A Note On Heat Conduction By Moving Heat Source

Abstract

The present report discusses on heat conduction in an infinite body in which a point heat source of intensity q (cal/sec) moves at a constant speed v along x-axis as shown in Fig. 1. The problem has been well known since Rosenthal reported a mathematical analysis in 1941. However, analysis in the present report shows that temperature at a point during cooling by a moving heat source is approximately the same as temperature when using an instantaneous line or plane heat source.
For the three-dimensional quasi-stationary heat flow of an infinite body the temperature θ during cooling at a point P in Fig. 1 is approximately given by eq. (1) or the temperature θ_L under heating by an instantaneous line heat source of intensity q/v (cal/cm) along x-axis, in which c is specific heat, ρ is density, k is heat diffusivity and t is the time after the point heat source comes to the point O₁ in Fig. 1.
For the two-dimensional quasi-stationary heat flow of an infinite plate of thickness h the temperature θ during cooling at a point P is approximately given by eq. (2) or the temperature θ_p under heating by an instantaneous plane heat source of intensity q/vh (cal/cm²) on x-z plane.