Due to its comparatively large thermal conductivity, water is a preferred fluid for convection cooling. However, in applications involving electronic devices water must not come into contact with the devices, which would therefore have to be hermetically sealed. To circumvent related design and operational complexities and to ensure that the devices are not rendered inoperable by contact with the coolant a dielectric fluid is commonly used in lieu of water. Many gases have excellent dielectric characteristics and despite its poor heat transfer properties, air is the common choice for electronic cooling. However, there is an alternative, which involves a class of per-fluorinated liquids that are excellent dielectrics and have heat transfer properties superior to those of gases. Consider the micro-channel chip cooling application of Problem 8.102, but now for a perfluorinated liquid with properties of cp = 1050 J/kg ∙ K. k = 0.065 W/m ∙ K, μ = 0.0012 N ∙ s/m2 and Pr = 15.

(a) For channel dimensions of H = 200μm, W = 50μm and S = 200μlm, a chip thermal conductivity of kch = 140 W/m ∙ K and width L = 10 mm, a channel base temperature (x = 0) of T, = 350 K, a channel inlet temperature of Tm,i = 290 K, and a flow rate of In 1 = 10-4 kg/s per channel, determine the outlet temperature and the chip power dissipation for the dielectric liquid.

(b) Consider the foregoing conditions, but with air at a flow rate of m1 = 10-6 kg/s used as the coolant. Using properties of c p = 1007 J/kg ∙ K, k = 0.0263 W/m ∙ K, and μ = 185 X 10-7 N ∙ s/m2, determine the air outlet temperature and the chip power dissipation.