# A chip that is of length L = 5 mm on a side and thickness t =

## Question:

A chip that is of length L = 5 mm on a side and thickness t = 1 mm is encased in a ceramic substrate, and its exposed surface is convectively cooled by a dielectric liquid for which h = 150 W/m2 ∙ K and T = 20°C.

In the off-mode the chip is in thermal equilibrium with the coolant (Ti = T). When the chip is energized, however, its temperature increases until a new steady-state is established. For purposes of analysis, the energized chip is characterized by uniform volumetric heating with q = 9 x 106 W/m3 ∙ Assuming an infinite contact resistance between the chip and substrate and negligible conduction resistance within the chip, determine the steady-state chip temperature Tf' Following activation of the chip, how long does it take to come within 1°C of this temperature? The chip density and specific heat are p = 2000 kg/m3 and c = 700 J/kg ∙ K, respectively.

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Related Book For

## Fundamentals of Heat and Mass Transfer

ISBN: 978-0471457282

6th Edition

Authors: Incropera, Dewitt, Bergman, Lavine

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