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Consider a single fin with circular cross-section as shown in the figure below. Geometrical parameters of the fin : • r = 4 mm • L = 10 cm Fin material properties: • Fin thermal conductivity: k = 200 W/mK Thermal boundary conditions: = • Base temperature of the fin: Tbase 80°C Air temperature: Tair = 25°C • Convective heat transfer coefficient: h=10 W/m²K Tbase L/4 T1 L/2 L/4 r T2 a) Express the heat transfer problem through the fin as a thermal resistance network, derive equations for the unknown temperatures T, and T₂ representing the average temperatures for the control volumes shown in the figure above. b) Express the equations derived in a) in the form of AT = b where T: unknown temperature vector and A: coefficient matrix and solve for T₁ and T₂ c) Now, imagine a very thin wire is located at the center of the fin. The electrical current that goes through the wire generates heat uniformly along the length of the wire. The wire generates heat 9 = 2 W/m. Update the energy balance equations accordingly. gen

Consider a single fin with circular cross-section as shown in the figure below. Geometrical parameters of the fin : • r = 4 mm • L = 10 cm Fin material properties: • Fin thermal conductivity: k = 200 W/mK Thermal boundary conditions: = • Base temperature of the fin: Tbase 80°C Air temperature: Tair = 25°C • Convective heat transfer coefficient: h=10 W/m²K Tbase L/4 T1 L/2 L/4 r T2 a) Express the heat transfer problem through the fin as a thermal resistance network, derive equations for the unknown temperatures T, and T₂ representing the average temperatures for the control volumes shown in the figure above. b) Express the equations derived in a) in the form of AT = b where T: unknown temperature vector and A: coefficient matrix and solve for T₁ and T₂ c) Now, imagine a very thin wire is located at the center of the fin. The electrical current that goes through the wire generates heat uniformly along the length of the wire. The wire generates heat 9 = 2 W/m. Update the energy balance equations accordingly. gen

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.12P
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Consider a single fin with circular cross-section as shown in the figure below. Geometrical parameters of the fin : • r = 4 mm • L = 10 cm Fin material properties: • Fin thermal conductivity: k = 200 W/mK Thermal boundary conditions: • Base temperature of the fin: Tbase = 80°C • Air temperature: Tair = 25°C • Convective heat transfer coefficient : h= 10 W/m²K Tbase L/4 T1 L/2 L/4 T2 a) Express the heat transfer problem through the fin as a thermal resistance network, derive equations for the unknown temperatures T, and T₂ representing the average temperatures for the control volumes shown in the figure above. b) Express the equations derived in a) in the form of AT = b where T: unknown temperature vector and A: coefficient matrix and solve for T₁ and T₂ c) Now, imagine a very thin wire is located at the center of the fin. The electrical current that goes through the wire generates heat uniformly along the length of the wire. The wire generates heat q = 2 W/m. Update the energy balance equations accordingly. gen
Transcribed Image Text:Consider a single fin with circular cross-section as shown in the figure below. Geometrical parameters of the fin : • r = 4 mm • L = 10 cm Fin material properties: • Fin thermal conductivity: k = 200 W/mK Thermal boundary conditions: • Base temperature of the fin: Tbase = 80°C • Air temperature: Tair = 25°C • Convective heat transfer coefficient : h= 10 W/m²K Tbase L/4 T1 L/2 L/4 T2 a) Express the heat transfer problem through the fin as a thermal resistance network, derive equations for the unknown temperatures T, and T₂ representing the average temperatures for the control volumes shown in the figure above. b) Express the equations derived in a) in the form of AT = b where T: unknown temperature vector and A: coefficient matrix and solve for T₁ and T₂ c) Now, imagine a very thin wire is located at the center of the fin. The electrical current that goes through the wire generates heat uniformly along the length of the wire. The wire generates heat q = 2 W/m. Update the energy balance equations accordingly. gen
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