Cold water (cp = 4.18 kj/kg⋅°c) leading to a shower enters a well-insulated, thin-walled, double-pipe, counterflow heat exchanger at 10°c at a rate of 0.95 kg/s and is heated to 70°c by hot water (cp = 4.19 kj/kg⋅°c) that enters at 85°c at a rate of 1.6 kg/s. determine (a) the rate of heat transfer and (b) the rate of entropy generation in the heat exchanger.

(a) The rate of heat transfer is 238.26 kW.

(b) Rate of entropy generation is 0.063 kW/K.

Explanation:

(a) Taking the heat gained by the cold water into consideration,

Q = (0.95 kg/s)(4.18 kJ/kg.⁰C)(70-10) = 238.26 kW.

(b)  Entropy generation = entropy in cold water + entropy in hot water

But

∴ = (0.95)(4.18)(ln(343/283)) + (1.6)(4.19)(ln(1- (238.26/((1.6)(4.19)(358))))

= 0.7636 + (- 0.7009) = 0.0627 kW/K.