Solve the below:
Q: A silicon chip (k = 150 W/m · K, p = 2300 kg/m3, c p = 700 J/kg · K), 10 mm on a side and 1 mm thick, is connected to a substrate by solder balls (k = 40 W/m · K. p = 10,000 kg/m3, c p = 150 J/kg · K) of I mm diameter, and during an accelerated thermal stress test, the system is exposed to the flow of a dielectric liquid (k = 0.064 W/m · K. v = 10-6 m2/s, Pr = 25). As first approximations, treat the top and bottom surfaces of the chip as flat plates in turbulent, parallel flow and assume the substrate and lower chip surfaces to have a negligible effect on flow over the solder balls. Also assume point contact between the chip and the solder, thereby neglecting heat transfer by conduction between the components.
(a) The stress test begins with the components at ambient temperature (Ti = 20°C) and proceeds with heating by the fluid at T8 = 80°C. If the fluid velocity is V = 0.2 m/s, estimate the ratio of the time constant of the chip to that of a solder ball. Which component responds more rapidly to the heating process?
(b) The thermal stress acting on the solder joint is proportional to the chip-to-solder temperature difference. What is this temperature difference 0.25s after the start of heating?
