A new methodology for the global optimization of heat exchanger networks is presented, based on an outer approximation methodology, aided by physical insights. The problem is formulated as a mixed-integer nonlinear problem (MINLP). Two lower bounding convex MINLP problems are constructed, including piecewise underestimators of the nonconvex terms. A solution of the bounding problems gives an approximated optimal solution that is used as an initial point for solving the reduced NLP problem, or that proves there is no better solution. Meanwhile, the global bounding problem selects feasible structures with improved objective value. In order to reduce the number of feasible structures to be explored, rigorous constraints obtained from physical insights are included in the bounding problems. Networks with up to 9 process streams have been solved to global optimality, improving considerably the computing time required to solve them. Networks with more than 10 process streams have been solved with the global optimization strategy, giving as results a set of feasible structures, with total cost near the optimal value. This offers the possibility of alternatives to be analyzed, considering other aspects not reflected in the original MINLP model.