Modeling and Analysis of a heat sink

I. Aim: To perform thermal analysis of a cabinet containing the following:

(a) An array of five high-power devices (each source dissipates power at the rate of 33W)

(b) A backing plate

(c) Ten fins

(d) Three fans (each fan has a total volumetric flow rate of 18cfm)

(e) An opening

The figure attached below shows the schematic for the problem:

The aim of the analysis is to check if the base of the devices exceed a temperature of 65 deg. C when air sweeps the fins at an ambient temperature of 20 deg. C.

II. Introduction: In the current project, the cabinet (including all the elements) is created in ANSYS ICEPAK and the following two simulations are performed:

i. Sim 1: The simulation is performed using coarse mesh.

ii. Sim 2: The simulation is performed using fine mesh.

The following simulation results are discussed:

i. Residuals

ii. Temperature at monitor points

iii. Cut-plane velocity contours

iv. Cut-plane temperature contours

v. Cut-plane velocity vectors

vi. Object face temperature contours

III. Theory

Electronic devices function properly only if they are operated within a certain temperature range. If the operating temperature of an electronic device falls outside this range it may cease to function and this failure may be accompanied with accidental damage. Electronic failures due to higher operating temperature are more common than those due to lower operating temperature. Hence thermal management is becoming an increasingly important aspect of designing electronic devices.

Heat sink is a device used frequently in electronic applications to remove the heat generated in the electronic circuits. Heat sink basically consists of an array of fins attached to a backing plate which is in direct contact with the heat dissipating components. Since heat transfer in the backing plate and fins takes place by conduction, the material chosen for making heat sink should have a high thermal conductivity (such as aluminium or copper). The main purpose of fins is to increase the area of heat transfer for convection heat transfer to the surrounding fluid. The image attached below shows schematic of a heat sink.

The fins lose their heat to the surrounding fluid by convection. Hence in order to increase the heat removed by the fins, the surrounding fluid can be forced to move over them creating forced convection conditions.

IV. Case setup

This section discusses the process of case setup for both the simulations.

1. Object

1.1. Cabinet: The region encompassing the computational domain is defined using cabinet in the model section of ICEPAK. The figure attached below shows the cabinet used for both simulations performed in the current project.

The following settings are used for defining the geometry of the cabinet.

1.2. Backing plate: It forms the backbone of fins and is in direct contact with the high-power devices. It is created using the object "Blocks" available in the model section of ICEPAK. The following settings are applied:

The image attached below shows the backing plate.

1.3. Fins: The backing plate and the fins together constitute the heat sink. The backing plate transfers the heat generated by the high-power devices to the fins via. conduction. This heat is finally convected to the surrounding fluid (stagnant or in-motion) throughout the length of the fins. The main purpose nehind using fins is to increase the heat transfer area which ultimately results in an increase in the overall heat transfer. Each fin is created using the object "Blocks" available in the model section of ICEPAK. The following settings are applied:

Each fin has the following dimensions: `69mmtimes2.5mmtimes281mm`

Every two fins are placed `25mm` apart.

The image attached below shows the array of ten fins used for both the simulations.

1.4. Fans: Three intake type fans are provided on the `Z_(min)` boundary of the cabinet to allow air flow past the array of fins. This increases the rate of heat transfer (by convection) between the fins and the surrounding air. Each fan is created using the object "Fans" available in the model section of ICEPAK. The following settings are applied for each fan:

i. Model as: 2d

ii. Shape: Circular

iii. Plane: X-Y

iv. External radius: 30mm

v. Internal radius: 10mm

The image attached below shows the three fans used in both the simulations.

1.5. High-power devices: According to the design specifications given in the problem, five high-power devices are created inside the cabinet such that they are in direct contact with the backing plate. These devices dissipate heat which is then carried away by the heat sink (backing plate + fins). The object "Sources", available in the model section of ICEPAK, is used to model these high-power devices. The following settings are usedfor each device:

i. Shape: Rectangular

ii. Plane: Y-Z

iii. Dimensions in the Y-Z plane: `10mmtimes30mm`

The image attached below shows the five high-power devices used in both thesimulations.

2. Geometry

The figure attached below shows the complete geometry of the problem.

3. Mesh

The following two meshes are used for simulations:

i. Sim 1: Coarse mesh is employed with the following settings:

It is evident that the coarse mesh contains 54672 elements and 59494 nodes. The image attached below shows the coarse mesh used for Sim 1.

ii. Sim 2: Fine mesh is employed with the following settings:

It is evident that the fine mesh contains 112256 elements and 120522 nodes. The image attached below shows the fine mesh used in Sim 2.

4. Solver

The following settings are used for both the simulations:

i. Number of iterations: 500 (Sim 1) and 1000 (Sim 2)

ii. Convergence criteria:

(a) Flow: 0.001 (Sim 1) and 0.0001 (Sim 2)

(b) Energy: 1e-7

(c) Joule heating: 1e-7

iii. The image attached below shows the advanced solver settings applied in both the simulations.

iv. Parallel settings:

(a) Configuration: Parallel

(b) Number of GPUs: 1

(c) Number ofprocessors: 4

(d) Monitor point output frequency: 10

V. Results

1. Residuals

Residuals of the governing equations are helpful in determining whether the solution has reached a steady state.

