标题： 通道中用于传热的波浪最优流 显示英文标题

标题： Wavy optimal flows for heat transfer in channels

摘要： 我们计算不可压缩的二维流体流动，这些流动在给定特定的流输入功率$Pe^{2}$的情况下，最大化从直通道壁的传热速率，其中$Pe$是佩克莱特数。 我们使用布罗伊登-弗莱彻-戈尔德法布-夏诺（BFGS）算法结合伴随方法来计算梯度。 最优流动大约是单向的，直到临界值$Pe \approx 2^{12}$。 超过这个值后，流动呈现出波浪状模式，其特征是来自通道顶部和底部壁的指状突出物。 这些波浪状流动的传热速率比之前确定的单向最优值高出 3% 到 30%，对于$2^{13} \leq Pe \leq 2^{17}$来说。 波浪状流动通过通道的通量远小于单向流动，其中缓慢移动的流体区域几乎具有均匀温度，穿插着快速移动的蛇形区域。 因此，热流体和冷流体之间的界面面积增加了。 显示英文摘要

摘要： 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 P\'{e}clet 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.