Question

Design a counter-current heat exchanger to cool 10,000 liters per hour of cyclohexane at 110°C down to 50°C, while heating 7,500 liters per hour of water at 25°C up to 80°C. The cyclohexane will be cooled by water which enters the heat exchanger at 90°C and exits at 60°C. The overall heat transfer coefficient is expected to be 1,000 W/m2K. Determine the required heat transfer area and the pressure drop across the heat exchanger.

Answer 1

To design the heat exchanger, we first need to determine the heat duty  Q  for both the cyclohexane and the water. We can do this using the equation:Q = m * Cp * Twhere m is the mass flow rate  kg/s , Cp is the specific heat capacity  J/kgK , and T is the temperature change  K .First, we need to convert the volumetric flow rates to mass flow rates. The density of cyclohexane is approximately 780 kg/m, and the density of water is 1,000 kg/m.Mass flow rate of cyclohexane:m_cyclohexane = 10,000 L/h *  1 m/1,000 L  *  780 kg/m  *  1 h/3600 s   2.167 kg/sMass flow rate of water:m_water = 7,500 L/h *  1 m/1,000 L  *  1,000 kg/m  *  1 h/3600 s   2.083 kg/sNext, we need the specific heat capacities. For cyclohexane, Cp_cyclohexane  1,960 J/kgK, and for water, Cp_water  4,186 J/kgK.Now we can calculate the heat duty for both fluids:Q_cyclohexane = m_cyclohexane * Cp_cyclohexane * T_cyclohexaneQ_cyclohexane = 2.167 kg/s * 1,960 J/kgK *  110C - 50C Q_cyclohexane  214,000 WQ_water = m_water * Cp_water * T_waterQ_water = 2.083 kg/s * 4,186 J/kgK *  80C - 25C Q_water  479,000 WSince the heat transfer between the two fluids must be equal, we will use the average of the two calculated heat duties:Q_avg =  Q_cyclohexane + Q_water  / 2Q_avg  346,500 WNow we can determine the required heat transfer area  A  using the equation:Q = U * A * LMTDwhere U is the overall heat transfer coefficient  1,000 W/mK  and LMTD is the log mean temperature difference.First, we need to calculate the LMTD:LMTD =  T1 - T2  / ln T1/T2 where T1 is the temperature difference at one end of the heat exchanger and T2 is the temperature difference at the other end.T1 = T_cyclohexane,in - T_water,out = 110C - 60C = 50CT2 = T_cyclohexane,out - T_water,in = 50C - 25C = 25CLMTD =  50C - 25C  / ln 50C/25C   35.3CNow we can calculate the required heat transfer area:A = Q /  U * LMTD A = 346,500 W /  1,000 W/mK * 35.3 K A  9.81 mAs for the pressure drop across the heat exchanger, it depends on factors such as the geometry and dimensions of the heat exchanger, the flow rates, and the properties of the fluids. This information is not provided, so we cannot calculate the pressure drop. However, in practice, this would be determined using empirical correlations or computational fluid dynamics simulations.