Problem $4\backslash (=0\mathrm{.}33\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$g$\}.\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ specific heat in the liquid stay $($density is $\backslash (7800\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ melting point $\backslash (=800^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$; specific heat

$[5$ Points$]$ from room temperature $(\backslash (25\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ))$ to liquid state $\backslash (0\mathrm{.}29\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$g$\}\backslash ).\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$; and heat of fusion$=\backslash (=160\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$g$\}\backslash ))$ will be hecated in a cant in the solid state has been designed to avoid aspiration and above its melting point in sand casting. A down$-$sprue shown in Fig. $\backslash (10\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ below for the metal shrinkage, a cylindrical riser deliver the liquid alloy to the mold at a rate of e $10$ kg sec $.$ To $.$ compensate part to be cast is shown in Fig. $2.$ The rer is designed, the length of the cylinder is to be $2$ times its diameter. The sleeve line is located at the top of tha elo... The sleeve part cavity $($made by pattem$)$ is fully placed in the drag where the parting $0$ mm diameter$),$ compute the following.

Fig. $1$

a$)$ How much heat energy must be added to accomplish the heating $($J$),$ assuming no losses?

$(2$ points$)$

b$)$ Determine the dimension of the riser that will ensure that the riser will take $\backslash (30\backslash \%\backslash )$ longer time to solidify compared to the casting.