Heat Transfer from a Heating Coil

In this case it is assumed that heat is transferred from the coil to the tank contents, the discussion for heat withdrawal is similar. The sitrration is shown in Fig. 14.1. 

Process Dynamics and Control Modeling for Control and Prediction. Brian Roffel and Ben Betlem. 2006 John Wiley Sons Ltd. 

Let us make several assumptions so as not to eomplicate matters too much  

Generally, one will be interested in the response of the temperature T to changes in the flow F, the inlet temperature Ti and the flow F. These relationships can easily be derived from Eqn. (14.1) by linearizing it and taking the Laplace transform, the result is  

As can be seen from Eqn. (14.2), the temperature will show a first-order response to all changes. Equation (14.3) shows that the gain for temperature changes, either inlet temperature or steam temperature, is always less than one. 

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Each term refers to a control volume, which for a BR is the volume of the reacting system. The input of energy nicy be by heat transfer from a heating coil or jacket, and/or by generation by reaction. Similarly, the output of energy may be by heat transfer to a coil or jaded, and/or by loss by reaction. The accumulation is the nd result of the inputs and outputs, and may result in an increase or decrease in T of the reading system. 

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