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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\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\epsilon &gt; 0$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03f5<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    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\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varepsilon \\rightarrow 0$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03b5<\/mml:mi>\n                            <mml:mo>\u2192<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    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\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03b5<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -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.\n                  <\/jats:p>","DOI":"10.1007\/s00332-026-10260-0","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T11:27:09Z","timestamp":1776338829000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain"],"prefix":"10.1007","volume":"36","author":[{"given":"Tom","family":"Freudenberg","sequence":"first","affiliation":[]},{"given":"Michael","family":"Eden","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,4,16]]},"reference":[{"key":"10260_CR1","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1016\/0362-546X(92)90015-7","volume":"18","author":"E Acerbi","year":"1992","unstructured":"Acerbi, E., Chiad\u00f2 Piat, V., Dal Maso, G., Percivale, D.: An extension theorem from connected sets, and homogenization in general periodic domains. 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