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Low-Finned Tubes for Condensation

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Abstract

Low-finned tubes offer a wide potential for applications in heat exchangers where condensation occurs on the outside of the heat exchanger tubes. Typically, the fin height and the inter-fin spacing is smaller than 1 mm. This leads to an increased surface area, which is usually increased by a factor of 2–5. Additionally to this, fluid dynamic effects come into play, which reduce the condensate layer on the tube and thereby increase the heat transfer coefficient, too. With horizontally arranged smooth tubes a bundle effect can be seen since the condensate layer increases from row to row. This negative effect can be reduced with low-finned tubes where the condensate is withdrawn due to capillary forces and higher heat transfer coefficients can be observed. Pure component condensation with free convection can be described with the theory derived by Nusselt (1916) for smooth tubes. For low-finned tubes a wide range of experimental data is presented along with a newly developed model to predict the outer heat transfer coefficients. The condensation of mixtures differs from the condensation of pure substances, since the thermal resistance in the vapour phase cannot be neglected. Thereby, the heat transfer coefficients are lowered for both smooth and low-finned tubes. An innovative model, which includes the effect of the mole fraction of the mixture components on the heat transfer, is presented. As compared to the well-known film model the new model is based on a fit of the thermodynamic correction factor and can describe the experimentally measured heat transfer coefficients much better.

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Notes

  1. 1.

    The tubes listed in this table were investigated in various publications and are mentioned in this article. Nevertheless, this table does of course not show the whole variety nor all possible structures and dimensions of low-finned tubes. It rather shall give a short overview to get a feeling for the values.

  2. 2.

    In tube bundles the row on top has the number 1, the row below the number 2 and so on. Thus, a high row number means this row is somewhere at the bottom of the bundle.

  3. 3.

    In the original publication the factor in the equation is not 0.728 but 0.725 due to the graphical integration Nusselt applied. With numerical integration the factor of 0.728 is obtained and used in today’s textbooks (Baehr and Stephan 2011).

  4. 4.

    Both publications do not actually write that \(\varepsilon_{{\dot{q}}}\) is independent of \(\dot{q}\), but in case of Briggs and Rose (1994) their equation for ε is independent of the heat flux and in case of Kumar et al. (2002a) the dependency between the outer heat transfer coefficient and the heat flux in their model is actually fixed to be the same as in Nusselt’s Theory.

Abbreviations

a :

Thermal diffusivity (m2/s)

A :

Area (m2)

\(c_{p}\) :

Specific heat capacity (J/kg K)

C:

Constant in Eq. (11)

d :

Diameter (mm)

g :

Gravity constant (m/s2)

h :

Fin height (mm)

\(\Delta h\) :

Specific enthalpy difference (kJ/kg)

\(\Delta h_{V}\) :

Specific enthalpy of evaporation (kJ/kg)

k :

Overall heat transfer coefficient (W/m2 K)

L :

Length (m)

m :

Exponent Eq. (4)

\(\dot{m}\) :

Mass flux (kg/(m2 s))

n :

Number

p :

Pressure (bar)

\(\dot{q}\) :

Heat flux (kW/m2)

\(\dot{Q}\) :

Heat (kW)

r :

Radius (mm)

\(R_{\text{th}}\) :

Thermal resistance (K/W)

s :

Fin spacing (mm)

t :

Fin thickness (mm)

T :

Temperature (°C, K)

\(T_{\theta }\) :

Temperature at the angle \(\theta\) (°C, K)

u :

Velocity (m/s)

x :

Liquid mole fraction

y :

Vapour mole fraction

Z :

Thermodynamic factor

\(\alpha\) :

Heat transfer coefficient (W/m2 K)

\(\beta\) :

Inclination angle of fin (°)

\(\Delta\) :

Difference

\(\Delta T_{\text{outside}}\) :

Temperature difference between vapour and wall (K)

\(\varepsilon\) :

Enhancement factor

\(\eta\) :

Dynamic viscosity (Pa s)

\(\lambda\) :

Thermal conductivity (W/m K)

\(\varrho\) :

Density (kg/m3)

\(\sigma\) :

Surface tension (N/m)

\(\phi_{f}\) :

Flooding angle (°)

*:

Equilibrium

\({\blacksquare }\) :

Ackermann-corrected

-:

Mean

1:

Component 1, lighter boiling component, row 1

b :

Boiling

Bulk :

Bulk

c :

Condensing

cond :

Condensate

CW :

Cooling water

eq :

Equilibrium

experiment :

Measured, retrieved by experiment

fin :

Fin

fin root :

Fin root

fin spacing :

Fin spacing

fin tip :

Fin tip

flooded :

Flooded

G :

Vapour phase

inside :

Inside

lft :

Low-finned tube

model :

Calculated with a theoretical model

outside :

Outside

Ph :

Phase boundary

\(\dot{q}\) :

At constant heat flux

root :

Root

s :

At saturation

st :

Smooth tube

\(\Delta T\) :

At constant temperature difference

tip :

Tip

tot :

Total

tube :

Tube

\(u_{v}\) :

At constant gas flow velocity

v :

Vapour, vapour flow

vapour :

Vapour phase

W :

Wall

Bo :

Bond number

Cn :

Condensation number

Ja :

Jakob number

Pr :

Prandtl number

Re :

Reynolds number

Ro :

Tube number

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Authors and Affiliations

  1. Fakultät Für Maschinenwesen, Technische Universität München, Boltzmannstraße 15, 85748, Garching, Germany

    Harald Klein & Alexander Büchner

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  1. Harald Klein
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  2. Alexander Büchner
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Correspondence to Harald Klein .

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  1. Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Hans-Jörg Bart

  2. TU Braunschweig, Braunschweig, Germany

    Stephan Scholl

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Klein, H., Büchner, A. (2018). Low-Finned Tubes for Condensation. In: Bart, HJ., Scholl, S. (eds) Innovative Heat Exchangers. Springer, Cham. https://doi.org/10.1007/978-3-319-71641-1_6

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  • DOI: https://doi.org/10.1007/978-3-319-71641-1_6

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