In a thermal system water enters a 25-mm-diameter and 23-m-long circular tube with a mass flow rate of 0.1 kg/s at 25C. The heat transfer from the tube surface to the water can be expressed in terms of heat flux as s(x) = ax. The coefficient a is 400 W/m3 and the axial distance from the tube inlet is x measured in meters. Determine (a) an expression for the mean temperature Tm(x) of the water (b) the outlet mean temperature of the water and (c) the value of a uniform heat flux s on the tube surface that would result in the same outlet mean temperature calculated in part (b). Evaluate water properties at 35C.
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