Steady state heat conduction to cylinder up to three layer.

Under side radius =r1

Out side radius.    =r2

Under side temperature =t2

Out side temperature =t1

Thickness =dr

Area=2πrl

Q=-KA (dt/dx)---(1)

Q=-K(2πrl)dt/dr

Q=-k2πrl(dt/dr)

dr/r=-k2πl/Q.dt---(2)

In equ 2 intigreting r and t

∫dr/r=-k2πl/Q ∫dt

lnr2 - lnr1=-k2πl/Q(t2 - t1)

ln[r2/r1] =-k2πl/Q(t1 - t2)

Q= k2πl(t2 - t2)/ln[r2/r1]

This is the final equation of cylinder up to three layer