A composite rod is made from stainless steel and iron and has a length of 0.516

Question

A composite rod is made from stainless steel and iron and has a length of 0.516 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 1.47 cm on a side, The temperature at one end of the rod is 78.1 degree C, while it is 16.9 degree 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 five minutes. 4.54 times 10^2J (in J)

Explanation / Answer

cross section area of steel = L^2 = 1.47^2 = 2.16 cm^2 = 2.16 x 10^-4 m^2

dx = 0.516 m

dT = 78.1 - 16.9 = 61.2 deg C

Thermal of steel, k = 16 W/mK

Q1/t = k A dT/dx

Q1/t = (16)(2.16 x 10^-4)(61.2)/(0.516) = 0.41 J/s

for Iron:

cross section area = pi r^2 - L^2

r = L /sqrt(2) = 1.47/sqrt(2) = 1.04 cm

A = pi r^2 - L^2 = 1.234 x 10^-4 m^2

dx = 0.516 m

dT = 78.1 - 16.9 = 61.2 deg C

Thermal of iron , k = 80 W/mK

Q2/t = k A dT/dx

Q2/t = (80)(1.234x 10^-4)(61.2)/(0.516) =1.167 J/s

Q/t = 0.41 + 1.167

Q = 1.577 x (5 x 60) = 473.1 J

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