Wavy optimal flows for heat transfer in channels
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912478385930240 |
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| author | Prabala, Shivani Alben, Silas |
| author_facet | Prabala, Shivani Alben, Silas |
| contents | We compute incompressible two-dimensional fluid flows that maximize the rate of heat transfer from the walls of a straight channel given a specified flow input power $Pe^{2}$, where $Pe$ is the Péclet number. We use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm together with an adjoint method to compute gradients. The optimal flows are approximately unidirectional up to a critical $Pe \approx 2^{12}$. Above this value the flows assume wavy patterns characterized by finger-like protrusions emanating from both the top and bottom walls of the channel. The rate of heat transfer for these wavy flows is 3% to 30% greater than that of the previously identified unidirectional optima for $2^{13} \leq Pe \leq 2^{17}$. The wavy flows have a much smaller flux through the channel than the unidirectional flows, with regions of slow-moving fluid at nearly homogeneous temperature interspersed with serpentine regions of fast-moving fluid. Consequently, the area of the interface between hot and cold fluid is increased. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavy optimal flows for heat transfer in channels Prabala, Shivani Alben, Silas Fluid Dynamics We compute incompressible two-dimensional fluid flows that maximize the rate of heat transfer from the walls of a straight channel given a specified flow input power $Pe^{2}$, where $Pe$ is the Péclet number. We use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm together with an adjoint method to compute gradients. The optimal flows are approximately unidirectional up to a critical $Pe \approx 2^{12}$. Above this value the flows assume wavy patterns characterized by finger-like protrusions emanating from both the top and bottom walls of the channel. The rate of heat transfer for these wavy flows is 3% to 30% greater than that of the previously identified unidirectional optima for $2^{13} \leq Pe \leq 2^{17}$. The wavy flows have a much smaller flux through the channel than the unidirectional flows, with regions of slow-moving fluid at nearly homogeneous temperature interspersed with serpentine regions of fast-moving fluid. Consequently, the area of the interface between hot and cold fluid is increased. |
| title | Wavy optimal flows for heat transfer in channels |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2507.09027 |