Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Pažanin, Igor Suárez-Grau, Francisco J. |
| author_facet | Pažanin, Igor Suárez-Grau, Francisco J. |
| contents | This study investigates the steady-state Darcy-Brinkman flow within a thin, saturated porous domain, focusing on the effects of viscous dissipation and non-homogeneous boundary condition for the temperature. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the simplified coupled model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions. The resulting limit model incorporates contributions of viscous dissipation and thermal boundary conditions and thus could prove useful in the engineering applications involving porous media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition Pažanin, Igor Suárez-Grau, Francisco J. Analysis of PDEs 35B40, 35Q35, 76S05 This study investigates the steady-state Darcy-Brinkman flow within a thin, saturated porous domain, focusing on the effects of viscous dissipation and non-homogeneous boundary condition for the temperature. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the simplified coupled model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions. The resulting limit model incorporates contributions of viscous dissipation and thermal boundary conditions and thus could prove useful in the engineering applications involving porous media. |
| title | Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition |
| topic | Analysis of PDEs 35B40, 35Q35, 76S05 |
| url | https://arxiv.org/abs/2508.04615 |