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We investigate channel assignment for a multichannel wireless mesh network backbone, where each router is equipped with multiple interfaces. Of particular interest is the development of channel assignment heuristics for multiple flows. We present an optimization formulation and then propose two iterative flow oriented heuristics for the conflict-free and interference-aware cases, respectively. To maximize the aggregate useful end-to-end flow rates, both algorithms identify and resolve congestion at instantaneous bottleneck link in each iteration. Then the link rate is optimally allocated among contending flows that share this link by solving a linear programming (LP) problem. A thorough performance evaluation is undertaken as a function of the number of channels and interfaces/node and the number of contending flows. The performance of our algorithm is shown to be significantly superior to best known algorithm in its class in multichannel limited radio scenarios.