The Non-Incompressibility on Heat-Conducting Fluids. The Stationary Case

Consiglieri, Luisa

doi:10.1007/s00021-009-0294-5

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2012

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Cited by 2 publications

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“…Then Theorem 7.3 guarantees the existence of a saddle-point (u,p) to L. This saddle-point is the required solution to Theorem 3.10, since the problem (7.6)-(7.7) is exactly (cf. [11])…”

Section: Proofmentioning

confidence: 99%

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Heat-conducting viscous fluids over porous media

Consiglieri¹

2012

Communications in Mathematical Sciences

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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.

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“…Then Theorem 7.3 guarantees the existence of a saddle-point (u,p) to L. This saddle-point is the required solution to Theorem 3.10, since the problem (7.6)-(7.7) is exactly (cf. [11])…”

Section: Proofmentioning

confidence: 99%

“…Notwithstanding, we deal with the Newtonian fluid (linearly viscous fluid). The heat-conducting behavior on mechanically incompressible non-Newtonian fluids, as in [11], overlying porous media will be handled in a forthcoming work.…”

Section: Introductionmentioning

confidence: 99%