A methodology has been developed for coupling the one-dimensional (1D) solution of flow inside the nonpermeable channels with the 3D outer flow in shell and tube type of configurations. In the proposed reacting channel, the 1D channels have detailed reactions while the outer 3D flow can be reactive or nonreactive. The channels are discretized into 1D grid points and a parabolic solver is used to solve the species transport and energy equations inside the channels. Since the walls of the channels are nonpermeable, the two zones are coupled only through the heat transfer. The current approach is tested and validated for a series of problems with increasing complexities. The predictions of the channel model (CM) are compared with 3D modeling of the channels and experimental data. The CM predictions are in excellent agreement with the fully resolved (FR) model with much less computational cost. The discussed methodology is useful for applications such as fuel reformers, hydrocarbon cracking furnaces, heat exchangers, etc.