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**8.2.7 Pressure drop in the heat exchanger**

Pressure drop calculation is an important task in heat exchanger design. The pressure drops in the tube side as well as shell side are very important and quite a few co-relations are available in the literature. One such co-relation is given below in the subsequent subsection.

**8.2.7.1 Correlation for tube side pressure drop (eq. 8.10)**

(8.10)

where,

ΔP_{t,f} = total pressure drop in the bundle of tube

f = friction factor (can be found out from Moody’s chart)

G_{t} = mass velocity of the fluid in the tube

L = tube length

n = no of tube passes

g = gravitational acceleration

ρ_{t} = density of the tube fluid

d_{i} = inside diameter of the tube

m =0.14 for Re > 2100

0.25 for Re < 2100

The above correlation is for the pressure drop in the tubes owing to the frictional losses. However in case of multi pass flow direction of the flow in the tube changes when flow is from 1-pass to another pass and the pressure losses due to the change in direction is called return-loss. The return-loss (ΔP_{t,r}) is given by eq.8.11,

(8.11)

n = no of tube pass

v_{t} = velocity of the tube fluid

ρ_{t} = density of the tube fluid

Therefore, the total tube side pressure drop will be,

Δp_{t} = ΔP_{t,f} + ΔP_{t,r}

**8.2.7.2 Correlation for shell side pressure drop**

The following correlation (eq.8.12) may be used for an unbaffled shell,

(8.12)

The above equation can be modified to the following form (eq.8.13) for a baffled shell,

(8.13)

where

L = shell length

n_{s} = no of shell pass

n_{b} = no of baffles

ρ_{s} = shell side fluid density

G_{s} = shell side mass velocity

D_{h} = hydraulic diameter of the shell

D_{si} = inside diameter of shell_{fs} = shell side friction factor

The hydraulic diameter (D_{h}) for the shell can be calculated by the following equation (eq. 8.14),

(8.14)

where,

n_{t} = number of tubes in the shell

d_{o} = outer diameter of the tube

The friction factor (f_{s}) can be obtained by the Moody’s chart for the corresponding Reynolds number

**8.2.8. Heat transfer effectiveness and number of transfer units (NTU)**

The LMTD is required to be calculated for the evaluation of heat exchanger performance. However, the LMTD cannot be directly calculated unless all the four terminal temperatures (T_{c,i}, T_{c,o}, T_{h,i}, T_{h,o}) of both the fluids are known.

Sometimes the estimation of the exchanger performance (q) is required to be calculated on the given inlet conditions, and the outlet temperature are not known until q is determined. Thus the problem depends on the iterative calculations. This type of problem may be taken care of using performance equivalent in terms of heating effectiveness parameter (η), which is defined as the ratio of the actual heat transfer to the maximum possible heat transfer. Thus,

(8.15)

For an infinite transfer area the most heat would be transferred in counter-current flow and the q_{max} will be dependent on the lower heat capacity fluid as such,

The actual heat transfer

The capacity ratio, which is the relative thermal size of the two fluid streams, is defined as,

On careful analysis, we can say that

U·A: Heat exchange capacities per unit temperature difference.

This thermal sizing (U·A) can be non-dimensionalised by dividing it to the storage capacity of one of the fluid streams. Given limits the maximum heat transfers. The non-dimensional term obtained is known as the number of transfer units (NTU)

It should be noted that

The actual determination of this function may be done using heat balances for the streams. For a parallel flow exchanger the relation is shown below

The above relation is true for both the condition

Similarly the functional relationship for counter –current exchanger is

(8.16 & 8.17)

The previous relation (eq. 8.16 and 8.17) were for 1-1 exchanger. The relation for 1-2 exchanger (counter current) is given by eq. 8.18, 8.19),

(8.18)

(8.19)

When the fluid streams are condensing in a 1-1 pass exchanger (fig. 8.15) as shown below,

Fig.8.15: Condenser with the temperature nomenclature

the following relation arrives.

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