Heat transfer coefficients for drop wise condensation are four to eight times higher than those for film wise. Steam is the only pure vapour known to condense in drop wise manner under certain required conditions. Film of condensate on the tubethan those for film wise. Steam is the only pure vapour known to condense in drop wise manner under certain required conditions. Film of condensate on the tube wall contributes the controlling resistance (Pg - 252 -253, D.Q .Kern "Process Heat Transfer")
With downward flow of condensing vapours at high velocity, the measured heat transfer coefficients are as much as ten times higher than those predicted for film type condensation neglecting the effect of vapour velocity (Pg -336, McAdams, Heat Transfer) An increase in the mass velocity of the fluid past the surface is accompanied by an increase in the individual coefficient.
If corresponding - individual resistance 1/h is a substantial fraction of the total resistance 1/u, the overall coefficient will increase (Pg - 189, McAdams) Tube side
*Nu = h,i D / K = 0.0115 (Re) 0.90 (Pr) 0.33
Re = Reynolds Number
Pr = Prandtl Number
Nu = Nusselt Number
Calendria side (outer wall of tubes)
ho De /K = 0.36 (DeGs 55 (Cp m / K ) 0.33 )( m/ms)0.14
De - Shell side equivalent diameter
G - s Mass velocity
jH = (hoDe/K ) (Cp m / K ) 0.33 (m/ms)0.14
(Pg 137 DQ Kern)
1/U = 1/ho + 1/hio + Rd [hio =hi(A 1 /Ao ]
smaller coefficient is the controlling film coefficient. If the difference is large, enough for sugar solution is significantly lower than that for steam with sweeping calendria technology even if h steam is increased further, it will not affect you.
All these equations are applicable for Newtonian fluids and for sensible heat transfer or in other words these equations are not applicable for two phase fluid flow i.e. (vapour +Liquid inside the tube) and simultaneous phase change from liquid phase to vapour phase with instant transfer of latent heat of vaporization. The only Newtonian equation which holds good and applicable is Q= =WCp DT = UA LMDT
Measurement of Q in the evaporator is calculated as W x l
By substituting the Q value and LMDT in last equation, overall U is calculated which is most practical. In this particular case, condensation is very rapid due to sweeping of calendria and increase in mass velocity inside the tube in the ratio as per calculation given below:
1. In case of 1700 m2 heating surface, one body having 45 mm OD and 42 mm ID and 2m thick. and when the heating surface is divided in the ratio 1100 m2
and 600 m2 for Primary to secondary calendria respectively.
2.1 The primary calendria having heating surface 1100 m2 the no of tubes of same dimension 45 mm OD, 42 mm ID and tube length 2 m, no of tubes would be 4121.
2.2 The secondary calendria having heating surface 600 m2 the tube sizes having 45 mm OD, 42 mm ID and 1.5 m length the no of tubes is 3000.
2.3 The cross sectional area of each tube, both in primary and secondary is same which is equivalent to .00138 m2. Say, this is called as A.
2.4 The total cross sectional area of primary calendria would be A x 4121. Similarly total cross sectional area of secondary calendria would be A x 3000.
Total cross sectional area of single body evaporator would be A x 6390.
Since we are concerned with mass velocity as the controlling factor for overall heat transfer coefficient, the ratio of mass velocity for primary and secondary will be in the ratio 1:1.55 and for secondary calendria 1:2.1. That is with respect to single body mass velocity would be 1.55 times more in primary calendria and 2.1 times more in secondary calendria.
The weighted average as far as distribution of heating surface and number of tubes due to difference in length (2 m effective length in primary and 1.5 m in secondary) is calculated.
The weighted average of increase in heat transfer coefficient with respect to one single body having equivalent heating surface will be 1.96 times more. However, we have taken a conservative figure of 1.4 times than the theoretical calculation of 1.96 times.
The maximum heat transfer coefficient inside the tube having boiling liquid as reported in literature is 5678 W/M2 H.S./oC. and the condensing steam as 11356 W/M2 H.S./oC.and overall U 2981 W/M2 H.S./oC.. Whereas in the duplex evaporator resulting U has been calculated as 7966 W/M2 H.S./oC.. This figure is very much realistic and achievable.
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