A thin-walled container with a hot process fluid at 50°C is placed in a quiescent, cold water bath at 10°C. Heat transfer at the inner and outer surfaces of the container may be approximated by free convection from a vertical plate.

  (a) Determine the overall heat transfer coefficient between the hot process fluid and the cold water bath. Assume the properties of the hot process fluid are those of water.

  (b) Generate a plot of the overall heat transfer coefficient as a function of the hot process fluid temperature T_∞fl for the range 20 to 60°C, with all other conditions remaining the same.