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A novel approach to the numerical simulation of conjugate heat transfer is presented. Heat conduction in a solid is implicitly coupled with heat convection in viscous fluid flow. The frame of the solution is the Navier-Stokes equations set for viscous Newtonian fluid. A formulation for planar geometry is described in detail. The main advantage of the presented approach is implicit handling of the heat transfer conditions at the solid-fluid interface. Computed test examples include conjugate forced convection in a channel and conjugate natural convection in a cavity.