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
• T_s is the temperature of the heating coil
• W is the flowrate of the feed stream (kg s^-1)
• C_p 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 T_n of the nth tank connected in series, as predicted by this equation.

Download Excel Spreadsheet to Calculate Temperature Dynamics of Heated Tanks Connected in Series