Consider a horizontal pipe with a constant diameter. Water (constant density p = 1000 kg/m^3) enters the pipe at steady-state with a specific enthalpy of 1000 kJ/kg, and a mass flow rate of 0.5 kg/s. The specific enthalpy at the exit is 500 kJ/kg. Determine the rate of heat transfer between the pipe and its surroundings. Rework the problem if instead of constant, the inner diameter of the pipe is 20 cm at the entrance and 10 cm at the exit.