Mathematical Theory of Heat Conduction due to Heat Source (Report I)

Abstract

In this research, heat conduction is limited to physical systemes governed by linear differential equations. Generalizing the conception of heat source, the author proposes a general solution of unsteady heat flow due to the heat sources which change the distribution, shape and place of growing heat energy such as chemical change, radioactivity, Joule's heat of electric current etc. Main solutions are shown in equations (P-1) to (P-7).
Specializing equations (P-1) and (P-7), the general solutions of heat flow corresponding to all welding conditions of heat flow in simple form solid are derived.
But the above-mentioned limit is doubtful in such high temperature phenomenon as welding, there-fore their effects should be investigated in the future.