Consider the counter flow, concentric tube heat exchanger of Example 11.1. The designer wishes to consider the effect of the cooling water flow rate on the tube length. All other conditions, including the outlet oil temperature of 60°C, remain the same.

(a) From the analysis of Example 11.1, we saw that the overall coefficient U is dominated by the hot-side convection coefficient. Assuming the water properties are independent of temperature, calculate U as a function of the water flow rate. Justify a constant value of U in the calculations of part (b).

(b) Calculate and plot the required exchanger tube length L and the water outlet temperature Tc,o as a function of the cooling water flow rate for 0.15 < mc < 0.30 kg/s.