A cylindrical riser of $$6$$ $$cm$$ diameter and $$6$$ $$cm$$ height has to be designed for a sand casting mould for producing a steel rectangular plate casting of $$7cm \times 10cm \times 2cm$$ dimensions having the total solidification time of $$1.36$$ minute. The total solidification time (in minute) of the riser is ___________________

In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness of the metal sheet, mainly depends on which pair of the following parameters?
$$P:$$ Strain
$$Q:$$ Strength of the work material
$$R:$$ Roll diameter
$$S:$$ Roll velocity
$$T:$$ Coefficient of friction between roll and work.

Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes

A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $$500$$ $$MPa$$ and $$700$$ $$MPa,$$ respectively. The thickness of the plates is $$8mm$$ and width is $$20mm.$$ Improper selection of welding parameters caused an undercut of $$3mm$$ depth along the weld. The maximum transverse tensile load (in $$kN$$) carrying capacity of the developed weld joint is _________________