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 q_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,

(c) The value of a uniform heat flux q s on the tube surface that would result in the same outlet mean temperature calculated in part (b). Evaluate water properties at 35°C.