The non-isothermal filling of a flat mould cavity by a Newtonian fluid with simultaneous two-dimensional impregnation of the porous (reinforcing) layer is investigated. The flow in the cavity is described by inertialess Navier–Stokes equations, the flow in the porous layer by Darcy's law, and the flow in the region adjacent to the ‘liquid–porous layer’ boundary by the Brinkman equation. Viscosity is considered to be temperature dependent. The temperature fields in the channel region and in the permeable layer are interrelated by conjugate boundary conditions of the fourth kind.
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