Three dimensional conjugate mixed convection in a rectangular channel is numerically investigated. The focus is on the effects of local buoyancy generated by a discrete heat source mounted on a thermally conducting board. Calculations cover 0.126 less than or equal to Re less than or equal to 1260, Gr = 7.8789 x 10(7), 1 less than or equal to kappa less than or equal to 100, and Pr = 0.71, respectively. Flow fields show active interaction between the buoyancy-induced thermal plume and the approaching external flow in the mixed convection regime where the temperature distribution, heat flux, and heat transfer coefficients all strongly depend on such flow interaction. In addition, the Nusselt number on top of the heat source indicates significant three-dimensional effects. The 'modified 5% deviation rule' is proposed in an effort to define the natural, mixed and forced convection regimes. The proposed rule is especially appropriate for conjugate heat transfer problems in which the thermal conductivity of the board plays an important role in determining the heat transfer mode. A correlation for theta(max)/kappa(1/2) is sought, and the mixed convection regime is accordingly determined as 1.81 x 10(-3) less than or equal to Re/Gr(1/2) < 2.80 x 10(-2).