6. Heat Conduction in a Semi-Infinite Bar

Impulsive heat conduction in a laterally-insulated semi-infinite bar is considered. This problem is solved by a similarity solution method that methodology being introduced in a pastoral interlude. That yields a temperature distribution involving the complementary error function the asymptotic behavior of which is deduced by means of Watson’s Lemma introduced in pastoral interludes. Then this problem is solved by using an approximation solution method and the results compared with the exact similarity solution. Finally a periodic boundary condition is imposed and the solution to that problem is used to examine heat conduction underground in the Earth’s crust from which it is deduced that when it summer on the surface it is winter 4.44 meters underground. The problems consider heat conduction in a laterally insulated infinite bar and in an axially insulated planar layer with a one-time introduction of heat at the respective center lines of each configurations, both of which are solved by similarity solution methods; and a real solution method for semi-infinite bar heat conduction in contact with a periodic bath which is solved by a complex solution method in this chapter.