In a thermal system, water enters a 25-mm-diameter and 23-m-long circular tube with a mass...

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 25°C. The heat transfer from the tube surface to the water can be expressed in terms of heat flux as  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 T_m(x) of the water, (b) the outlet mean temperature of the water, and (c) the value of a uniform heat flux  on the tube surface that would result in the same outlet mean temperature calculated in part (b). Evaluate water properties at 35°C.