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Consider a thick cylindrical wall with insulation at both the inner and outer walls. The inner and outer radii of the thick cylinder are 1₂ = 40 cm and 13 = 80 cm, respectively. The length of cylinder is 1 meter. The thermal conductivity of the wall is k₂ = 120- W mk The thickness of outer insulation is 5 cm and its thermal conductivity is k3 = 12 The thickness of the inner insulation W mk W mk wall k2 = 120 W/mK . The heat r3=80 cm 2 = 40 cm is also 5 cm, but the thermal conductivity is k₁ = 8 dissipates through the surface of outer sides of the insulation W through convention with h, = 50 and the ambient m²K temperature outside the pipe is T = 25°C. The inner most surface is maintained at 80°C. Compute the heat transfer through the wall and the temperature of the outer most surface. Use resistance models to solve this problem. r1 = 35 cm r4 = 85 cm inner insulation k1 = 8 W/mK outer insulation k3 = 12 W/mK

Consider a thick cylindrical wall with insulation at both the inner and outer walls. The inner and outer radii of the thick cylinder are 1₂ = 40 cm and 13 = 80 cm, respectively. The length of cylinder is 1 meter. The thermal conductivity of the wall is k₂ = 120- W mk The thickness of outer insulation is 5 cm and its thermal conductivity is k3 = 12 The thickness of the inner insulation W mk W mk wall k2 = 120 W/mK . The heat r3=80 cm 2 = 40 cm is also 5 cm, but the thermal conductivity is k₁ = 8 dissipates through the surface of outer sides of the insulation W through convention with h, = 50 and the ambient m²K temperature outside the pipe is T = 25°C. The inner most surface is maintained at 80°C. Compute the heat transfer through the wall and the temperature of the outer most surface. Use resistance models to solve this problem. r1 = 35 cm r4 = 85 cm inner insulation k1 = 8 W/mK outer insulation k3 = 12 W/mK

Elements Of Electromagnetics
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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The first part of the question has been worked on, where the heat transfer was calculated to be 6.770 kilowatt, but the problem also asks to calculate the temperature of the outer most surface. What is the temperature of the outer most surface?

 

Consider a thick cylindrical wall with insulation at both the inner and outer walls. The inner and outer radii of the thick cylinder are 12 = 40 cm and 13 = 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 W mk W mk W The heat mk = is also 5 cm, but the thermal conductivity is k₁ = 8 dissipates through the surface of outer sides of the insulation through convention with h, 50- and the ambient temperature outside the pipe is T surface is maintained at 80°C. Compute the heat transfer through the wall and the temperature of the outer most surface. W m²K = 25°C. The inner most Use resistance models to solve this problem. wall k2 = 120 W/mK r3= 80 cm r2 = 40 cm r1 = 35 cm inner insulation k1 = 8 W/mK r4 = 85 cm outer insulation k3 = 12 W/mK
Transcribed Image Text:Consider a thick cylindrical wall with insulation at both the inner and outer walls. The inner and outer radii of the thick cylinder are 12 = 40 cm and 13 = 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 W mk W mk W The heat mk = is also 5 cm, but the thermal conductivity is k₁ = 8 dissipates through the surface of outer sides of the insulation through convention with h, 50- and the ambient temperature outside the pipe is T surface is maintained at 80°C. Compute the heat transfer through the wall and the temperature of the outer most surface. W m²K = 25°C. The inner most Use resistance models to solve this problem. wall k2 = 120 W/mK r3= 80 cm r2 = 40 cm r1 = 35 cm inner insulation k1 = 8 W/mK r4 = 85 cm outer insulation k3 = 12 W/mK
બબતો/ K₂= /20 1=350m = 0.35m N₂ = = 400m = 0.4mu V3 = 80cm = 0.8m Vy=85cm = 0.85m 1 W/mk los (only sli) 82 luf Inner Insulation K₁=8 W/mk ry к ты www Ti In (²4) In (13) 27 K₂L 2741 Total Resisterna Rtotal = pthi + R+42 +R+h3 + Room Rotol In [/2) + In (141) Dim tr₂/ + 27K11 27/24 Y3 27K3L ho= ambient temperature outside pipe Too = 2.5°C Inner most surfde Tou perature Ti = 80°C convection Heat transfer coefficient of outside surpree ho= 50w m² k Length of cylinder = IM RT42 kth 3 Heat dispitale through surfree outer Insulation 50 W = 1²15 k3= 12W/mk t Rconv mm Too ㅗ ho (27 XL) 1 10:45) + In (0:50) + In (0.65) 0.8 27x8x1 27 x (20x) 27X12X1 27 KL ho(2784L) f. Rolal = 2.6565X10 3 +9.193x10-4+8.04659 × 10 ++3.744x10-3 Rotol = 8.1238 X1b-3 k/w Heat dissipates through surface 50x (27x 0.85X1, (T₁ - Too) walt R Total (80-25) 8.1238 X103 = 6770.18 watt -6.770 kilowatt Ar
Transcribed Image Text:બબતો/ K₂= /20 1=350m = 0.35m N₂ = = 400m = 0.4mu V3 = 80cm = 0.8m Vy=85cm = 0.85m 1 W/mk los (only sli) 82 luf Inner Insulation K₁=8 W/mk ry к ты www Ti In (²4) In (13) 27 K₂L 2741 Total Resisterna Rtotal = pthi + R+42 +R+h3 + Room Rotol In [/2) + In (141) Dim tr₂/ + 27K11 27/24 Y3 27K3L ho= ambient temperature outside pipe Too = 2.5°C Inner most surfde Tou perature Ti = 80°C convection Heat transfer coefficient of outside surpree ho= 50w m² k Length of cylinder = IM RT42 kth 3 Heat dispitale through surfree outer Insulation 50 W = 1²15 k3= 12W/mk t Rconv mm Too ㅗ ho (27 XL) 1 10:45) + In (0:50) + In (0.65) 0.8 27x8x1 27 x (20x) 27X12X1 27 KL ho(2784L) f. Rolal = 2.6565X10 3 +9.193x10-4+8.04659 × 10 ++3.744x10-3 Rotol = 8.1238 X1b-3 k/w Heat dissipates through surface 50x (27x 0.85X1, (T₁ - Too) walt R Total (80-25) 8.1238 X103 = 6770.18 watt -6.770 kilowatt Ar
Expert Solution
Step 1

Given:

Tin= 80°CT∞=25°CRth1 = 2.6565×10-3 °CWRth2 = 9.193×10-3 °CWRth3 = 2.6565×10-3 °CWRconv = 8.04059×10-4 °CWQ = 6.77 kW

To find:

Outer surface temperature To

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