Project ForgeDuring open-heart surgery, a patient's blood is cooled down to 25°C from 37°C using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4°C and leaves at 18°C. Blood flow rate during the surgery is 5 L/minute. Blood: density 1050 kg/m³, specific heat 3740 J/kg.K. Water: density 1000 kg/m³, specific heat 4200 J/kg.K. Effectiveness of the heat exchanger is _________ (round off to 2 decimal places).
Explanation
ṁ_blood=5×10⁻³m³/min×1050kg/m³/60s≈0.0875kg/s. C_blood=0.0875×3740≈327.25W/K. Energy balance: Q=C_blood×(37−25)≈3927W. C_water=Q/(18−4)≈280.5W/K. Since C_water<C_blood, C_min=C_water. Effectiveness ε=Q/(C_min×ΔT_max)=Q/(280.5×33)≈3927/9256.5≈0.42 (equivalently, ε=ΔT_water/ΔT_max=(18−4)/(37−4)=14/33≈0.42).
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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