Theory

The SYNOTHERM^® heat exchangers are designed with the aid of self-contained computer-aided design software. Thus the best and most cost-effective solution for you can be found.

The maximum transferable power of a heat exchanger depends on the heat transfer area A in m², the heat transfer coefficient k in W / m²K and the logarithmic temperature difference $\Delta\vartheta_l_n$ ab [1].

$Q = k \times A \times \Delta\vartheta_l_n$

The VDI-heat-atlas gives a heat transfer coefficient k of 150 – 1200 W / m²K for tube bundle heat exchangers. For double-pipe heat exchangers, a k-value of 300 – 1400 W / m²K applies. A thermal transmittance k in the range 1000 – 4000 W / m²K is given for heat exchangers [2].

In addition, the maximum heat flow which can be emitted or absorbed by the heat exchanger medium is determined by the mass flow ṁ in kg / s, the specific heat capacity c_p in kJ / kg ° C, and the temperature difference between the inlet flow temperature $\vartheta_{inlet}$ and the outlet flow temperature $\vartheta_{outlet}$ in °C bestimmt [3].

$Q = \dot{m} \times c_p \times (\vartheta_{inlet} - \vartheta_{outlet})$

These two benefits must be the same. The maximum transferable capacity of the plate heat exchanger must not exceed the heat flow that can be delivered by the heat exchanger medium.

For heat exchangers, there are two different functional principles: the countercurrent and direct current principle. The heat exchangers SYNOTHERM^® work according to the countercurrent principle. The heat exchanger is located in a container, which is filled with a certain process liquid. The heat exchanger medium flows within the heat exchanger through the channel guide in the opposite direction to the process liquid.

With the countercurrent principle, a larger logarithmic temperature difference can be used for heat exchange or heat transfer. The logarithmic temperature difference for the countercurrent principle is calculated as follows [4]:

$\vartheta_l_n = \frac{\Delta\vartheta_{max} - \Delta\vartheta_{min}}{ln\frac{\Delta\vartheta_{max}}{\Delta\vartheta_{min}}}$

The heat transfer coefficient k is calculated for each individual application. In essence, it depends on the heat transfer coefficients $\alpha_{inside}$ und $\alpha_{outside}$ , the thickness of the sheet, the thickness of the inflatable material and the thermal conductivity of the sheet material [5]:

$\frac{1}{k} = ( \frac{1}{\alpha_{inside}} + \frac{d_{inside}}{2\cdot\lambda} \times \ln( \frac{d_{outside}}{d_{inside}} ) + \frac{d_{inside}}{d_{outside}} \times \frac{1}{\alpha_{outside}} )$

The pillow-shaped surface of the heat exchangers SYNOTHERM^® produces differently sized lenses, which are flowed through by the heat exchanger medium. Special arrangements of the weld point pattern produce turbulences in the heat exchanger and the Reynolds numbers Re result which are in the turbulent flow range. This effect is reinforced by additional deflections of the channels. The characteristic cushioning structure of the plate heat exchangers allows higher heat transfer coefficients α on the inside and consequently a higher heat transfer coefficient k. As the following basic formula shows, less heat transfer area A is required to obtain the same heat transfer performance Q.

The heat transfer coefficient $\alpha_{inside}$ applies to the heat exchanger medium, which flows through the channels of the heat exchanger. It is determined by the Reynolds number, the geometrical characteristics of the channel, the volume flow and the physical properties of the heat exchanger medium. The physical properties of the heat exchanger medium are taken into account by the Prandtl number. In addition, the density, the kinematic viscosity and the thermal conductivity of the heat exchanger medium are calculated. A further characteristic number, which is required to determine the heat transfer coefficient, is the nut number.

The heat transfer coefficient $\alpha_{outside}$ is based on experience gained over many years, which depends on the temperature of the process liquid and the movement of the process liquid.

The pressure loss caused by the heat exchanger can be calculated with the following basic formula [6]:

$\Delta p = \frac{\rho \times L \times w^2 \times \lambda}{2 \times d}$

Where $L$ is the total channel length in mm, $w$ is the flow velocity in m/s, $\lambda$ is the pipe friction coefficient and $d$ is the hydraulic diameter of a lens.

[1] von Böckh, P./Wetzel T. (Hrsg.) (2015): Wärmeübertragung, Grundlagen und Praxis, 6.Auflage, Karlsruhe, S.9
[2] Gesellschaft, VDI (2013): VDI-Wärmeatlas, 11. Auflage,Wiesbaden,S.85-87
[3] von Böckh, P./Wetzel T. (Hrsg.) (2015): Wärmeübertragung, Grundlagen und Praxis, 6.Auflage, Karlsruhe, S.8
[4] von Böckh, P./Wetzel T. (Hrsg.) (2015): Wärmeübertragung, Grundlagen und Praxis, 6.Auflage, Karlsruhe, S.9
[5] von Böckh, P./Wetzel T. (Hrsg.) (2015): Wärmeübertragung, Grundlagen und Praxis, 6.Auflage, Karlsruhe, S.28
[6] Khartchenko N. V. (1997): Umweltschonende Energietechnik, 1. Auflage, Würzburg, S.28