Consider an aluminum heat sink (k =240 W/m-K), where the inner and outer widths of the square channel are w =20 mm and W =40 mm, respectively, and an outer surface temperature of T = 56°C is maintained by the array of electronic chips. The inner surface temperature is not known, but the conditions ( Th) associated with coolant flow through the channel are, and we wish to determine the rate of heat transfer to the coolant per unit length of channel. For this purpose, consider a symmetrical section of the channel and a two-dimensional grid with Ax = Ay =5 mm. Heat sink, k TA -T, Th T2 •Ts T3 T -Coolant, T, h For T =20°C and h =5000 W/m².K, determine the unknown temperatures, T1,., T7, all in °C, and the rate of heat transfer per unit length of channel, q', in W/m.

Consider an aluminum heat sink (k =240 W/m-K), where the inner and outer widths of the square channel are w =20 mm and W =40 mm, respectively, and an outer surface temperature of T = 56°C is maintained by the array of electronic chips. The inner surface temperature is not known, but the conditions ( Th) associated with coolant flow through the channel are, and we wish to determine the rate of heat transfer to the coolant per unit length of channel. For this purpose, consider a symmetrical section of the channel and a two-dimensional grid with Ax = Ay =5 mm. Heat sink, k TA -T, Th T2 •Ts T3 T -Coolant, T, h For T =20°C and h =5000 W/m².K, determine the unknown temperatures, T1,., T7, all in °C, and the rate of heat transfer per unit length of channel, q', in W/m.

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

Consider an aluminum heat sink (k =240 W/m-K),
where the inner and outer widths of the square
channel are w =20 mm and W =40 mm,
respectively, and an outer surface temperature of
T, = 56°C is maintained by the array of electronic
chips. The inner surface temperature is not known,
but the conditions ( T) associated with coolant
0,h
flow through the channel are, and we wish to
determine the rate of heat transfer to the coolant
per unit length of channel. For this purpose,
consider a symmetrical section of the channel and
a two-dimensional grid with Ax = Ay =5 mm.
Heat sink, k
-T,
T, h 72 •Ts
T3 _ T7
- Coolant, T, h
For T =20°C and h =5000 W/m2-K, determine
the unknown temperatures, T1, ..., T7, all in °C,
and the rate of heat transfer per unit length of
channel, q', in W/m.

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