In the first part of this article, heat exchanger design basics were introduced. In the following article, the design formulations and calculations are introduced.

As mentioned in part 1, overall heat transfer in heat exchanger in increased in the flow are set to be countercurrent. As a result, only countercurrent double pipe heat exchanger design is discussed here. To start the design of a double pipe heat exchanger, the first step is to calculate the heat duty of the heat exchanger. It must be noted that for easier design, it’s better to ignore heat loss in heat exchanger for primary design. The heat duty can be defined as the heat gained by cold fluid which is equal to the heat loss of the hot fluid. It can be calculated as:

In this equation, the subscript c indicates the parameters related to cold flow and h relates to hot flow. is the mass flow rate of streams, C is the specific thermal heat capacity and is the difference of the flow input and output temperatures. Note that heat capacities are measured at average temperature equal to:

As was mentioned in the heat exchanger design part 1, for calculation of convective heat transfer LMTD or logarithmic mean temperature difference is used:

Fluid flow properties usually are functions of the flow temperature. To apply these changes, an average temperature is used at which the fluid properties are measured. This average temperature is called *caloric temperature. *Since the calculation of this temperature depends on several factors, it may not be calculated easily. In heat exchanger design, if the temperature difference of flow are moderate or the flows have viscosity less than 1cP at cold terminal temperature, linear average temperature is used instead of caloric temperature.

The most important limiting factor in heat exchanger design is the pressure drop through the inner pipe side and the annulus side. Therefore, the flow with higher volumetric flow rate is usually sent to the side with higher flow cross sectional area.

Let’s start the calculations of the annulus site. The first step here is the calculation of the flow area:

*D _{2}* is the internal diameter of the outer pipe and

*D*is the outer diameter of the inner pipe.

_{1}For heat transfer calculations, an equivalent diameter is needed calculated as:

Having the equivalent diameter, the Reynolds number will be:

To calculate the convective heat transfer, outside convection heat transfer coefficient, h_{o}, is needed. This parameter is obtained using j_{H} which can be calculated from figure 1. H_{o} can be calculated as follows:

To here, the same procedure can be applied to the inner pipe. The only differences are the flow area and the equivalent diameter:

Where D is the inner diameter of the inner pipe and inside convection heat transfer coefficient is calculated as:

To estimate the overall heat transfer coefficient, both heat transfer coefficients must be based on the outer surface of the inner pipe or its inner surface. To write h_{i} based on outer surface following equation is used and overall heat transfer coefficient is calculated:

,

ID and OD are inside and outside diameter of the inner pipe, respectively. The subscript c in U_{c} indicates that it is the *clean* heat transfer coefficient. U_{c }cannot be used to calculate heat transfer rate directly, because of the resistance caused by fouling, sedimentation and other factors. As a result, it will be converted to dirty heat transfer coefficient using dirt factor R_{d}.

In the next part, more information about dirt factor and heat exchanger design will be represented. Also pressure drop in double pipe heat exchanger will be discussed.

Resource:

“Process Heat Transfer”, Donald Q. Kern.

Written by P.Jowkar