A $\backslash (70\backslash$mathrm$\{$~mm$\}\backslash$times $70\backslash$mathrm$\{$~mm$\}\backslash )$ flat surface heat sink at a plate temperature of $\backslash (125^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ has ten equally spaced rectangular cross$-$section cooling fins protruding perpendicular to the surface. Each fin has a thickness of $1\mathrm{.}5$ mm $,$ height of $20$ mm and width of $70$ mm $.$ The surrounding air temperature is at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The thermal conductivity of the fin material is $150\backslash (\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}.\backslash$mathrm$\{$K$\}\backslash )$ and the convective heat transfer coefficient is $50\backslash (\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}.\backslash$mathrm$\{$K$\}\backslash ).$ Neglect heat loss from the edges of each fin.

$($a$)$ What is the heat flow through the heat sink?

$(10$ marks$)$

$($b$)$ Determine the fin effectiveness.

$(5$ marks$)$

$($c$)$ Determine the fin efficiency.

$(5$ marks$)$

$($d$)$ Find the temperature at the tip of the fins.

$(5$ marks$)$