Consider a thick spherical wall with insulation at boththe inner and outer walls. The inner and outer radii of the 3-layersphere are 1₂ = 40 cm and r3 = 80 cm, respectively. Thelength of cylinder is 1 meter. The thermal conductivity of the wallis k₂= 120- 0 . The thickness of outer insulation is 5 cm and itswallk2 = 120 W/mKb.c.r3= 80 cm2 = 40 cmWthermal conductivity is k3 = 12 . The thickness of the innerinsulation is also 5 cm, but the thermal conductivity is k₁ =W8 The heat dissipates through the surface of outer sides ofmkthe insulation through convention with ho = 50. and theWm²Kambient temperature outside the pipe is To = 25°C. The inner most surface is maintained at100°C. Use resistance models to solve this problem.a. Compute the heat transfer through the wallr1 = 35 cminner insulationk1 = 8 W/mKr4 = 85 cmouter insulationk3 = 12 W/mKCompute the temperature of the outer most surface of the sphereCompute the heat transfer when thickness the outer most insulator is quadrupled - sothe outer most radius r4 = 100 cm. Comparing to the previous outcome (part a), doesthe heat transfer rate make sense?

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Consider a thick spherical wall with insulation at both mk mk the inner and outer walls. The inner and outer radii of the 3-layer sphere are ₂ = 40 cm and r3 = 80 cm, respectively. The length of cylinder is 1 meter. The thermal conductivity of the wall is k₂ = 120 . The thickness of outer insulation is 5 cm and its thermal conductivity is k3 = 12 The thickness of the inner insulation is also 5 cm, but the thermal conductivity is k₁ = 8 The heat dissipates through the surface of outer sides of the insulation through convention with ho = 50- and the ambient temperature outside the pipe is Too = 25°C. The inner most surface is maintained at 100°C. Use resistance models to solve this problem. mk W m²K a. Compute the heat transfer through the wall b. Compute the temperature of the outer most surface of the sphere wall k2 = 120 W/mK r3=80 cm 2 = 40 cm r1 = 35 cm inner insulation k1 = 8 W/mK r4 = 85 cm outer insulation k3= 12 W/mK

Consider a thick spherical wall with insulation at both mk mk the inner and outer walls. The inner and outer radii of the 3-layer sphere are ₂ = 40 cm and r3 = 80 cm, respectively. The length of cylinder is 1 meter. The thermal conductivity of the wall is k₂ = 120 . The thickness of outer insulation is 5 cm and its thermal conductivity is k3 = 12 The thickness of the inner insulation is also 5 cm, but the thermal conductivity is k₁ = 8 The heat dissipates through the surface of outer sides of the insulation through convention with ho = 50- and the ambient temperature outside the pipe is Too = 25°C. The inner most surface is maintained at 100°C. Use resistance models to solve this problem. mk W m²K a. Compute the heat transfer through the wall b. Compute the temperature of the outer most surface of the sphere wall k2 = 120 W/mK r3=80 cm 2 = 40 cm r1 = 35 cm inner insulation k1 = 8 W/mK r4 = 85 cm outer insulation k3= 12 W/mK

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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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

Consider a thick spherical wall with insulation at both
the inner and outer walls. The inner and outer radii of the 3-layer
sphere are 1₂ = 40 cm and r3 = 80 cm, respectively. The
length of cylinder is 1 meter. The thermal conductivity of the wall
is k₂= 120- 0 . The thickness of outer insulation is 5 cm and its
wall
k2 = 120 W/mK
b.
c.
r3= 80 cm
2 = 40 cm
W
thermal conductivity is k3 = 12 . The thickness of the inner
insulation is also 5 cm, but the thermal conductivity is k₁ =
W
8 The heat dissipates through the surface of outer sides of
mk
the insulation through convention with ho = 50. and the
W
m²K
ambient temperature outside the pipe is To = 25°C. The inner most surface is maintained at
100°C. Use resistance models to solve this problem.
a. Compute the heat transfer through the wall
r1 = 35 cm
inner insulation
k1 = 8 W/mK
r4 = 85 cm
outer insulation
k3 = 12 W/mK
Compute the temperature of the outer most surface of the sphere
Compute the heat transfer when thickness the outer most insulator is quadrupled - so
the outer most radius r4 = 100 cm. Comparing to the previous outcome (part a), does
the heat transfer rate make sense?

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