In the 2^{nd} part of this article, the calculation of convective heat transfer coefficient was explained. In a double pipe heat exchanger the internal and external heat transfer coefficients are different and it is required to use an overall heat transfer coefficient to perform the calculations.

As was mentioned before, U_{C}, is defined as follows based on convection heat transfer coefficients:

In heat exchangers, this overall heat transfer coefficient may change through the time. This is because factors such as fouling, precipitation or dirt reduce heat transfer rate. Therefore the dirt factor R_{d} is defined to take this effect into account:

U_{D} is the design overall heat transfer coefficient and can be used in the following form:

Using the above equation, for a given heat duty, it’s possible to calculate the heat transfer area needed in the heat exchanger.

Besides the thermal considerations, it’s important to calculate the pressure drop of the fluids in the inner and outer pipes. To perform this calculations, the first step is to calculate the Reynolds number:

Where D_{e} is the hydraulic equivalent diameter for the annuli:

D_{O} and D_{i} are outer pipe internal diameter and inner pipe external diameter, respectively. Equivalent diameter equals to pipe internal diameter for inner pipe.

Next step is the calculation of friction factor. The basic way is to use the friction factor chart, represented in figure 1. Other way is to use the correlations which are based on the figure 1.

For turbulent flow, friction factor in tubes is given by the following equation within ±5 percent:

For clean iron and steel pipes, friction factor is given by the following equation within ±10 percent:

The pressure drop through the annuli in is expressed in *length of liquid* as:

Where G_{a} is mass velocity of the fluid, g is the acceleration of gravity, ρ is fluid density and L_{a }is the length of the annuli. Similarly, for the inner pipe:

Beside the pressure drop inside pipes, there is a pressure drop in the entrance of each hairpin:

Where n is the number of hairpins and V is the fluid velocity. The total pressure drop in heat exchanger is:

Allowed pressure drop in a double pipe heat exchanger in 10 psi for both inner and outer pipes.

Resource:

“Process Heat Transfer”, Donald Q. Kern.

Written by P.Jowkar