Documentation

This LED cooling validation case, for high power LED packaging with one heat sink, aims of to validate the following parameters:

- Heat transfer solver
- Multiple materials and contact heat transfer

The simulation results of SimScale were compared to the theoretical results presented in [Adam]\(^1\).

The typical geometry used for the case is as follows:

It represents a heat sink of dimensions 100 x 100 \(mm\) with 25 LEDs attached through Thermal Interface Material (TIM) patches of dimensions 7 x 7 x 0.1 \(mm\). **Only one-quarter of the geometry is modeled to leverage the symmetry**. Gaps of 10, 5, and 1 \(mm\) between LEDs were tested, with each model shown below for comparison:

**Tool Type**: Code Aster

**Analysis Type**: Heat transfer, linear, steady-state.

**Mesh and Element Types**:

Case | Gap \([mm]\) | Mesh Type | Number of Nodes | Element Type |
---|---|---|---|---|

A | 10 | 1st order tetrahedral | 828917 | Standard |

B | 5 | 1st order tetrahedral | 824569 | Standard |

C | 1 | 1st order tetrahedral | 824369 | Standard |

The meshes were computed using the Tet-dominant algorithm with manual mesh sizing and local refinements for the TIM regions. The goal was to keep 2 elements across the thickness of the thin-walled parts, like the heat sink fins and TIM patches.

**Material**:

- Aluminum Heat Sink:
- Density \( \rho = \) 2700 \( kg/m^3 \)

- Thermal conductivity \( \kappa = \) 202.40 \( W/(mK) \)
- Specific heat \(C_p = \) 897 \( J/(kgK) \)

- TIM (Thermal Interface Material):
- Density \( \rho = \) 7870 \( kg/m^3 \)
- Thermal conductivity \( \kappa = \) 0.22 \( W/(mK) \)
- Specific heat \(C_p = \) 480 \( J/(kgK) \)

The thermal conductivity of the TIM was computed to achieve a total resistance of 9 \(K/W\), according to [INFINEON]\(^2\) with the relation:

$$ \kappa = \frac{t}{RA} $$

Where:

- \(\kappa\) is the conductivity, \( W/(mK) \)
- \(t\) is the thickness of the body, 0.1e-3 \(m\)
- \(R\) is the thermal resistance, 9 \(K/W\)
- \(A\) is the cross-sectional area, 4.9e-5 \(m^2\)

**Boundary Conditions**:

- Heat Flux Load:
- Surface heat fluxes of 1, 3, and 5 \(W\) per LED applied to the top surfaces of TIM bodies.

- Convective Heat Flux:
- Convective heat fluxes with heat transfer coefficients of 10, 25, 50, 75, and 100 \(W/(m^2K)\) with reference temperature of 300.15 \(K\) on all heat sink faces except the contact patches with TIM bodies and symmetry planes.

The following table relates the simulation runs for each case and the combinations of applied boundary conditions:

Run | Load 1 \([W]\) | Load 3 \([W]\) | Load 5 \([W]\) | Convective flux 10 \([\frac{W}{m^2K}]\) | Convective flux25 \([\frac{W}{m^2K}]\) | Convective flux50 \([\frac{W}{m^2K}]\) | Convective flux75 \([\frac{W}{m^2K}]\) | Convective flux100 \([\frac{W}{m^2K}]\) |
---|---|---|---|---|---|---|---|---|

1 | X | X | ||||||

2 | X | X | ||||||

3 | X | X | ||||||

4 | X | X | ||||||

5 | X | X | ||||||

6 | X | X | ||||||

7 | X | X | ||||||

8 | X | X | ||||||

9 | X | X | ||||||

10 | X | X | ||||||

11 | X | X | ||||||

12 | X | X | ||||||

13 | X | X | ||||||

14 | X | X |

The reference solution is of the analytical type, as presented in [ADAM]\(^1\). It is given in terms of the temperature at the center point as a function of the thermal load and convection coefficients.

Comparison of temperature at the mid point is shown for each case:

The deviation of the results with respect to [ADAM]\(^1\) in the cases of gap 5 mm and 1 mm can be attributed to a non-uniform temperature distribution at the base of the fins:

Tutorial: Thermal Analysis of a Differential Casing

References

- Christensen, Adam, and Samuel Graham. “Thermal effects in packaging high power light emitting diode arrays.” Applied Thermal Engineering 29.2 (2009): 364-371.
- “Thermal Resistance Theory and Practice – Infineon” http://www.infineon.com/dgdl/smdpack.pdf?fileId=db3a304330f6860601311905ea1d4599

Note

If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: March 22nd, 2021

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