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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.02150 |
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| _version_ | 1866913037485604864 |
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| author | Freudenberg, Tom Eden, Michael |
| author_facet | Freudenberg, Tom Eden, Michael |
| contents | We investigate the effective coupling between heat and fluid dynamics within a thin fluid layer in contact with a solid structure via a rough surface. Moreover, the opposing vertical surfaces of the thin layer are in relative motion. This setup is particularly relevant to grinding processes, where cooling lubricants interact with the rough surface of a rotating grinding wheel. The resulting model is non-linearly coupled through(i) temperature-dependent viscosity and (ii) convective heat transport. The underlying geometry is highly heterogeneous due to the thin, rough surface characterized by a small parameter representing both the height of the layer and the periodicity of the roughness. We analyze this non-linear system for existence, uniqueness, and energy estimates and study the limit behavior within the framework of two-scale convergence in thin domains. In this limit, we derive an effective interface model in 3D (a line in 2D) for the heat and fluid interactions inside the fluid. We implement the system numerically and validate the limit problem through direct comparison with the micromodel. Additionally, we investigate the influence of the temperature-dependent viscosity and various geometrical configurations via simulation experiments. The corresponding numerical code is freely available on GitHub. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain Freudenberg, Tom Eden, Michael Analysis of PDEs Numerical Analysis 35B27, 76-10, 76M50, 65N30, 80M40, 80A19 We investigate the effective coupling between heat and fluid dynamics within a thin fluid layer in contact with a solid structure via a rough surface. Moreover, the opposing vertical surfaces of the thin layer are in relative motion. This setup is particularly relevant to grinding processes, where cooling lubricants interact with the rough surface of a rotating grinding wheel. The resulting model is non-linearly coupled through(i) temperature-dependent viscosity and (ii) convective heat transport. The underlying geometry is highly heterogeneous due to the thin, rough surface characterized by a small parameter representing both the height of the layer and the periodicity of the roughness. We analyze this non-linear system for existence, uniqueness, and energy estimates and study the limit behavior within the framework of two-scale convergence in thin domains. In this limit, we derive an effective interface model in 3D (a line in 2D) for the heat and fluid interactions inside the fluid. We implement the system numerically and validate the limit problem through direct comparison with the micromodel. Additionally, we investigate the influence of the temperature-dependent viscosity and various geometrical configurations via simulation experiments. The corresponding numerical code is freely available on GitHub. |
| title | Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain |
| topic | Analysis of PDEs Numerical Analysis 35B27, 76-10, 76M50, 65N30, 80M40, 80A19 |
| url | https://arxiv.org/abs/2406.02150 |