A $90mm90mm$ flat surface heat sink has sixteen circular

cross$-$section studs attached with their axes perpendicular to

the surface. The heat sink primary surface is at a plate

temperature of $70C.$ Each fin has a diameter of $12$ mm and

height of $70$ mm $.$ The surrounding air temperature is at $28C.$

The thermal conductivity of the fin material is $35\frac{W}{m}.K$

and the convective heat transfer coefficient is $120\frac{W}{m^2}*K.$

Neglect heat loss from the tip of each fin.

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

$(15$ marks$)$

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

$(6$ marks$)$

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

$(4$ marks$)$