Thermal conductivity through a cylinder?

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SUMMARY

The discussion centers on calculating the rate of heat transfer through a copper tube containing water at 68°C, with an ambient temperature of 26.65°C. The parameters include an internal radius of 6.959mm, an overall radius of 7.975mm, and a thickness of 1.016mm. The correct formula for heat conduction in cylindrical coordinates is essential, as the initial application of the plane conduction formula led to an unrealistic result of 850 kW. The appropriate approach involves using the radial heat conduction equation specific to cylindrical geometry.

PREREQUISITES
  • Understanding of thermal conductivity, specifically for copper (k = 401 W/mK).
  • Familiarity with heat transfer equations, particularly Q/t = kAΔT/d.
  • Knowledge of cylindrical coordinates and their application in heat conduction.
  • Basic principles of thermodynamics, including temperature differentials.
NEXT STEPS
  • Study the heat conduction equation for cylindrical coordinates in detail.
  • Learn about the derivation and application of Fourier's law in cylindrical systems.
  • Explore practical examples of thermal conductivity calculations in engineering contexts.
  • Investigate the effects of material properties on heat transfer rates in various geometries.
USEFUL FOR

Students in engineering disciplines, particularly those focusing on thermal dynamics, mechanical engineers, and professionals involved in heat transfer analysis and design.

nelson_gslc
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Homework Statement



A copper tube, of internal radius 6.959mm, overall radius 7.975mm, thickness 1.016mm, contains water at 68 deg Celsius, and is present in a room with an ambient temp of 26.65 deg Celsius. If the tube is 1000mm long, what will be the rate of heat transferred from the copper tube?
k copper = 401 W/mK, A of tube = 0.050m, change in T=42.35 deg C, thickness =0.001016m.

Homework Equations



Q/t=kAΔT/d... or Heat transfer across length of cylindrical tubing equation (not specifically known)

The Attempt at a Solution



I have entered into the Q/t=kAΔT/d equation and received an answer of about 850 000 W, or 850kW, which seems entirely unrealistic. what am I doing wrong?
 
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