A composite rod is made from stainless steel and iron and has a length of 0.543

Question

A composite rod is made from stainless steel and iron and has a length of 0.543 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 1.19 cm on a side. The temperature at one end of the rod is 75.3 °C, while it is 19.4 °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 two minutes.

Explanation / Answer

Heat conducted, dQ = dt[kAdT/dx]
dQ(steel) = 2*60[16*0.0119^2 *(75.3 - 19.4)/0.543] = 27.99 J

radius if shaft = r
r*cos(45) = 0.0119/2
r = 8.41457*10^-3

dQ(iron) = 2*60[80*(3.14*[8.41457*10^-3]^2 - 0.0119^2)*(75.3 - 19.4)/0.543] = 79.7722 J
Net dQ = 107.7622 J

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