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A governing equation for injection mold‐filling of thin cavities with a power‐law fluid is derived. The interaction between upstream delivery channel flow and cavity flow results in a continuously changing gate condition as the total viscous dissipation of the delivery channel‐cavity assembly is minimized. Depending upon the relative magnitude of pressure drops or viscous dissipation across the channel and the cavity, the boundary conditions which determine the cavity filling process will lie between the following two limiting cases: a Cauchy type gate condition such that the location of the melt front is completely determined by the upstream flow; a Cauchy type melt front condition in which the gate condition is controlled by the downstream flow. For most injection molding cases this may be manifested as equilibration of dissipation density on the melt front. Experimentally observed melt front locations from isothermal, Newtonian filling of a constant gap rectangular cavity and of a bi‐gap rectangular cavity are reported and the validity of the limiting cases are tested.

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