Abstract: In the development of high-temperature and low-temperature chemical industries, design problems on nonadiabatic heat exchange equipments be-come gradually important. Differential equations of heat balances and transfer rates are given for cases with or without phase change of each fluid. These equations are solved under three different conditions includ-ing variation of overall transfer coefficients through both (tube and shell) walls. Conditions deviated from adiabatic operation have been discussed in case III. These methods are finally illustrated with a practical example and compared with results from adiabatic assumption, showing the import-ance of nonadiabatic consideration.