Acomposite rod is made from stainless steel and iron and has a length of 0.483 m. the cross section of this composite rod is shown in the drawing below and consists of a square within a circle.

the square cross section of the steel is 1.23 cm on a side. the temperature at one end of the rod is 80.8 °c, while it is 20.0 °c at the other end. assuming that no heat exits through the cylindrical outer surface, find the total amount of heat conducted through the rod in three minutes.

We are given with
L = 0.483 m
s = 1.23 cm = 0.0123 m (side of square)
T1 = 20.0 C
T2 = 80.8 C

This is a conductive heat transfer problem. We use this formula:
q = k A L (T2 - T1)
Since the rod is made out of two materials, the formula will be
q = ki Ai L (T2 - T1) + ks As L (T2 - T1)
where the subscript i refers to iron
and s to stainless steel

From literature:
ki = 55 W/ m K
ks = 29 W/m K

Using geometry:
As = 1.23²
Ai = π(1.23√2)²/4 - 1.23²

Substitute the values into the formula and solve for q