The Double-Pipe Heat exchanger Design Calculations formulas

The Double-Pipe Heat exchanger Design Calculations formulas

Heat exchangers can be classified in a number of ways, depending on their construction or on

how the fluids move relative to each other through the device. Now there will be looked at one particular heat exchanger to go a little deeper into the working principles and the practical utilizations.

A double-pipe heat exchanger consists of two concentric pipes or tubes. The outer tube is called the annulus. In one of the pipes a warmer fluid flows and in the other a colder one.

Due to the temperature difference between the fluids heat is transferred. By the word ‘fluid’ all substances that can ‘flow’ is meant. So the word fluid means not only liquids but also gases. In this part there will be looked at a double-pipe heat exchanger with parallel flow. This means that the hot fluid and the cold fluid flow in the same directions. There are also counter flow heat exchangers. In this situation the hot fluid and the cold fluid flow in opposite directions.

Schematically a double pipe heat exchanger with parallel flow is drawn in figure 2.1.

 

 

A double pipe heat exchanger with parallel flow

To understand what factors influence the dimensions of this heat exchanger when a certain heat rate is expected some simple equations will be examined.

First a simple heat balance:

 

 

The subscript c stands for cold.

But also the next equation is valid:

 

 

For the log mean temperature difference for parallel flow the following can be written down:

 

The next figure will show how the temperature of the hot and cold fluid changes along the length of the pipe

 

 

The course of the hot and the cold fluid along the length of the pipe

When the heat is transferred from the warmer fluid to the colder fluid it encounters resistances that will create several losses. There will be losses when the heat in the fluid transfers in direction of the wall, when the heat is transferred through the wall and when the heat is transferred from the wall to the flow in the annulus. In other words there will be a tube-film resistance, a tube-wall resistance and an annulus-film resistance. These losses are encountered for in the overall heat transfer coefficient U. When this coefficient is known and it is known what the several temperatures at the beginning and the end are or must be (material boundaries) a heat-transferring surface can be calculated for a desired heat rate.

Frequently it is wanted to get an idea of how big a heat exchanger will be for a certain performance. Size is one of the main factors in costs. The following properties must be known to perform a global calculation of the dimensions of a double-pipe heat exchanger with parallel flow.

-The required cooling down or heat up of the pipe fluid

-The temperatures of both fluids when entering the double-pipe heat exchanger

-The mass flows and heat capacity of both fluids ® the required heat rate can now be     calculated due to the heat balance equation (2.1)

-The LMTD can now be calculated; all the temperatures are known

-An estimate of the overall heat coefficient; this is very difficult. U depends, as one can see in equation (2.5), on inner and outer diameters, convection coefficients of both fluids and the transfer coefficient of the wall of the pipe (depending on wall thickness and material properties).

There are tables that can help make a good estimate for this parameter. Nevertheless has this parameter a great influence on the size of a heat exchanger and estimates must always be done with great care.

Now with the help of equation (2.2) the heat transferring area can be calculated. Knowing the heat transferring area gives a relation between the diameter of the pipe and the length of the heat exchanger. This gives a rough idea of the dimensions that can be expected.