Scholarlink

<p>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 motivated by grinding processes, where cooling lubricants interact with the rough surface of a rotating grinding wheel. The resulting model is nonlinearly 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\epsilon &gt; 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϵ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> that represents both the height of the layer and the periodicity of the roughness. We analyze this nonlinear system for existence, uniqueness, and energy estimates and study the limit behavior <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> 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-fluid interactions inside the fluid. We implement the system numerically and validate the limit problem through a direct comparison with the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-model. Furthermore, we investigate the influence of the temperature-dependent viscosity and various geometrical configurations with simulation experiments. The corresponding numerical code is freely available on GitHub.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月16日

查看全文
  • Tom Freudenberg,
  • Michael Eden

摘要

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 motivated by grinding processes, where cooling lubricants interact with the rough surface of a rotating grinding wheel. The resulting model is nonlinearly 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 \(\epsilon > 0\) ϵ > 0 that represents both the height of the layer and the periodicity of the roughness. We analyze this nonlinear system for existence, uniqueness, and energy estimates and study the limit behavior \(\varepsilon \rightarrow 0\) ε → 0 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-fluid interactions inside the fluid. We implement the system numerically and validate the limit problem through a direct comparison with the \(\varepsilon \) ε -model. Furthermore, we investigate the influence of the temperature-dependent viscosity and various geometrical configurations with simulation experiments. The corresponding numerical code is freely available on GitHub.