Rate of heat flux from from hot gas in a pipe to water outside

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SUMMARY

The discussion centers on the calculation of heat flux from hot gas in a pipe to surrounding water, specifically focusing on the equation T(x) - T0 = (T1 - T0)e^(-Φx/fc). The user successfully solved the first two parts of the problem and is seeking assistance in deriving the expression for heat transfer coefficient H. The conversation emphasizes the importance of understanding radial heat flow in a cylindrical geometry.

PREREQUISITES
  • Understanding of heat transfer principles
  • Familiarity with differential equations
  • Knowledge of thermal conductivity concepts
  • Basic grasp of cylindrical coordinate systems
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  • Research the derivation of heat transfer coefficients in cylindrical geometries
  • Study the application of Fourier's law in radial heat flow
  • Learn about transient heat conduction in pipes
  • Explore numerical methods for solving heat transfer problems
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Engineers, physicists, and students involved in thermal analysis, particularly those working with heat transfer in piping systems and fluid dynamics.

phantomvommand
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Homework Statement
Please see the picture below
Relevant Equations
Rate of heat conduction = constant
Screenshot 2021-03-13 at 12.33.29 PM.png

I have solved the first 2 parts.
For the 3rd part, I have obtained the equation:
T(x) - T0 = (T1 - T0)e^(-Φx/fc), where f = fm in the question.

How do I obtain that expression for H?

Thank you!
 
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Consider a section of pipe (x, x+dx). What is the rate of radial flow of heat there?
 
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haruspex said:
Consider a section of pipe (x, x+dx). What is the rate of radial flow of heat there?
Thank you so much for this! I have now obtained the answer
 

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