- M is the mass of liquid in each tank (kg)
- T
_{0}is the temperature of the feed stream (K) - T
_{1}(t), T_{2}(t) and T_{3}(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 (m
^{2})

The three differential equations were solved analytically to give symbolic equations for the three temperatures T

_{1}(t), T_{2}(t) and T_{3}(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.
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