Cylindrical general differential equation of conduction

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SUMMARY

The discussion focuses on the derivation of the cylindrical general differential equation of conduction, specifically for the temperature distribution T(r,0,z) in cylindrical coordinates. The user has successfully derived the equation for a square but encounters difficulties when applying the same principles to a cylinder. It is emphasized that the equations for rectangular coordinates cannot be directly applied to cylindrical coordinates; instead, Bessel functions must be utilized for solutions in this context. The user is advised to refer to their class text for further guidance.

PREREQUISITES
  • Cylindrical coordinates in mathematics
  • Understanding of differential equations
  • Knowledge of Bessel functions
  • Basic principles of heat conduction
NEXT STEPS
  • Study the derivation of the cylindrical heat conduction equation
  • Learn about Bessel functions and their applications in physics
  • Review the differences between rectangular and cylindrical coordinate systems
  • Examine examples of temperature distributions in cylindrical objects
USEFUL FOR

Students studying heat conduction, mathematicians focusing on differential equations, and engineers working with cylindrical systems in thermal analysis.

amish99
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Homework Statement


Desperate help needed on the derivation of the differential equation on conduction on a clyinder, i have come close to the answer and working with the co-ordinates scale of T(r,0,z).


I am sure that i have made a simple mistake but am blind to it right now, i have derived the equation for a square no problem and when i sub in the values for that of a cylinder i get into difficulties, any help would be appreciated
 
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You cannot use the equation for a rectangle when considering a cylinder; use the corresponding expressions in cylindrical coordinates instead. Solutions to the first are sines and cosines, the other are Bessel functions. (Hint: take a look in the text for your class.)

Edit: clean up wording
 
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