Proper gating design in metal casting

$$P:$$ Influences the freezing range of the melt
$$Q:$$ Compensates the loss of fluidity of the melt
$$R:$$ Facilitates top feeding of the melt
$$S:$$ Avoids misrun

A $$10$$ $$mm$$ thick steel bar is to be horizontally cast with two correctly spaced top risers of adequate feeding capacity. Assuming end effect without chill, what should be the theoretical length of the bar?

In spot pulsed laser welding of aluminium plates (density $$ = 2700kg/{m^3},$$ specific heat $$=896J/kg,$$ melting temp $$=933K,$$ latent heat of melting $$ = 398\,\,kJ/kg)$$ at a temp of $${30^ \circ }C,$$ pulse with energy of $$0.5J$$ is focused onto an area of $$0.05m{m^2}.$$ If the entire energy is coupled into the material, what will be the depth of weld assuming the $$CS$$ area of the weld is circular and is uniform throughout its depth and only heat conduction in the direction of penetration