high heat flux in the electronic components is the result of a constant push for packing more processing power in smaller packages. in many applications, the heat flux values have reached a point where traditional air cooling solutions are no longer sufficient. liquid cooling is now being pursued by many electronic firms as the future of thermal management. central to a liquid cooled system is the liquid cold plate. the conventional liquid cold plates are simply small heat exchangers with swaged tubes that are designed to enhance the heat transfer. for demanding applications, however, the thermal resistivity required is beyond the values attainable by swaged tube cold plates and one must consider micro-channel cold plates.

what is a micro-channel cold plate?

there is really nothing magic about a micro-channel cold plate. there is no clear point where the macro-channel cold plate becomes a micro-channel one. the central premise of a micro-channel is that it reduces the thickness of the fluid layer next to the wall in order to enhance the heat transfer. let’s investigate this further using the analysis described by tuckerman and pease [1].

consider an ic and its associated cold plate as shown in figure 1.

figure 1. schamatic of an cold plate attached to a semi-conductor device

the total thermal resistance from the device junction to the ambient can be viewed as the sum of 5 distinct components:

• r_spread is the spreading resistance from the individual devices in the semi-conductor substrate
•  r_bulk is the resistance due to heat transfer through the bulk semi-conductor.
•  r_interface is the resistance due to the interface material used between the semi-conductor and the cold plate
•   r_core represents the convective resistance and depends on the specific configuration of the cold plate micro-channels
•     r_flow is the “caloric” resistance stemming from the heating of the fluid as it absorbs energy passing through the cold plate.

the bulk resistance can be minimized by thinning out the substrate as much as possible. the spreading due to the individual devices is probably of less significance for highly packed integrated circuits. it is also a resistance not under the control of the thermal designer.

the flow resistance is inversely proportional to the mass flow rate and the specific heat. this resistance can be made very small by increasing the flow rate and by using fluids with high specific heat (such as water).

the two remaining resistances are the most critical as far as the thermal designer is concerned. the interface resistance depends on the material used for attaching the cold plate to the semi-conductor device. in the remaining of this article we focus on the last component which is the core resistance offered by the specific design of the cold plate and its micro-channels.

now, consider a collection of n identical parallel ducts each of length l (in the x-direction) attached to a substrate of the same length and width w as shown in figure 2.

figure 2. schematic of a simple micro-channel

a coolant flows through the ducts absorbing heat from its walls. the aspect ratio, a, is defined as the ratio of the total surface to that of the substrate alone and is equal to np/w where p is the cross-sectional perimeter of each duct. assuming the temperature to be constant at each location x, the local convective heat transfer coefficient is defined as:

where t_c(x) is the mixed mean fluid temperature.

assuming a uniform heat capacity for the coolant, we have:

where t_c(0) is the initial coolant temperature at the inlet denoted hereafter as ti and f is the total volumetric flow rate in all ducts. writing h as k_cnu/d and using the definition of hydraulic radius for a duct, d=4a/p, we get:

where k_c is the coolant thermal conductivity.

the maximum wall temperature occurs at the exit of the channels allowing us to write:

the first term is the caloric thermal resistance and the second term is the convective or core resistance. to minimize the core resistance for this configuration, we must minimize the quantity d/(anu_l). using larger values of a is obviously one way of reducing the core resistance. in micro-channels the focus is, however, on reducing d as well as increasing the nu. so, as you see, the conclusion is quite simple. to reduce the core resistance of a cold plate, you must reduce d. the lower limit is usually dictated by the penalty you are willing to pay for the pressure drop and by manufacturing limitations and cost.

in selecting a micro-channel, you always have to consider the trade-off between the increased thermal performance and increased pressure. ideally you want a cold plate that has very low thermal resistance and a low pressure drop. such a cold plate will make your entire loop more efficient.

reference

d.b. tuckerman and r.f.w. pease, high performance heat sinking for vlsi, ieee electron device letters, vol. edl-2, no. 5, may 1981