To design a heat exchanger that meets the given requirements, we will use a parallel-flow heat exchanger. In this type of heat exchanger, both the hot and cold fluids flow in the same direction, which allows for a more effective heat transfer.1. Calculate the heat transfer required:First, we need to determine the amount of heat that needs to be transferred from the ethanol to the water. We can do this using the formula:Q = m * c * Twhere Q is the heat transfer, m is the mass flow rate, c is the specific heat capacity, and T is the temperature difference.For ethanol:m_ethanol = 2 kg/sc_ethanol = 2.44 kJ/kgK specific heat capacity of ethanol T_ethanol = 80C - 30C = 50CQ_ethanol = 2 kg/s * 2.44 kJ/kgK * 50 K = 244 kJ/sFor water:m_water = 5 kg/sc_water = 4.18 kJ/kgK specific heat capacity of water T_water = 35C - 20C = 15CQ_water = 5 kg/s * 4.18 kJ/kgK * 15 K = 313.5 kJ/sSince the heat transfer from ethanol to water should be equal, we will use the lower value of Q_ethanol = 244 kJ/s.2. Determine the required heat transfer coefficient and surface area:The heat transfer coefficient U is given as 500 W/m^2K. We can now calculate the required surface area A using the formula:Q = U * A * T_lmwhere T_lm is the logarithmic mean temperature difference, calculated as:T_lm = T_hot_inlet - T_cold_inlet - T_hot_outlet + T_cold_outlet / ln T_hot_inlet - T_cold_inlet / T_hot_outlet - T_cold_outlet T_lm = 80 - 20 - 30 + 35 / ln 80 - 20 / 30 - 35 T_lm 32.1CNow we can calculate the required surface area:A = Q / U * T_lm A = 244,000 W / 500 W/m^2K * 32.1 K A 15.1 m^2Since the maximum allowed surface area is 10 m^2, we need to increase the heat transfer coefficient to meet this requirement. We can do this by increasing the flow turbulence, using fins, or selecting a more efficient heat exchanger design, such as a plate heat exchanger.3. Design the heat exchanger:Based on the calculations, we will design a plate heat exchanger with a surface area of 10 m^2 and a heat transfer coefficient of at least 500 W/m^2K. The plates will be arranged in a parallel-flow configuration to ensure effective heat transfer between the ethanol and water streams. The heat exchanger will be designed to handle the specified flow rates of 2 kg/s for ethanol and 5 kg/s for water, and the inlet and outlet temperatures will be maintained as required.In conclusion, a plate heat exchanger with a surface area of 10 m^2 and a heat transfer coefficient of at least 500 W/m^2K will effectively transfer heat between the hot ethanol and cold water streams, meeting the specified temperature and flow rate requirements.