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

[phantomvommand]

Homework Statement

Please see the picture below

Relevant Equations

Rate of heat conduction = constant

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!

 

[haruspex]

Consider a section of pipe (x, x+dx). What is the rate of radial flow of heat there?

 

[phantomvommand]

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