A square (12.5 mm × 12.5 mm) silicon chip is insulated on one side and cooled on the opposite side by atmospheric air in parallel flow at [infinity] 20 m/s and [infinity] 24°C. When in use, electrical power dissipation within the chip maintains a uniform heat flux at the cooled surface. Assume the critical Reynolds number is 5x105.

(a) If the chip temperature may not exceed 80°C at any point on its surface, what is the maximum allowable power?
(b) What is the maximum allowable power if the chip is flush mounted in a substrate that provides for an unheated starting length of 20 mm?

a) q = 0.927 W

b) q = 0.73 W

Explanation:

Our assumptions are that:

Chip temperature,

Temperature of the film,

Atmospheric air is used to insulate the chip. i.e the film is an atmospheric air

1 atm of 325 K of air has the following properties:

viscosity, v = 18.4 × 10⁻⁶ m²/s

k = 0.0282 w/mk

Pr = 0.703

Nuselt number, Nu = ..............(i)

Nu = ................(2)

The Reynold number, Re, is calculated by the equation

, L = 12.5 mm = 12.5 * 10⁻³ m

Re =

Re = 13586.96

Equating (1) and (2) and substituting necessary values

..........(3)

47.006 = h * 0.4433

h = 47.006/0.4433

h = 106.05

The maximum allowable power is given by the equation,

Area, A = length * Breadth = 0.0125*0.0125

A = 0.000156 m²

b) When the lenght, L = 20 mm = 0.02 m

Reynold number, Re =

Re = 21739.13

By replacing Re and L, Equation (3) becomes:

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