I am planning to build a light from 12 LEDs (CREE XML RGBW). These are 4 diodes on one star - a red, a blue, a green, and a white - with a total forward voltage of 13.9V at 350mA. Is there any kind of "slim profile" (i.e. max. 24-30cm long and max. 3 cm high) heat sink that could dissipate 170W? Also, shouldn't it really be able to dissipate whatever the max. forward Voltage is at 1,000mA (the max current drive these LEDs support), just to be safe? I have looked everywhere, and I haven't found any. I am working on using some of the calculators online, but so far I get different results than expected and I am also having some difficulty identifying some of the parameters (e.g. junction-to-case thermal resistance and thermal resistance of the heat sink in question).
For example, using this Celsia calculator, I set Q = 170, Tcase Max = 100 (the default, I don't know where to find this), Max Ambient T = 30 (because the light will be in open case suspended in air in my house), and I play with different values of Volumetric Thermal Resistance across the range in their table, I get heat sink volume estimates between 121 cm^3 (Rv = 50) and 1943 cm^3 (Rv = 800). A 30cm piece of the MakersLED HeatSink SLIM has a volume of 1801 cm^3. Based on the calculator, that heat sink should most likely be adequate for all 12 of my LEDs. However, the manufacturer recommends no more than 33 W per 1 ft (approx. 30cm) of heat sink. 33 W is very different from 170 W. I'm thoroughly confused. I'd appreciate some help, even if it's just links to resources that will help me figure this out for myself. Thanks.