Hot water is transported from a cogeneration power station to commercial and industrial users through steel pipes of diameter D = 150 mm, with each pipe centered in concrete (k = 1.4 W/m ∙ K) of square cross section (w = 300 mm). The outer surfaces of the concrete are exposed to ambient air for which T∞, = 0°C and h = 25 W/m2 ∙ K.

(a) If the inlet temperature of water flowing through the pipe is Ti = 90°C, what is the heat loss per unit length of pipe in proximity to the inlet? The temperature of the pipe T1 may be assumed to be that of the inlet water.

(b) If the difference between the inlet and outlet temperatures of water flowing through a 100-m-long pipe is not to exceed 5°C, estimate the minimum allowable flow rate m. A value of c = 4207 J/kg ∙ K may be used for the specific heat of the water.

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Concrete, k Air T, h D. Water T m