A silicon chip of thickness L = 2.5 mm and thermal conductivity ks = 135 W/m ∙ K is cooled by boiling a saturated fluorocarbon liquid (T_sat = 57°C) on its surface. The electronic circuits on the bottom of the chip produce a uniform heat flux of q"_o = 5 x 10⁴ W/m², while the sides of the chip are perfectly insulated. Properties of the saturated fluorocarbon are c_p,l = 1100J/kg ∙ K, h_fg = 84,400Jlkg, p₁= 1619.2 kg/m³, Pv = 13.4 kg/m³, σ = 8.1 x 10^-3 kg/s², μ₁ = 440 x 10^-6 kg/m ∙ s, and Pr₁ = 9.01. In addition, the nucleate boiling constants are C_s,f = 0.005 and n = 1.7.

(a) What is the steady-state temperature T_o at the bottom of the chip? If, during testing of the chip, q"_o is increased to 90% of the critical heat flux, what is the new steady-state value of T_o?

(b) Compute and plot the chip surface temperatures (top and bottom) as a function of heat flux for 0.20 < q"_o/q"_max < 0.90. If the maximum allowable chip temperature is 80°C, what is the maximum allowable value of q"_o?

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Saturated fluorocarbon Silicon chip