A stema pipe with a radius `R_(1)` is surrounded by an insulating jacket with an outer radius of `R_(0)` If the temperature of the inner `(theta_(1))` and outer `(theta_(0))` surface are fixed `(theta_(1) gt theta_(0))` find the heat flow through the jacket. (Apply the heat conduction euation to steady state radial heat flow corresponding to cylindrical symmetry) .

Explanation

Consider a cylindrical shell of thickness 'dr' and radius 'r' Cross sectional view of steam pipe is as shown in Let `L` be the length of the cylinder The heat transferred per second
`q =(dQ)/(dt) =-KA (d theta)/(dr) =-K(2pirL) (d theta)/(dr) rArrunderset(R_(1))overset(R_(0))int(dr)/(r)`
`= - (2pi LK)/(q) underset(0_(1))overset(0_(0))intd theta:. q = (2pi KL(theta_(1)-theta_(0)))/(In(R_(0)//R_(1))`
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