How to calculate a heat exchanger
Definition of the process for the calculation of heat exchangers
A heat exchanger is an energy (in the form of heat) exchange system between a hot and a cold fluid. In practice, all the thermal duty of the hot fluid (fc) is transferred to the cold fluid (ff), thereby fulfilling the next energy balance:
The thermal duty of a fluid in liquid state depends on the mass flowrate and the temperature differential between the inlet and outlet sections. In a fluid with a change of phase in saturated conditions (either condensation or evaporation), the heat power depends on the mass flowrate and the enthalpy of the phase change, that is determined by the saturation pressure.
The process is defined when all the features have been fixed by the client, except of one, that will be calculated by means of the above-mentioned thermal balance. As an example:
- Liquid product (p), Liquid service (s). The practice is to define the flowrate and the inlet and outlet temperatures of the product, thus leaving free one of these 3 values in the service fluid:
- Liquid product (p), service with change of phase (s). It is common to set the flowrate and the inlet and outlet temperatures of the product side, as well as the service pressure, leaving free the service flowrate.
Thermal properties for the calculation of heat exchangers
The knowledge of the next thermal properties (both for the product and the service side) is a requisite for the design of the heat exchanger: density, specific heat, conductivity and viscosity. It is generally interesting for the designer to know the variation of these properties at different temperatures within the working range.
However, in the food industry, this information takes a special relevance: the viscosity of the food fluids can abruptly change with the temperature (even more for low temperatures), being common that the product has a non-newtonian behaviour, in which the viscosity depends also on the process velocity through the heat exchanger.
Therefore, a suitable modelling of the thermal properties is the basis for an optimal design of the heat exchanger.
SACOME provides you a complete database of more than 600 food products in order to ensure a correct determining of the thermal properties. For complex products, SACOME offers its clients the possibility to do rheological tests, starting from a little sample, in order to get the properties in an accurate way.
Definition of the heat exchanger
Once the process has been established and the thermal properties of the fluids have been modelled, the task of defining the heat exchanger starts itself.
Selection of the materials for the heat exchanger
SACOME manufactures its heat exchangers in stainless steel and carbon steel, and offers its customers other special materials for applications with a high risk of corrosion.
Selection of the geometry for the heat exchanger
This choice will depend on the type of process and the nature of the product. The Technical Department of SACOME will guide you to select the appropriate tubular exchanger, by evaluating the different requirements of the client: flow rate, pressure drop, available space, etc.
The tubular geometries most used for heat exchangers are Tube in Tube, Annular Space and Shell & Tube.
Configuration and surface finish for the heat exchanger
The configuration of the heat exchanger will depend on the type of process and the nature of the product.
The Technical Department of SACOME will advise you in order to choose the most suitable heat exchanger, assessing the different requirements of the client: process velocities, pressure drops, available space, etc.
Thermal design of the heat exchanger
Starting from the definition of the heat exchanger, the key task for the designer is the sizing of the heat exchanger. The designer must calculate the optimal exchange area that can fulfill all the requirements imposed by the client.
To that end, the next heat transfer equation is applied, where Q is the thermal exchange duty, U is the global thermal exchange coefficient, A is the exchange area, and LMTD is the logarithmic mean temperature difference.
This equation must be discretised along the heat exchanger into a suitable number of sections: the heat transfer efficiency between the fluids varies along the heat exchanger as, among other reasons, the thermal properties change with temperature and complex thermal phenomena take place inside the heat exchanger.
In order to be able to understand the calculation procedure, the heat transfer equation can be applied to the whole heat exchanger, thus obtaining an initial approach to the required exchange area. This process is explained below for a 2 concentrical tubes heat exchanger in counter-current.
Determining of the thermal duty
This is obtained from the process data already settled for the product, that will usually be processed through the inner tube.
Calculation of the Logarithmic Mean Temperature Difference (LMTD)
This is defined between 2 sections of the heat exchanger, and it depends on the inlet and outlet temperatures of the product and service fluids. Speaking about the whole heat exchanger, these 4 temperatures are well known. However, if we wish to discretise the heat exchanger into several increments and calculate the LMTD for each of them, there are some values unknown at a first glance, being necessary to execute a process of iteration and convergence.
Determining of the overall heat transfer coefficient
This is the result of the addition of the different thermal resistances:
Convection thermal resistance
This resistance assesses the thermal exchange produced by convection in both fluid channels. It is in inverse ratio to the thermal exchange coefficient of the fluid, h.
For the product side, being Dp and dp the external and internal diameters of the inner tube, it is:
while for the service channel, it is:
The critical issue when designing the heat exchanger is the determining of the thermal exchange coefficients reliably and accurately: a wrong calculation will result in a lack of performance, and the heat exchanger may even not reach the required temperatures.
Depending on the flow path (tube, annular space, etc.) and on the flow regime (laminar, turbulent, etc.) it will also be necessary to establish an empirical correlation for Nusselt Nu, as it is the dimensionless parameter from which the heat exchange coefficient can be calculated. Generally speaking, Nusselt will depend on other dimensionless parameters as Reynolds, Prandtl, Graetz, Grashof, etc.
As a registered member of Heat Transfer Research, Inc., SACOME performs the design of its exchangers according to the newest version of the software HTRI Xchanger Suite v7.00.
Conduction thermal resistance
It is used for the assessment of the heat exchange produced by conduction through the wall that separates both fluids. For a circular tube, being k the thermal conductivity of the metal, it is defined as:
Fouling thermal resistance
As the heat exchanger is operating, a layer composed of the impurities of the product (it happens in a similar way with the service side) is being deposited on the surfaces being in contact with the fluids. These fouling resistances worsen the heat exchange process.
For the applications (mainly within the industrial field) in which the shutdown for cleaning tasks is required to be delayed, it is common practice to consider these additional resistances since the beginning, thereby oversizing the equipment. For food applications they are not contemplated, since the cleaning tasks are carried out more frequently.
In the product side, it is:
Whereas in the service channel, it is:
Calculation of the required exchange area
By applying the heat exchange equation, it is possible to obtain the required exchange area. Given that the diameter of the inner tube has already been set, the solution to the problem consists on obtaining the total length of the heat exchanger Lt:
The result we get is the theoretical required area. However, as it is necessary to choose a length of the tube available on the market, L: if this length is less than the theoretical one, then a set of heat exchangers, n, is required to be placed in series:
Anyhow, it’s always advisable that the exchange area is higher than the theoretical one, depending on the uncertainty when determining the thermal properties of the fluids, the fouling resistances or the heat transfer coefficients. In order to quantify this overdesign, an overall thermal exchange coefficient, or “fouled K-value”, is defined: