This paper presents the derivation of the Clausius-Duhem inequality for quasi-1D transient flows of compressible fluids in radially deformable pipes of varying cross-section area. To do so, a decomposition of the normal stress in spherical and deviatoric components was considered, so that the power expended to radially deform the fluid could be properly accounted for in the first law of thermodynamics, generating a coherent Clausius-Duhem inequality. Based on the derived inequality for Newtonian-Fourier fluids, we focus on their implications and applications. As implications we show that the restrictions imposed on the dynamic and bulk viscosities are different from those retrieved from the 1D and 3D contexts. As applications, we present two distinct studies concerning pipe flows. The first shows by appealing to numerical simulations that the weighting-function and local-balance unsteady friction models violate the second law of thermodynamics since they present negative local rate of energy dissipation. The second presents an analysis to estimate upper bounds of the local rate of energy dissipation associated with shear, and volumetric and axial deformations for laminar and turbulent transient regimes, under flow conditions characterized by the Ghidaoui's dimensionless parameter $\widehat{P}$, for liquids with different bulk to shear viscosity ratios. Although the dissipation is dominated by shear, that one due to volumetric deformation may become more relevant for laminar flows, when small numbers $\widehat{P}$ and high bulk viscosities liquids are considered.

本文介绍了 Clausius-Duhem 不等式的推导，用于不同横截面积的径向可变形管道中可压缩流体的准一维瞬态流动。为此，考虑了球面分量和偏分量中法向应力的分解，以便可以在热力学第一定律中适当考虑用于使流体径向变形的功率，从而产生一致的克劳修斯-杜恒不等式。基于牛顿-傅立叶流体的导出不等式，我们关注它们的含义和应用。作为暗示，我们表明对动态和体积粘度施加的限制与从 1D 和 3D 上下文中检索到的限制不同。作为应用，我们提出了两项​​关于管道流动的不同研究。第一个通过数值模拟表明加权函数和局部平衡非定常摩擦模型违反热力学第二定律，因为它们呈现负的局部能量耗散率。第二部分分析了在以 Ghidaoui 的无量纲参数为特征的流动条件下，估计与层流和湍流瞬态状态的剪切、体积和轴向变形相关的局部能量耗散率的上限$\widehat{磷}$，对于具有不同体积与剪切粘度比的液体。尽管耗散主要受剪切力的影响，但当数量较少时，由于体积变形引起的损耗可能与层流更相关$\widehat{磷}$ 和高体积粘度的液体被考虑。