Heat Exchanger - 2

LMTD & Correction Factor (F)

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---------------------------------------------------- (1)

Q = Heat transferred in H-E-X

U = Overall Heat transfer coefficient

F = Correction Factor.

 = Logarithmic Mean Temperature Difference (LMTD)

* LMTD is dependent only on inlet and outlet temperatures and is independent of type of HE used.

where, 

1-stands for Inlet                                                  

2-Stands for Outlet

• Normal Practice if to calculate LMTD for counter flow and apply correction factor F to it.

Fig.1. LMTD for single pass STHE

Fig.2. LMTD for 1/2 STHE

F (Correction Factor)

• Shows departure form true counter current flow
• F is correction factor for multi-pass and crossflow heat exchanger and given for two-pass shell-and-tube heat exchangers in equation (4) below.
• 0 < F < 1
• fn { fluid Temperature, no. of passes }
• F > 0.8, if not then redesign the HEX with more no. of passes or larger LMTD

Find F value:

1. Find R using:

------------------------- (2)


 
     2. Find P using:

----------------------------------------- (3)

   3. F Value Analytically

From equations (2) and (3) get the values of R & P and substitute in equation (4)

 

------------------------------------- (4)

4. Graphical F value:

Fig.3. 1-Shell pass, 2 or more even Tube passes

Fig. 4. 2-Shell Pass, Multiples of 4 Tube passes

   

Fig. 5. Divided Shell Flow & Multiples of 2 Tube passes

Fig. 6. Split shell Flow & 2 Tube passes

Example:

Is 1/2 Shell & Tube HE suitable for following condition ? 

Tc1 = 70 deg., Tc2 = 130 deg.

Th1 = 240 deg., Th2 = 120 deg

Solution:

• From fig. 3 we see that F = 0.735, which is very low value, Since for F < 0.75, F falls rapidly with smal increase in P which implies that basis assumptions made cannot be neglected.
• Thus, 1/2 Shell & Tube HE is not suitable for this condition.
• Try Increasing value of LMTD or redesign with more passes.

Calculate, using software, the F values for different shell and tube pass combination here and decide whether the combination is suitable for the following temperature conditions.

The above discussed LMTD & correction factor is useful only when both inlet and outlet temperature conditions are known.

Effectiveness-NTU method is used when one of the temperature is not known.

Effectiveness-NTU method is more useful for Rating rather than design, hence will not be discussed here.
Refer

• Incropera & dewitt (2001)
• Engineering Science data unit in their design guides 98003-98007 ( 1998 ).