Consider a shell of thickness (dr) and of radii ( r ) and the temperature of inner and outer surfaces of this shell be T, (T−dT).
dQ
dt
= rate of flow of heat through it =
kA[(T−dT)−T]
dr
=
−KAdT
dr
=−4πkr2
dT
dT
[∵A=4πr2] To measure the radial rate of heat flow, integration technique is used, since the area of the surface through which heat will flow is not constant. Then, (