The condenser of a steam power plant contains N = 1000 brass tubes (k_t = 110 W/m ∙ K), each of inner and outer diameters, D_i = 25 mm and D_o = 28 mm. respectively. Steam condensation on the outer surfaces of the tubes is characterized by a convection coefficient of h_o = 10,000 W/m² ∙ K.

(a) If cooling water from a large lake is pumped through the condenser tubes at m_c = 400 kg/s, what is the overall heat transfer coefficient U_o based on the outer surface area of a tube? Properties of the water may be approximated as μ = 9.60 x 10^–4 N ∙ s/m², k = 0.60 W/m ∙ K. and Pr = 6.6.

(b) If, after extended operation, fouling provides a resistance of Rⁿ_f,i = 10^–4 m² ∙ K/W, at the inner surface, what is the value of U_o?

(c) If water is extracted from the lake at 15°C and 10 kg/s of steam at 0.0622 bars are to be condensed, what is the corresponding temperature of the water leaving the condenser? The specific heat of the water is 4180 J/kg ∙ K.