The heat transfer coefficient for the heating of a vessel must be determined the same way any overall coefficient is calculated: summation of resistances. One must first determine the coil inside coefficient by utilizing a Dittus-Boelter type equation; then determine the vessel side heat film coefficient utilizing an appropriate correlation (John Bourne has published a good correlation utilizing power input per unit volume for transitional to turbulent regimes with no phase change). Once these critical values have been determined, the overall coefficient may be calculated by addition of resistances. Do not forget to correct for the difference between inside and outside areas when calculating an overall coefficient and only consider the inside wetted surface as effective for inside area. The Outside area should only include the wetted coil surface up to the point where the inside liquid level is located.