A chip that is of length L = 5.5 mm on a side and thickness t = 2.0 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. Th Chip, q. T., P. Cp The time is i Substrate In the off-mode the chip is in thermal equilibrium with the coolant (T; = 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. The steady-state chip temperature T, is i S. °C.

A chip that is of length L = 5.5 mm on a side and thickness t = 2.0 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. Th Chip, q. T., P. Cp The time is i Substrate In the off-mode the chip is in thermal equilibrium with the coolant (T; = 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. The steady-state chip temperature T, is i S. °C.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A chip that is of length L = 5.5 mm on a side and thickness t = 2.0 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 To
= 20°C.
.
Th
Chip,
q, T₁, P, Cp
The time is
Substrate
In the off-mode the chip is in thermal equilibrium with the coolant (T; = 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 a = 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 Tƒ. 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.
The steady-state chip temperature Tf is i
S.
°C.

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Step 2: Calculating steady state temperature of the chip as:-

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Step 3: The time required to get 1 degree C of temperature:-

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Step 4: Calculating a and b values :-

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Step 5: Finally the time required:-

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