Question

Saturated vapor at 200°C condenses to saturated liquid at 150 kg/s on the shell side of a heat exchanger (latent heat $h_{fg} = 2400$ kJ/kg). A fluid with $c_p = 4$ kJ·kg$^{-1}$·K$^{-1}$ enters the tube side at 100°C. Effectiveness = 0.9. The required tube-side mass flow rate is __________ kg/s (in integer).

Hint:

Condensing steam provides constant-temperature heat; therefore all latent heat directly enters the effectiveness formula.

Answer 1

Correct Answer: 1000

Heat released by condensation per second: \[ \dot{Q}_{\text{hot}} = \dot{m}_h\, h_{fg} = 150 \times 2400 = 360000\ \text{kJ/s} \] Effectiveness equation: \[ \varepsilon = \frac{\dot{Q}_{\text{actual}}}{\dot{Q}_{\max}} \] The maximum heat transfer (cold fluid capacity is the minimum): \[ \dot{Q}_{\max} = \dot{m}_c\, c_p (T_{h,in} - T_{c,in}) \] Here: \[ T_{h,in} = 200^\circ C,\quad T_{c,in} = 100^\circ C \] \[ T_{h,in} - T_{c,in} = 100^\circ C \] Actual heat transfer from condensation: \[ \dot{Q}_{\text{actual}} = 360000\ \text{kJ/s} \] Effectiveness: \[ 0.9 = \frac{360000}{\dot{m}_c\, 4 \times 100} \] Solve for tube-side mass flow rate: \[ 0.9 = \frac{360000}{400\, \dot{m}_c} \] \[ 400 \dot{m}_c \times 0.9 = 360000 \] \[ 360 \dot{m}_c = 360000 \] \[ \dot{m}_c = 1000\ \text{kg/s} \] Thus, \[ \boxed{1000\ \text{kg/s}} \]