We present a theoretical proof that the entropy production due to heat exchange in a heat exchanger is minimum Mien the local entropy production is constant in all part of the system. The solution for the minimum is independent of the value of the heat transfer coefficient. The general case is compared to the minimization problem that has equi-partition Of forces as Solution, It is found that equipartition of forces predict the minimum from the general solution well for typical heat exchange condition. The discrepancy between the MO Solutions depends largely on the temperature dependency of the heat transfer coefficient. The optimal heat exchange conditions are very well approximated in practice with a counter-current heat exchanger: since the minimum in the entropy production space probably is flat.