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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18787 |
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| _version_ | 1866917388171083776 |
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| author | Anguiano, María Pažanin, Igor Suárez-Grau, Francisco J. |
| author_facet | Anguiano, María Pažanin, Igor Suárez-Grau, Francisco J. |
| contents | We analyze a non-isothermal Darcy-Brinkman thin-film flow with a periodically oscillating boundary and viscous dissipation acting as a heat source. Using asymptotic analysis and the periodic unfolding method, we establish the convergence of velocity, pressure, and temperature fields as the small parameter (related to the film thickness and the period of the roughness) tends to zero. The limit problems depend on the relative scaling of the roughness wavelength and consist of coupled elliptic systems combining Reynolds-type equations with Darcy-Brinkman cell problems and reduced energy equation. In the critical roughness regime, the effective model exhibits a strong coupling induced by the oscillatory geometry, which does not occur in a smooth-boundary case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the effects of surface roughness in non-isothermal porous medium flow Anguiano, María Pažanin, Igor Suárez-Grau, Francisco J. Analysis of PDEs 35B27, 35Q35, 76S05 We analyze a non-isothermal Darcy-Brinkman thin-film flow with a periodically oscillating boundary and viscous dissipation acting as a heat source. Using asymptotic analysis and the periodic unfolding method, we establish the convergence of velocity, pressure, and temperature fields as the small parameter (related to the film thickness and the period of the roughness) tends to zero. The limit problems depend on the relative scaling of the roughness wavelength and consist of coupled elliptic systems combining Reynolds-type equations with Darcy-Brinkman cell problems and reduced energy equation. In the critical roughness regime, the effective model exhibits a strong coupling induced by the oscillatory geometry, which does not occur in a smooth-boundary case. |
| title | On the effects of surface roughness in non-isothermal porous medium flow |
| topic | Analysis of PDEs 35B27, 35Q35, 76S05 |
| url | https://arxiv.org/abs/2512.18787 |