Consider laminar flow of 2 kg/s water through a tube of diameter 5 cm. The water enters at an inlet temperature of 20 C. As a thermal engineer, you are asked to provide sizing of a heater coil wrapped around the tube that provides constant heat flux conditions into the tube. The goal is for water to reach a temperature of 60 C within a length of 1 m. Please determine the heat flux needed to be obtained from the heater coil in order to achieve this goal. 2. For the design in problem #1 with the heat flux calculated above, it is proposed to tweak the flow rate of the water in order to achieve the same goal within a shortened length of 0.5 m. Should the flow rate be reduced or increased? Please calculate the value of the flow rate that must be chosen for this purpose. 3. Consider the same problem as #1 above, but in this case, the temperature of the tube is held constant at 100 C instead of providing a constant heat flux. Assuming laminar and fully developed flow conditions, (a) what is the Nusselt number along the length of the tube, and, from