The images attached below shows the residuals of the following equations as function of number of iterations for both the simulations:

i. Continuity equation

ii. X-Momentum equation

iii. Y-Momentum equation

iv. Z-Momentum equation

v. Energy equation

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. The plot for Sim 1 (coarse mesh) shows that the residuals continuously decrease with an increase in the number of iterations. Eventually, after approximately 300 iterations, the residuals cease to change significantly, indicating that the solution has reached a steady state.

ii. The plot for Sim 2 (fine mesh) shows that the residuals continuously decrease with an increase in the number of iterations. Eventually, after approximately 800 iterations, the residuals cease to change significantly, indicating that the solution has reached a steady state.

2. Temperature at monitor points

Monitor points can be used to quantify different variables (such as velocity and temperature) at any specific location within the computational domain. Two temperature monitor points - named Inlet and Outlet - are defined using the following settings:

Inlet

Outlet

The images attached below show the temperature measured at the two monitor points as a function of number of iterations, for both the simulations:

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. Inlet monitor point indicates that the incoming air is at a temperature of `20^oC`.

ii. Outlet monitor point indicates that the outgoing air is at a temperature of `23.5^oC` according to Sim 1 (coarse mesh) and `23.4^oC` according to Sim 2 (fine mesh).

Note: The monitor points record the air temperature only at specific locations. In order to estimate the average temperature of incoming/outgoing air, the temperature measurements from multiple monitor points (placed across the inlet/outlet sections of the cabinet) must be averaged.

3. Cut-plane velocity contours

For plotting the velocity vectors and contours of variables, a cut-plane is defined parallel to the Y-Z plane using the following settings:

The images attached below show the velocity contours, plotted over the cut-plane, for both the simulations.

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. Both the simulations are able to predict the correct qualitative distribution of velocity. For instance, both the simulations predict a high velocity of air near the inlet (fans).

ii. It can be seen that the velocity contours for Sim 2 (fine mesh) are much smoother than the velocity contours for Sim 1 (coarse mesh).

4. Cut-plane temperature contours

The images attached below show the temperature contours, over the cut-plane, for both the simulations.

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. Both simulations predict the same qualitative distribution of temperature. For instance, the results from both simulations show that the temperature of air is lower near the inlet (fans) but as it moves past the array of fins its temperature increases. This is expected since air takes away the heat from the fins as it moves over them.

ii. The contours for Sim 2 (fine mesh) are much smoother than the contours for Sim 1 (coarse mesh). This is expected since the fine mesh contains more computational elements.

iii. The maximum temperature over the cut-plane, as predicted by Sim 1 (coarse mesh) and Sim 2 (fine mesh) are `51.29^oC` and `46.09^oC` respectively. The results from Sim 2 (fine mesh) are expected to be more accurate since the discretization error (error caused by discretiation of continuous PDE(s)) is small for fine mesh.

5. Cut-plane velocity vectors

The images attached below show the velocity vectors, plotted over the cut-plane, for both the simulations.

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. The density of velocity vectors is higher in case of Sim 2 (fine mesh) which is expected since fine mesh has more computational elements.

ii. Both simulations predict high air velocity near the inlet (fans).

iii. The recirculation zones are more promptly visible in case of Sim 2 (fine mesh).

6. Object face temperature contours

The images attached below show the temperature contours, plotted over the object faces, for both the simulations.

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. The temperature contours for Sim 2 (fine mesh) are smoother than the temperature contours for Sim 1 (coarse mesh).

ii. The highest temperature on any object face, as predicted by Sim 1 (coarse mesh) and Sim 2 (fine mesh) are `61.9^oC` and `56.58^oC` respectively.

As per the design objective the temperature at the back of the high-power devices should not exceed `65^oC`. Hence it is more convenient to view the temperature contours over the backing plate.

The images attached below show the temperature contours over the backing plate for both the simulations.

(a) Sim 1 (Coarse mesh)

(b) Sim 2 (Fine mesh)

Discussion:

i. The temperature contours for Sim 2 (fine mesh) are smoother than the temperature contours for Sim 1 (coarse mesh).

ii. The regions on the backing plate which are in direct contact with the high-power devices are identified as hotspots by both the simulations.

iii. The temperature at the base of the high-power devices (highest temperature on the backing plate) as predicted by Sim 1 (coarse mesh) and Sim 2 (fine mesh) are `61.9^oC` and `56.58^oC` respectively. Hence according to both the simulations the temperature of the base of the high-power devices don't exceed `65^oC` under the given conditions.

VI. Conclusions

The following conclusions can be drawn based on the simulation results:

i. Both the simulations are able to capture the qualitative distribution of variables (such as velocity and temperature) throughout the domain.

ii. The contours obtained in case of Sim 2 (fine mesh) are much smoother due to the availability of more computational elements.

iii. Quantitatively, the results obtained from Sim 2 (fine mesh) are more accurate since the discretization error is small for fine mesh.

iv. The temperature of the base of high-power devices doesn't exceed `65^oC` under the given conditions.

v. The air leaving the cabinet is approximately `3.5^oC` hotter than the air entering it.