Question 29 on the morning of the first day of 2014
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29. A reactor contains 1.4 m3 of reaction medium with a density of 1250 kg/m3 and a heat capacity of 4.2 kJ/(kg·K). An immersed coiled tube heater is used to heat the reaction medium with saturated steam at 127°C; the heat transfer coefficient is 650 W/(m2·K). Ignoring heat losses from the reactor and the volume occupied by the coiled tubes, what is the minimum heating area (in m2) required to raise the temperature of the reaction medium from 25°C to 95°C within 2 hours? (A) 0.98 (B) 1.45 (C) 1.82 (D) 2.09 How do I solve this problem? Please help!
Choose C. Heat balance: the rate at which heat is transferred to the reaction medium = the heat transfer rate of the heater. That is, ρVC△t/τ=KA△tm; simply substitute the values and calculate.
But what is △tm? In the actual heating process, △tm keeps changing. It should be an integration process. As time passes, the temperature inside the kettle gradually increases, and △tm gradually decreases. How can one calculate the area under this linear variation?