Develop the mathematical model for the system shown in the following figure by
developing the mass and energy balances.
ii. Express the energy given by two steam flows in two different ways: (a) in terms of steam
flowrates and heat of condensations and (b) in terms of heat exchange (e.g. heat transfer
coefficients, heat transfer areas and and temperatures)
The cross-sectional areas of two tanks are A1 and A2 measured in m2
All flowrates are volumetric measured in m3
Flowrates F2 and F3 are proportional to level H1 and H2 measured in meter, respectively.
Q1 kg/min of saturated steam at Ts1 flowing in the steam coil is used to heat the first tank.
Q2 kg/min of saturated steam at Ts2 flowing in the steam coil is used to heat the second.
The tanks are well mixed. No vapour is produced either in the first or the second tank.
The steam coming out from the steam coils are condensates (or liquid water) at the same
temperatures of the steam entering the coils. The heat of condensation (or latent heats) at
Ts1 and Ts2 are H1 and H2 (kJ/kg of steam), respectively.
The heat exchange areas of the two steam coils are Ac1 and Ac2, respectively. The heat
transfer coefficients based on the surface areas of the steam coils are h1 and h2
It can be assumed constant density (kg/m3
and constant heat capacity Cp (kJ/kgC) for
the liquid water in the system