# Regime of unsteady flow over heat sink

For my master thesis I'm simulating the cooling of an 2.5D microchip (2 dies next to each other on an interposer (slice of silicium with interconnections)). So I want to calculate the flow over the chip and the attached ducted straight fin heat sink. The fluid can only flow through the fins of the heat sink. The inlet velocity is over 2 m/s so that there is no influence of natural convection. The flow can be seen as a combination of a forward facing step and a backward facing step.

I calculated the Reynolds number between the fins and it was 1075. So the flow should be laminar (or at least that is what i think). Because of the high velocity the flow because unsteady behind the heat sink (I can only calculate the flow with the transient option in fluent). I assumed that it was an unsteady laminar flow. But when I look to the velocity in a point, it isn't periodic in time. So the flow behind the heatsink could be in the transitional or turbulent regime. But I'm not sure of that.

Is there a way to check the regime behind the heatsink?

• Do you have images of the heat sink geometry and simulation results? If I had to guess you're heat sink doesn't smoothly transition into free stream again so you end up with some separation at the tailing edge of the fins. – helloworld922 Feb 20 '14 at 18:45
• This seems like more of a question of fluid dynamics than electronics. – Spehro Pefhany Feb 20 '14 at 18:53
• @Spehro - indeed it is, but it's certainly a valid concern for electronics design; a good answer would be a useful resource. – Brian Drummond Feb 20 '14 at 18:59
• @BrianDrummond Indeed. I wonder if he might have a better chance of getting a good answer elsewhere though. – Spehro Pefhany Feb 20 '14 at 19:51
• The heat sink is 28 by 28mm. There are 10 fins with a height of 10 mm. The cross section of the channel between the fins is 2x10mm. The entrance and exit duct has a width of 28 mm and a height of 15.24 mm. The complete flow has to go through the fins. – user3329103 Feb 22 '14 at 14:32

Even if the flow was otherwise laminar, a square pin will have detached flow with a turbulent wake at anything but the slowest velocities. Where the laminar-turbulent transition occurs depends on the exact geometry, but roughness and sudden steps tend to promote turbulence. The flow through the duct ahead of the heat sink is also likely to be turbulent, being fast and most likely driven by a turbulence-producing fan. Don't place too much stock in the Reynolds number for determining if a flow is laminar, because once a flow becomes turbulent, it tends to stay turbulent. It's possible for the turbulence to dampen out, but usually that takes special design effort.

Having done both CFD simulations and simplified closed-form calculations of similar problems, I prefer closed-form. My approach would be to use the fin geometry and flow rate to calculate an equivalent film coefficient $h$ for a flat plate the same size as the base of the heat sink. Incropera and DeWitt's intro to heat transfer book is a good source for the formulas for that. Then use that as a boundary condition for conductive heat transfer from the dies to the heat sink surface. A steady-state heat conduction problem is much easier to set up, and faster to solve, than a transient CFD problem would ever be. At a minimum, it will be a good check against the simulation.

• Thanks for your answer! But the goal for my master thesis is finding an efficient way of calculating the cooling for 2.5D microchips. So I wanted to proove that a FEM simulation with a convective heat transfer coefficient h out of correlations is accurate enough by a comparison with a complete CFD-calculation. And as you say the flow behind the heat sink is most likely not a laminar flow. Then the question remains what kind of flow it is. It could be in transitional or turbulent regime. It is important to know this to use the right equations (k-epsilon model, etc). – user3329103 Feb 22 '14 at 14:25