Temperature Dynamics of Heated Tanks Connected in Series

This Excel spreadsheet models the temperature dynamics of a feed stream heated in three tanks connected in series. Each tank has a heating coil at a fixed temperature, and it is assumed that each tank is perfectly mixed

The temperature dynamics are modeled by these three differential equations.

  • M is the mass of liquid in each tank (kg)
  • T0 is the temperature of the feed stream (K)
  • T1(t), T2(t) and T3(t) are the temperatures in each tank
  • Ts is the temperature of the heating coil
  • W is the flowrate of the feed stream (kg s-1)
  • Cp is the specific heat capacity of the feed stream (J kg-1 K-1)
  • U is the overall heat transfer coefficient (W m-2 K-1)
  • A is the heat transfer area (m2)
The three differential equations were solved analytically to give symbolic equations for the three temperatures T1(t), T2(t) and T3(t) . These  equations were then translated into Visual Basic and implemented in Excel.

The spreadsheet also gives the steady-state temperature Tn of the nth tank connected in series, as predicted by this equation.


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