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The arrangement of a forward feed triple effect evaporator is shown in Figure 3.9 . The energy balance equations in all effects are given below:

Figure 3.9. Flow rates and pressure in a triple effect evaporator ([2] page 399) .

Effect I :                                          (3.1)

If the sensible heat of the steam is neglected this equation can be rewritten as-

                                                                        (3.2)

Effect II :                                 (3.3)

Effect III :            (3.4)

where,

is the rate of vapor generated in the k^th effect

m_f and m_s are the feed and steam flow rate

H_k is the enthalpy of the solution leaving the k^th effect at T_s and P_s

is the enthalpy of vapor (steam) generated in the k^th effect

H_lk is the enthalpy of liquid in the k^th effect

λ_s is latent heat of steam introduced in the 1^st effect at P_s.

and are the latent heats of steam condensation at pressure P₁ and P₂ respectively.

If U_D1 , U_D2 and U_D3 are the corresponding overall heat transfer coefficients and A₁ , A₂ and A₃ are the heat transfer area required, then it may be written as -

Effect I:                                                       (3.5)

Effect II :                                               (3.6)

Effect III :                                             (3.7)

where,

is the quantity of heat transferred in k^th effect

is the boiling point of the solution in k^th effect at the prevailing pressure

T_s is the steam temperature entered to the 1^st effect

is the boiling point elevation in the k^th effect, where is the boiling point of pure solvent (water) in k^th effect at the prevailing pressure

Eqs. 3.2 to 3.7 are solved to calculate the heat transfer area by trial-and-error calculations.