Heat-conducting viscous fluids over porous media

A new model is introduced for describing the heat-conducting viscous fluids over porous media. The innovative features of the presented model are the nonlinear character given by temperature dependence of the physical parameters such as the viscosities, the permeability, and complementary the thermal conductivity and thermal expansion. The flow velocities are small (for steady processes) and mainly driven by the pressure gradient in porous media such that the Stokes-Darcy system is completed by the energy equation with the heat flux given by the Fourier law. The existence of solutions is established for the Stokes-Darcy-Fourier system either with the Beavers-Joseph-Saffman or Beavers-Joseph interface boundary conditions. Both problems are solved by means a fixed point procedure and Lagrange multiplier approach.

Keywords

Stokes-Darcy equations, Beavers-Joseph boundary condition, Fourier law

2010 Mathematics Subject Classification

35J88, 76S05, 86A60

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Published 9 April 2012