question archive A pasteurizer in a dairy receives 1
A pasteurizer in a dairy receives 1
Subject:Mechanical EngineeringPrice: Bought3
A pasteurizer in a dairy receives 1.8 kg/s of raw milk at 15 C, preheats it on one side of a regenerative heat exchanger, and then brings the temperature up to 70"C in a steam heater for pasteurization, as shown in Fig. 2 . The hot milk is then cooled on the other side of the heat exchanger and then cooled further in a refrigeration plant to 3"C. The U value of the regenerator is 0.4 kW/(m' - K), and the specific heat of milk is 3.9 kJ/(kg . K). The sizes of the regenerator, steam heater, and refrigeration unit are to be chosen such that the total lifetime cost of the facility is a minimum. The expressions for the present worth of these lifetime costs of the three components are steam heater (including steam costs), $ =400(70 - 1) 14 regenerator, $ = 180(A, m?) refrigerating unit (including electric power), $ = 160((2 - 3) 1.5 * Steam 1.8 kg/s, Milk, 15 C Cp = 3.9 kJ/<kg K) 70*C U = 0.4 k W/(m' K) 3. C 12 A = area, m 10 Refrigerating unit Regenerative heat exchanger (a) Develop the expressions for the objective function and constraint(s) in 4 terms of 1, fa, and A to minimize the total lifetime costs. (b) Formulate the optimization problem by the Lagrange multiplier method (c) Obtain the solutions by using the Newton-Raphson method to solve for the optimized parameters.
