Approximately 40 percent of the water that is pumped in the United States is used to cool power plants. Sufficient quantities of water may not be available in arid regions, necessitating use of air-cooled condensers. Consider the power plant and operating conditions of Example 1.7, but with the plant's water-cooled condenser replaced with an air-cooled condenser. The cold-side thermal resistance can be approximated as \(R_{t, c}=1 /\left(h_{c} A\right)\), where \(h_{c}\) is the convection heat transfer coefficient for the flow in the condenser tubes and \(A\) is the heat transfer surface area. The heat transfer surface area of the air condenser is 10 times larger than that of the water condenser, and the convection heat transfer coefficient for the water condenser is 25 times larger than that of the air condenser. Determine the modified efficiency and power output of the plant with the aircooled condenser. Knowing that the condenser cost is proportional to its heat transfer area, is the higher cost of the air-cooled condenser offset by better power plant efficiency and/or higher power output with air cooling? Assume clean conditions.

Data From Example 1.7:-

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In a large steam power plant, the combustion of coal provides a heat rate of qin 2500 MW at a flame temperature of T = 1000 K. Heat is rejected from the plant to a river flowing at T = 300 K. Heat is transferred from the combustion products to the exterior of large tubes in the boiler by way of radiation and convection, through the boiler tubes by conduction, and then from the interior tube surface to the working fluid (water) by convection. On the cold side, heat is extracted from the power plant by condensation of steam on the exterior condenser tube surfaces, through the condenser tube walls by conduction, and from the interior of the condenser tubes to the river water by convection. Hot and cold side thermal resistances account for the combined effects of conduction, convection, and radiation and, under design conditions, they are Rth=8 10-8 K/W and R = 2 108 K/W, respectively. 1. Determine the efficiency and power output of the power plant, accounting for heat transfer effects to and from the cold and hot reservoirs. Treat the power plant as an internally reversible heat engine. 2. Over time, coal slag will accumulate on the combustion side of the boiler tubes. This fouling process increases the hot side resistance to R = 9 x 108 K/W. Concur- rently, biological matter can accumulate on the river water side of the condenser tubes, increasing the cold side resistance to R = 2.2 108 K/W. Find the efficiency and power output of the plant under fouled conditions.