Sections of the trans-Alaska pipeline run above the ground and are supported by vertical steel shafts (k = 25 W/m ?£? K) that are 1 m long and have a cross-sectional area of 0.005 m2. Under normal operating conditions, the temperature variation along the length of a shaft is known to be governed by an expression of the form T = 100150x + I0x2 where T and x have units of ???C and meters, respectively. Temperature variations are small over the shaft cross section. Evaluate the temperature and conduction heat rate at the shaft-pipeline joint (x = 0) and at the shaft-ground interface (x = 1 m). Explain the difference in the heat rates.
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