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Electronic component cooling inside switch cabinets: combined radiation and natural convection heat transfer

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Abstract

The thermal conditions inside switch cabinets for industrial applications without cooling devices are equally influenced by natural convection and radiation heat transfer. In this work the open source library OpenFOAM is applied and enhanced, in order to simulate the temperature field of the air inside the cabinet. Turbulent natural convection heat transfer is modeled using Menter’s SST model. Radiation heat transfer is modeled using a surface-to-surface model, whereas the view factors are computed based on a Monte Carlo algorithm. Numerical results obtained with different flow models are compared with measurements and correlations from literature for a cavity and a Rayleigh-Bénard test case. The Radiation model is validated against comparative numerical data. Finally, the models are applied to calculate the temperature field of a switch cabinet test rig. These numerical results are compared with experimental data.

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Abbreviations

a 1 :

Bradshaw’s structural parameter (−)

A :

surface area (m2)

B :

Turbulence production due to buoyancy (kg m−1 s−3)

c p :

Specific heat capacity at constant pressure (J kg−1 K−1)

C :

Weights (−)

C BVG :

Constant in buoyant vorticity generation term CBVG = 0.35 (−)

F 1 ,F 2 :

Blending function (−)

\( \overline{\overline{F}} \) :

View factor matrix (−)

\( {\overline{\overline{F}}}^{\ast } \) :

View factor matrix after the first smoothing step (−)

\( {\overline{\overline{F}}}_{ij}^{\ast \ast } \) :

View factor matrix after the second smoothing step (−)

\( \overrightarrow{\boldsymbol{g}} \) :

Gravitational acceleration (m s−2)

h :

Specific enthalpy (J kg−1)

H :

Height (m)

\( \overline{\overline{I}} \) :

Identity matrix (−)

k :

Specific turbulence kinetic energy (m2 s−2)

K :

Specific kinetic energy (m2 s−2)

L :

Length (m)

n wall :

Wall distance of the midpoint of the first cell (m)

N :

Number of radiating surfaces inside the switch cabinet (−)

N i :

Number of photons emitted from surface i (−)

N ij :

Number of photons emitted from surface i, that hit surface j (−)

N P :

Number of photons emitted per subarea (−)

N sub :

Number of subareas (−)

Nu :

Local Nusselt number (−)

\( \overline{\boldsymbol{Nu}} \) :

Average Nusselt number (−)

p :

Pressure (Pa)

p tot :

Total pressure \( {p}_{tot}=p+\frac{\rho }{2}\ {\left|\overrightarrow{\mathrm{U}}\right|}^2+\rho \overrightarrow{g}\bullet \overrightarrow{r} \) (Pa)

P k :

Production of specific turbulence kinetic energy \( {P}_k={\mu}_t\frac{\partial {U}_i}{\partial {x}_j}\left(\frac{\partial {U}_i}{\partial {x}_j}+\frac{\partial {U}_j}{\partial {x}_i}\right)\left( kg\ {m}^{-1}\ {s}^{-3}\right) \)

\( {\overset{\sim }{\boldsymbol{P}}}_{\boldsymbol{k}} \) :

Limiter function of Pk, \( {\overset{\sim }{P}}_k=\min \left({P}_k,10\ {\beta}^{\ast }\ \rho\ k\ \omega \right) \) (kg m−1 s−3)

Pr :

Prandtl number (−)

Pr t :

Turbulent Prandtl number (−)

\( \dot{\boldsymbol{Q}} \) :

Heat flow (W)

\( \dot{\boldsymbol{q}} \) :

Heat flux (W m−2)

R :

Specific gas constant (J kg−1 K−1)

Ra :

Rayleigh number (−)

S :

Absolute value of the strain rate \( S=\sqrt{2\ {S}_{ij}} \) (s−1)

\( \overline{\overline{S}} \) :

Strain rate tensor \( \overline{\overline{S}}=\frac{1}{2}\left(\frac{\partial {U}_i}{\partial {x}_j}+\frac{\partial {U}_j}{\partial {x}_i}\right) \) (s−1)

t :

Time (s)

T :

Temperature (K)

\( \overrightarrow{\boldsymbol{U}} \) :

Velocity (m s−1)

β,β ∗ :

Turbulence model coefficients (−)

γ :

Turbulence model coefficient (−)

\( \overline{\overline{\delta}} \) :

Kronecker symbol (−)

ε :

Total hemispherical emissivity (−)

λ :

Molecular thermal conductivity (W m−1 K−1)

λ t :

Turbulent thermal conductivity (W m−1 K−1)

μ :

Molecular viscosity (kg m−1 s−1)

μ t :

Eddy viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

σ :

Stefan-Boltzmann constant (W m−2 K−4)

σ k ,σ ω ,σ ω 2 :

Turbulence model coefficients (−)

\( \overline{\overline{\tau}} \) :

Stress tensor (N m−2)

ω :

Specific dissipation rate (s−1)

air:

Air

amb:

Ambient

BVG:

Buoyant vorticity generation

c:

Cold

con:

Convection

h:

Hot

PISO:

Pressure-Implicit with Splitting of Operators

PIMPLE:

Combined PISO and SIMPLE

PLC:

Programmable logic controller

RANS:

Reynolds averaged Navier-Stokes

rad:

Radiation

SGDH:

Simple gradient diffusion hypothesis

SIMPLE:

Semi-implicit Method for Pressure Linked Equations

SST:

Shear stress transport

URANS:

Unsteady Reynolds averaged Navier-Stokes

wall:

Wall

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Acknowledgments

This research was supported by a foundation of Friedrich Lütze GmbH. The authors gratefully acknowledge this support.

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Authors and Affiliations

  1. University of Stuttgart, Institute of Thermodynamics and Thermal Engineering (ITW), Pfaffenwaldring 6, 70569, Stuttgart, Germany

    Alexander Frank, Wolfgang Heidemann & Klaus Spindler

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  1. Alexander Frank
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  2. Wolfgang Heidemann
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Correspondence to Alexander Frank.

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Frank, A., Heidemann, W. & Spindler, K. Electronic component cooling inside switch cabinets: combined radiation and natural convection heat transfer. Heat Mass Transfer 55, 699–709 (2019). https://doi.org/10.1007/s00231-018-2427-y

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