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A composite 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.

A composite rod is made from stainless steel and iron and has a length of 0483 m The cross section of this composite rod is shown in the drawing below and consi class=

Respuesta :

Hagrid
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

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