Conduction heat transfer mechanisms

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SUMMARY

The discussion centers on the calculation of thermal conductivity for a rod subjected to a temperature gradient. The rod, measuring 20 cm in length and 2 cm in diameter, conducts heat at a rate of 4.5 x 104 J/h. The initial calculations converted this to 12.5 J/s and incorrectly used the total surface area instead of the cross-sectional area in the formula Q/dt = k(A/L)dT. The correct cross-sectional area should be used to determine the thermal conductivity, which is essential for identifying the material of the rod, expected to be iron with a thermal conductivity of 80 W/m·K.

PREREQUISITES
  • Understanding of heat transfer principles, specifically conduction.
  • Familiarity with the formula Q/dt = k(A/L)dT for thermal conductivity.
  • Knowledge of converting energy units from J/h to J/s.
  • Ability to calculate the cross-sectional area of cylindrical objects.
NEXT STEPS
  • Review the derivation and application of Fourier's law of heat conduction.
  • Learn how to calculate the cross-sectional area of cylinders for thermal analysis.
  • Study the properties of materials, focusing on thermal conductivity values for various substances.
  • Explore practical applications of thermal conductivity in engineering and materials science.
USEFUL FOR

Students in thermodynamics, engineers working with heat transfer systems, and anyone involved in material selection based on thermal properties.

Jennifer001
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1. Homework Statement [/b
the ends of a 20cm long,2cm diameter rod are maintained at 0degrees and 100degrees by immersion in an ice-water bath and boiling water. heat is conducted through the rod at 4.5x10^4J/h. of what material is the rod made?

Homework Equations



Q/dt=k(A/L)dT

The Attempt at a Solution



i first changed the heat energy conducted into watts which is = J/s

4.5x10^4J/h*1h/60min*1min/60s=12.5J/s

then i found the surface area of the rod

A=2(pi0.01^2)+(2pi0.01)0.2=0.01319m^2

now plug it into Q/dt=k(A/L)dT

12.5=k(0.01319)/0.2(100-0)
k=1.895

with this number i found that the rod is made of ice which has a k value of 1.7 (the closest number) but i checked the back and it suppose to be iron which has a k value of 80.. what did i do wrong?
 
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Your area is incorrect:
A in this equation is the cross sectional area of the conducting rod... not the entire surface area.
 

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