th cases, the coolant is a dielectric liquid at 20°C. A heat transfer c of the unfinned package and on all surfaces of the exposed silicon nk includes a 50 x 50 array of nanofins. Determine the maximum a that its temperature is maintained at T, < 75°C for (a) the unfinn

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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 silicon carbide (T ≈ 300 K): k = 490 W/m⋅K 

Silicon carbide nanowires of diameter D = 15 nm can be grown onto a solid silicon carbide surface by carefully depositing droplets of
catalyst liquid onto a flat silicon carbide substrate. Silicon carbide nanowires grow upward from the deposited drops, and if the drops
are deposited in a pattern, an array of nanowire fins can be grown, forming a silicon carbide nano-heat sink. Consider finned and
unfinned electronics packages in which an extremely small, 10 µm x 10 μm electronics device is sandwiched between two d = 100-
nm-thick silicon carbide sheets. In both cases, the coolant is a dielectric liquid at 20°C. A heat transfer coefficient of h = 1.0×105
W/m².K exists on the top and bottom of the unfinned package and on all surfaces of the exposed silicon carbide fins, which are each
L = 300 nm long. Each nano-heat sink includes a 50 × 50 array of nanofins. Determine the maximum allowable heat rate that can be
generated by the electronic device so that its temperature is maintained at T, < 75°C for (a) the unfinned and (b) the finned packages.
T., h
-W= 10 μm-
T., h
Th
Unfinned
(a) 9₁ =
(b) 9₂ =
i
i
D
Th
Nano-finned
W
W
T
Transcribed Image Text:Silicon carbide nanowires of diameter D = 15 nm can be grown onto a solid silicon carbide surface by carefully depositing droplets of catalyst liquid onto a flat silicon carbide substrate. Silicon carbide nanowires grow upward from the deposited drops, and if the drops are deposited in a pattern, an array of nanowire fins can be grown, forming a silicon carbide nano-heat sink. Consider finned and unfinned electronics packages in which an extremely small, 10 µm x 10 μm electronics device is sandwiched between two d = 100- nm-thick silicon carbide sheets. In both cases, the coolant is a dielectric liquid at 20°C. A heat transfer coefficient of h = 1.0×105 W/m².K exists on the top and bottom of the unfinned package and on all surfaces of the exposed silicon carbide fins, which are each L = 300 nm long. Each nano-heat sink includes a 50 × 50 array of nanofins. Determine the maximum allowable heat rate that can be generated by the electronic device so that its temperature is maintained at T, < 75°C for (a) the unfinned and (b) the finned packages. T., h -W= 10 μm- T., h Th Unfinned (a) 9₁ = (b) 9₂ = i i D Th Nano-finned W W T
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