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Thermal enhancement factors for 3D printed elements in square tube

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Abstract

In this paper, the increases in heat transfer intensity in a square tube as well as the pressure losses from 3D printed elements are experimentally measured. To measure the heat transfer coefficient, we chose a dynamic, thermal oscillation method (or TOIRT method), which we validated on a well-known experiment of water flow in a pipe and compared the data with the most frequently cited Gnielinski correlation with Hausen correction. A twisted tape with different pitches was chosen as an element and its pressure loss was measured simultaneously, which we converted to a Fanning friction factor. We determined the thermal enhancemet factor by the ratio of heat transfer gain and pressure loss and found the optimal helix pitch \(p = 0.87h\).

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Abbreviations

a :

Thermal diffusivity (\(\mathrm m^2/s\))

\(a_{1, 2}\) :

Model constants (−)

\(c_\mathrm{p}\) :

Specific heat capacity (\(\mathrm J/(kg\, K)\))

d :

Diameter (\(\mathrm m\))

h :

Tube width (\(\mathrm m\))

L :

Length (\(\mathrm m\))

\(\mathrm Nu\) :

Nusselt number (\(\mathrm -\))

O :

Circumference (\(\mathrm m\))

p :

Pitch (\(\mathrm m\))

\(\Delta p\) :

Pressure loss (\(\mathrm Pa\))

\(\mathrm Pr\) :

Prandtl number (\(\mathrm -\))

\(\mathrm Re\) :

Reynolds number (\(\mathrm -\))

S :

Surface (\(\mathrm m^2\))

T :

Temperature (\(^{\circ }C, K\))

\(\Delta T\) :

Temperature difference (\(^{\circ }C, K\))

u :

Velocity (\(\mathrm m/s\))

\(\dot{V}\) :

Volumetric flow rate (\(m^3/s\))

x, y, z :

Coordinates (\(\mathrm -\))

\(\alpha\) :

Heat transfer coefficient (\(W/(m^2\, K)\))

\(\delta\) :

Wall thickness (\(\mathrm m\))

\(\epsilon\) :

Emissivity (−)

\(\lambda\) :

Thermal conductivity (\(\mathrm W/(m\, K)\))

\(\varphi\) :

Phase shift (\(^{\circ }\))

\(\mu\) :

Dynamic viscosity (\(Pa\, s\))

\(\nu\) :

Kinematic viscosity (\(m^2/s\))

\(\eta\) :

Thermal enhancement factor (−)

\(\rho\) :

Density (\(kg/m^3\))

\(\xi\) :

Darcy Weisbach friction factor (\(\mathrm -\))

\(\mathrm E\) :

enhanced

\(\mathrm H\) :

hydraulic

\(\mathrm max\) :

maximum

\(\mathrm x\) :

local

−:

overall

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Acknowledgements

Authors acknowledge support from the ESIF, EU Operational Programme Research, Development and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague.

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  1. Faculty of Mechanical Engineering, Department of Process Engineering, Czech Technical University in Prague, Technicka 4, 166 00, Prague 6, Czech Republic

    S. Solnař & M. Dostál

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  1. S. Solnař
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Correspondence to S. Solnař.

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Solnař, S., Dostál, M. Thermal enhancement factors for 3D printed elements in square tube. Heat Mass Transfer 58, 657–667 (2022). https://doi.org/10.1007/s00231-021-03133-7

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