移動熱源による薄板の過渡温度上昇の計算について

Abstract

A new function mF0(δ) is introduced for the equation of the transient temperature rise, T=q/4πK·eX·mF0(δ) …(31) where mF0(δ), as well as m, δ are given in equ. (6), (32), (33). mF0(δ) has the following interesting characteristics mF0(δ)|m=1 = 1/2· mF0(δ)|m=∞ …(18)mF0(δ) + 1/mF0(δ) = ∞F0(δ) …(17)From equ. (17), the value of mF0(δ) for m>1 can be easily calculated from that of m<1.Fig. 3 shows the calculated results of mF0(δ) for range of m=0-1, in the form of ratio to ∞F0(δ), ∞F0(δ) being given in Table 1 for various values of δ.Equ. (18) suggests an interesting and useful understanding as to the transient temperature rise, namely when we neglect the radiation loss from the plate surface, the temperature of any point, whose distance from the arc point is equal to the distance of arc travel after arc starting, is just equal to the half of the quasi-stationary state value. See equ. (32).It is remarkable that the above mentioned relation expresed in equ. (18) holds true always independent of the thermal conduction constant of plate, arc traveling velocity and time elapsed after arc starting. The result holds under constant linear velocity with constant thermal input in thin plate.