The aim of this test case is to validate the following functions:

- Heat transfer solvers

The simulation results of SimScale were compared to the analytical results presented in [Adam]. The mesh used was created using first order tetrahedral with local refinements meshing algorithm on the SimScale platform.

Import validation project into workspace

The pitch is the Light Emitting Diodes (LEDs) separation distance between each other. Total of 25 LEDs with dimension and thickness of 7 mm x 7 mm and 100 μm respectively mounted on a heat sink of 10 cm x 10 cm were simulated. The pitch of 1 cm, 5 mm and 1 mm were tested. Due to symmetry, only quarter of the model was taken for the analysis. The geometries used for the analysis (with different LED pitches) are shown in the figure below:

**Tool Type** : CalculiX, Code_Aster

**Analysis Type** : Heat transfer

**Mesh and Element types** :

Case | Pitch | Mesh algorithm | No. of nodes | No. of 3D elements | Solver |
---|---|---|---|---|---|

A | 1 cm | Tetrahedral with local refinements | 766903 | 2826272 | CalculiX |

B | 1 cm | Tetrahedral with local refinements | 766904 | 2826273 | Code_Aster |

C | 5 mm | Tetrahedral with local refinements | 764085 | 2814528 | CalculiX |

D | 5 mm | Tetrahedral with local refinements | 764086 | 2814529 | Code_Aster |

E | 1 mm | Tetrahedral with local refinements | 760497 | 2799922 | CalculiX |

F | 1 mm | Tetrahedral with local refinements | 760498 | 2799923 | Code_Aster |

Mesh used for all the cases are shown below. In order to get better results, at least 2 elements were placed over the thickness of TIM (Thermal Interface Material) layer.

Material:

- Aluminum: isotropic: ρ

$\rho $= 2700 kg/m³, κ

$\kappa $= 202.4 W/(mK), Specific heat = 897 J/(kg K)

- TIM (Thermal Interface Material): isotropic: ρ

$\rho $= 7870 kg/m³, κ

$\kappa $= 0.22 W/(mK), Specific heat = 480 J/(kg K)

Initial Condition:

- Temperature = 300.15 K

Heat Flux Loads:

Each case contains total of 14 simulation runs with different configuration setups. The applied surface heat flux and convective heat flux boundary condition for all the simulation runs are given below:

**Surface heat flux:**

Surface heat flux of 1 W, 3 W and 5 W per LED was applied on all the red highlighted surface of different LED packages as shown in figure above under ‘Geometry’ section. The table below shows the run cases with applied surface heat flux:

Case | Surface heat flux [W/m²] |
---|---|

1 – 5 | 20408.2 (1 W/LED) |

6 – 10 | 61224.5 (3 W/LED) |

11 – 14 | 102040.8 (5 W/LED) |

**Convective heat flux:**

Convective heat flux of 10 W/(m²K), 25 W/(m²K), 50 W/(m²K), 75 W/(m²K) and 100 W/(m²K) was applied to all the heat sink surfaces accept the surfaces along symmetry plane and surfaces in contact with TIM. The table below shows the run cases with applied convective heat flux:

Case | Convective heat flux [W/(m²K)] | Reference temperature [K] |
---|---|---|

1 & 6 | 10 | 300.15 |

2, 7 & 11 | 25 | 300.15 |

3, 8 & 12 | 50 | 300.15 |

4, 9 & 13 | 75 | 300.15 |

5, 10 & 14 | 100 | 300.15 |

Since the overall resistance of 9 K/W was used for TIM (Thermal Interface Material) in [Adam], the resistance was converted to conductance in order to apply this value under material definition. The formulation used to convert this value is shown below:

κ=dR.A

$$\kappa =\frac{d}{R.A}$$

where,

Kappa, κ

$\kappa $= conductivity

thickness, d

$d$= 100 μm

Resistance, R

$R$= 9 K/W

Cross sectional area, A

$A$= 4.9e-5 m²

Putting all these values give conductance of:

κ=100e−69∗4.9e−5=0.22W/(mK)

$$\kappa =\frac{100e-6}{9\ast 4.9e-5}=0.22W/(mK)$$

The equation used to convert the resistance was taken from [infineon].

Comparison of the temperature results for Case A-F with different boundary conditions configuration taken from SimScale with [Adam].

The deviations of the results with [Adam] in case of 5 mm and 1 mm pitch is due to a non-uniform temperature distribution at the base of the fins.

[Adam] | (1, 2, 3, 4, 5, 6, 7) Christensen, Adam, and Samuel Graham. “Thermal effects in packaging high power light emitting diode arrays.” Applied Thermal Engineering 29.2 (2009): 364-371. |

[infineon] | “Thermal Resistance Theory and Practice – Infineon” http://www.infineon.com/dgdl/smdpack.pdf?fileId=db3a304330f6860601311905ea1d4599 |