075C / 1030C   1051.6CStep 3: Calculate the overall heat transfer coefficient  U The overall heat transfer coefficient  U  can be calculated using the formula:1/U = 1/h_t + 1/h_swhere h_t is the tubeside heat transfer coefficient, and h_s is the shellside heat transfer coefficient.Given h_t = 1000 W/mK and h_s = 500 W/mK, we can calculate U as follows:1/U = 1/1000 + 1/500 = 0.001 + 0.002 = 0.003U = 1/0.003  333.3 W/mKStep 4: Determine the required heat transfer area  A Now, we can calculate the required heat transfer area  A  using the formula:A = Q /  U * LMTD Plugging in the values, we get:A = 52,300 W /  333.3 W/mK * 1051.6C   0.153 mStep 5: Select the type of heat exchanger and finalize the designBased on the calculated heat transfer area, we can select an appropriate type of heat exchanger. A shell and tube heat exchanger would be suitable for this application, as it can handle high temperatures and a wide range of flow rates.To minimize the size and cost of the heat exchanger, we can choose a compact design with a high number of tubes per shell, a small tube diameter, and a high tube length-to-diameter ratio. The final design should also consider factors such as pressure drop, fouling, and ease of maintenance.In conclusion, the designed heat exchanger should have an overall heat transfer coefficient of 333.3 W/mK, a heat transfer area of approximately 0.153 m, and a shell and tube configuration with a compact design to minimize size and cost while meeting the thermal requirements of the process.