The article addresses the extended Graetz–Nusselt problem in finite-length microchannels for prescribed wall heat flux boundary conditions, including the effects of rarefaction, streamwise conduction, and viscous dissipation. The analytical solution proposed, valid for low-intermediate Peclet values, takes into account the presence of the thermal development region. The influence of all transport parameters (Peclet , Knudsen , and Brinkman ) and geometrical parameters (entry length and microchannel aspect ratio) is investigated. Performances of different wall heat flux functions have been analyzed in terms of the averaged Nusselt number. In the absence of viscous dissipation , the best heating protocol is a decreasing wall heat flux function. In the presence of dissipation , the best heating protocol is a uniform wall heat flux.

中文翻译：

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在扩展的Graetz-Nusselt问题上的回波，沿流传导和粘性耗散的意义：具有规定壁热通量的有限长度微通道的情况

本文针对规定的壁热通量边界条件解决了有限长微通道中的扩展Graetz-Nusselt问题，包括稀疏，流向传导和粘性耗散的影响。提出的分析解决方案对低中间Peclet值有效，并考虑了热显影区域的存在。所有的传输参数（Peclet准的影响，克努森，和布林克曼）和几何参数（条目长度和微通道纵横比）进行了研究。根据平均努塞尔数分析了不同壁热通量函数的性能。在没有粘性耗散的情况下，最佳的加热方案是降低壁热通量函数。在耗散的情况下，最好的加热方案是均匀的壁热通量。