A 10-m-long and 10-mm-inner-diameter pipe made of commercial steel is used to heat a liquid in an industrial process. The liquid enters the pipe with T_i = 25°C, V = 0.8 m/s. A uniform heat flux is maintained by an electric resistance heater wrapped around the outer surface of the pipe, so that the fluid exits at 758C. Assuming fully developed flow and taking the average fluid properties to be ρ = 1000 kg/m³, cp= 4000 J/kg · K, μ = 2 × 10^-3 kg/m · s, k = 0.48 W/m · K, and Pr = 10, determine:

(a) The required surface heat flux q̇_s, produced by the heater

(b) The surface temperature at the exit, T_s

(c) The pressure loss through the pipe and the minimum power required to overcome the resistance to flow.