The Thermal Distribution and Temperature Gradient in the Arc Welding of Oil Well Casing

Abstract

The problem studied here is the thermal distribution due to a number of moving heat sources. It is assumed that the pipe is a circular cylinder and that the welders move on a circle of the cylinder. The Kelvin method for determining the thermal distribution about a stationary source of heat is extended to a case in which the source of heat is moving with a constant velocity. By integration of the effect of stationary sources the general effect of a moving welder is obtained. It is shown that an infinite plate with an infinite number of sources on a line and w cm apart is equivalent to an infinite cylindrical shell with n = c/w sources spaced w cm apart around the cylinder (c = circumference). With the aid of this and Kelvin's solution it is possible to build a complete general solution of the problem. This method of constructing the solution of a heat problem has many practical applications—such as the determination of thermal distributions in the welding of plates, seamed pipe and other bounded objects.