introduction

although water provides the best thermal performance in a liquid cooling system, there are applications where other considerations, such as extended temperature range or dielectric properties, require the use of a different fluid.  other thermal management fluids commonly used include water-glycol mixtures, dynalene, and pao. 

the thermal designer needs to estimate the thermal resistance and pressure drop of a given cold plate for several candidate fluids in order to select the most advantageous one.  to assist in this task, we have tested the mikros ncp-a-10-20 with four fluids covering a wide range of properties.  as shown below, by suitably scaling the data it can all be collapsed into a single curve. this means that if the ncp performance with water is known, one can predict its performance with any other liquid if its properties are known.

fluids tested

the thermal resistivity and pressure drop of mikros ncp-a-10-20 was measured as a function of flow rate for four different fluids:  water, eg-50/50, dynalene hc-50, and pao (polyalphaolefin). the properties for these fluids normalized to those of water at 30 ^oc are given in table 1.

scaling the ncp thermal resistance

the measured thermal resistivity as a function of flow rate is shown in figure 1.   the thermal resistivity is defined as the ratio of approach temperature difference to the heat flux, where the approach temperature difference is defined as the difference between the ncp surface temperature and the coolant inlet temperature.

figure 1.  ncp-a-10-20 resistivity for different fluids

the total thermal resistivity of a cold plate can be viewed as the sum of two parts: the core resistivity and the flow resistivity. the core resistivity depends on the internal configuration of the micro-channels and how they interact with the coolant. the flow resistivity represents the portion of the approach temperature difference associated with temperature rise of the coolant as it flows through the cold plate. the flow resistivity can be made very small by increasing the flow rate.   

	(1)
	(2)

where the subscript  refers to a particular fluid of interest. 

by examining the heat transfer in the microchannel matrix in the limit of infinite flow rate (uniform fluid temperature), one finds that the core resistivity is inversely proportional to the square root of the fluid thermal conductivity.   hence, the core resistivity for fluid  can be expressed in terms of the resistivity for water as:

where k_w and  k_i are the thermal conductivities of water and the fluid of interest.

figure 2 shows that when the scaling approach of equations 1-3 is applied to the data shown in figure 1, the performance for all the fluids collapses on the line corresponding to water. 

figure 2. total resistivity for different fluids as a function of flow capacity

the solid black line in figure 2 corresponds to the flow resistivity defined in equation 2. the solid blue line corresponds to the total resistivity for a constant core resistivity of 0.035.   

scaling the ncp pressure drop

figure 3 shows the measured pressure drop for the four fluids tested. 

figure 3. ncp-a-10-20 pressure drop for different fluids

as shown in figure 4, the pressure drop data can also be collapsed into a single curve if expressed in terms of the following non-dimensional parameters:

	(4)
	(5)

where:

• g  is the characteristic dimension of the micro-channels (  g = 80 microns for the ncp-a-10-20), and
•  is the characteristic velocity in the microchannels (v_i=4* flow/area)

as shown in figure 4, the dimensionless pressure drop varies linearly with the gap reynolds number:

(6)

for the ncp-a-10-20 the constants in equation 6 have the values: c1=0.76 and c2 =0.025.

figure 4. modified pressure drop as a function of the gap reynolds number

the property scaling method described above is less accurate for the pressure drop than for the thermal resistance.   this is to be expected since the total pressure drop includes the pressure drops in the manifolds and the headers, in addition to the pressure drop in the microchannel matrix.  this simplified scaling approach ignores the effect of the reynolds number variation in the manifolds and the headers.  however, since in most configurations the pressure drop is dominated by the microchannels matrix pressure drop, scaling the pressure drop measured with water using this simplified approach will provide a good estimate of the anticipated pressure drop with a different fluid.

conclusion

the property scaling procedures described above, allow the thermal designer to accurately estimate the performance of mikros ncp for any fluid or operating temperature.  the only information required are the properties of the candidate fluid at the target operating conditions.  the room temperature water data provided in mikros data sheets can then be scaled to obtain the anticipated performance in the intended application. 

please note that the data provided here are only valid for the ncp-a-10-20. for other ncp configurations you need to obtain its corresponding thermal resistance and pressure drop data for water before using the above scaling method to estimate its performance for other fluids.