$($conduction with internal heat generation$)$

The passage of electrical current through conductors

generates inside the conductor heat. Derive a temperature

change equation as a function of radius when the

dissipation of the heat by conduction through a cylindrical

wire occurs. Here, the heat generated is removed through

the exterior surface by the Newton's law of cooling $($with

heat transfer coefficient h$).($hint$)$ heat production by

electrical current $($the rate of heat production per volume$)$ is where $I=$ current,

$R=$ resistance, $k_e=$ electrical conductivity$)$ and first set up heat balance on volume element.

unit operation in chemcal engineering