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In this study, forced convection of Fe<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>3</mn> </msub> </semantics> </math> </inline-formula>O<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>&#8315;water nanofluid in a bifurcating channel was numerically studied under the influence of variable magnetic. Galerkin residual finite element method was used for numerical simulations. Effects of various values of Reynolds number (between 100 and 500), Hartmann number (between 0 and 3), and solid nanoparticle volume fraction (between 0% and 4%) on the convective heat transfer characteristics were analyzed. It was observed that location and size of the re-circulation zones established in the walls of the bifurcating channel strongly influenced by the variable magnetic field and Reynolds number. Average Nusselt number versus Hartmann number showed different characteristics for hot walls of the vertical and horizontal branching channels. The average Nusselt number enhancements were in the range of 12&#8315;15% and 9&#8315;12% for hot walls of the branching channel in the absence and presence of magnetic field (at Hartmann number of 3).