question archive The flow rates of cooling water Ww and radiator cooling air Wa, both in kg/s, are to be chosen such that the total power in the engine cooling system, shown in Fig

The flow rates of cooling water Ww and radiator cooling air Wa, both in kg/s, are to be chosen such that the total power in the engine cooling system, shown in Fig

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The flow rates of cooling water Ww and radiator cooling air Wa, both in kg/s, are to be chosen such that the total power in the engine cooling system, shown in Fig. 1, is a minimum. W w 300 kW Input to Water Water = 4.19 (1/(kg-K) Engine Pump Air 35*C UA = 12 k W/K G = 1 \/(kg-K) Radiator Figure 1. Engine cooling system The outlet water temperature from the engine is 100 C and the temperature of the inlet air is 35*C. The radiator has a UA value of 12 kW/K. The equations for power in kW are pump power = 0.02 wa and fan power =0.01 wa For simplification, assume that the arithmetic-mean-temperature difference is sufficiently accurate in the heat-transfer rate equation, thus 12[(100 + 7w)/2 - (35 + 1.)/2] = 300 KW (a) Develop the objective function and constraint in terms of w, and w.. (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.

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