(Solved): Problem (1) A counterflow double-pipe heat exchanger operates with hot water ...

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Problem (1) A counterflow double-pipe heat exchanger operates with hot water with \( 1050 \mathrm{~W} / \mathrm{m}^{2} . \mathrm{K} \) heat transfer coefficient Hlowing inside the inner pipe and a polymer fluid with \( 320 \mathrm{~W} / \mathrm{m}^{2} . \mathrm{K} \) flowing in the annular space between the two pipes. The water and enters at a temperature of \( 85^{\circ} \mathrm{C} \). The polymer enters at a temperature of \( 10^{\circ}{ }^{\circ} \mathrm{C} \) and leaves at a temperature of \( 50^{\circ} \mathrm{C} \) while the water leaves the exchanger at a temperature of \( 55^{\circ} \mathrm{C} \). Calculate the heat transfer rate expressed in \( \mathrm{kW} \), thick walled inner pipe with inner diameter is \( 3.6 \mathrm{~cm} \) and the outer diameter is \( 52 \mathrm{~mm} \) with length \( 55 \mathrm{~cm} \) and thermal conductivity \( [\mathrm{k}=50 \mathrm{~W} / \mathrm{m} . \mathrm{K}] \), and fouling factor on one side is \( R_{f i}=0.0002 \mathrm{~m}^{2} . K / W \). (by using LMTD method).