A large cylindrical vessel is used as a batch reactor and is perfectly mixed.
The liquid inside is heated to keep the reactants at an elevated temperature.
Heat is lost through the portion of the vessel walls that is in contact with the liquid
contents, corresponding to an area of 25.9 m2
. The overall heat-transfer
coefficient, U, is 200 W m-2 K-1
.
The temperature of the ambient surroundings is 15 ºC, the mass of liquid in the
tank is 12.7 x 103
kg, and its specific heat capacity is 3000 J kg-1 K-1. There is no
flow into or out of the tank. The contribution of any chemical reactions to the heat
balance is very small, and should be neglected.
(a) Determine the rate of heating required to keep the contents of the tank at a
steady-state temperature of 100 ºC.
[2 marks]
(b) At a given moment (at t=0), it starts to rain. This causes an increase in the
rate of heat loss from the tank, manifested in a 10% increase in the overall
heat-transfer coefficient. The ambient temperature has not changed.
i. What is the steady-state gain in the temperature of the tank
contents, in response to changes in U?
A large cylindrical vessel is used as a batch reactor and is perfectly mixed.
The liquid inside is heated to keep the reactants at an elevated temperature.
Heat is lost through the portion of the vessel walls that is in contact with the liquid
contents, corresponding to an area of 25.9 m2
. The overall heat-transfer
coefficient, U, is 200 W m-2 K-1
.
The temperature of the ambient surroundings is 15 ºC, the mass of liquid in the
tank is 12.7 x 103
kg, and its specific heat capacity is 3000 J kg-1 K-1. There is no
flow into or out of the tank. The contribution of any chemical reactions to the heat
balance is very small, and should be neglected.
(a) Determine the rate of heating required to keep the contents of the tank at a
steady-state temperature of 100 ºC.
[2 marks]
(b) At a given moment (at t=0), it starts to rain. This causes an increase in the
rate of heat loss from the tank, manifested in a 10% increase in the overall
heat-transfer coefficient. The ambient temperature has not changed.
i. What is the steady-state gain in the temperature of the tank
contents, in response to changes in U?
