Cooling Rate of Thin Plate due to Instantaneously Delivered Line Heat

Comparison with that of moving Point Heat

Abstract

Temperature cooling rate is calculated for points near bead line in thin plate when linear heat source is applied instantaneuosly along all the range of bead whose length is l. Fig. 4 shows CR (cooling rate passing a definite temperature T_s) along the bead, and we see that CR at bead end is 4 times the bead center of infinite length. For the point whose distance from the bead end is 2 times y_m, CR is 0.37 times the bead end. Here y_m means the perpendicular distance from the bead, where the maximum temperature is equal to T_s, and y_m is shown in equ. (45). Equ. (28) gives the relation of CR and temperature T_s, input heat q₀.
Fig. 9 shows the effect of bead length, and we see that for l>3y_m, CR for the bead end is practically equal to that for l=∞, and for 1<1.5y_m, CR is equal to that of the point heat whose heat is equal to q₀⋅l.
For a moving point heat source it is already shown that the temperatures of the starting as well as stopping bead end are just equal to half of that of the center, where quasi-stationary state is established. So the relation of CR for these points derived in case of infinite velocity holds well for a moving point heat source. For points equally distant from the bead ends, the literature (1) shows that CR for starting side is a little higher than that of stopping side. CR for infinite velocity has an intermediate value.