Case B Heating in a Filling Tank

Liquid flows continuously into an initially empty tank, containing a full-depth heating coil. As the tank fills, an increasing proportion of the coil is covered by liquid. Once the tank is full, the liquid starts to overflow, but heating is maintained. A total mass balance is required to model the changing liquid volume and this is combined with a dynamic heat balance equation. 

Assuming constant density, the mass balance equation is 

Assuming Aq is the total heating surface in the full tank, with volume, Vq, and assuming a linear variation in heating area with respect to liquid depth, the heat transfer area may vary according to the simple relationship 

More complex relationships can of course be derived, depending on the particular tank geometry. 

Let us assume an adiabatic, semi-continuous reactor (see Sec. 3.2.4) with negligible input of mechanical energy (Fig. 1.22). 

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