具有随温度变化的粘性的流体中的粘性加热：对岩浆流动的影响
Viscous heating in fluids with temperature-dependent viscosity: implications for magma flows
摘要：
由于能量方程和动量方程之间的耦合，粘性加热在粘性强温变流体动力学中起着重要的作用。由粘性摩擦产生的热产生管壁附近的局部温度升高，从而粘度降低，这可能显著地改变温度和速度分布。这些过程主要受Peclét数、Nahme数、流速和热边界条件的控制。流体中的粘性加热问题在过去曾被研究过，因为它在聚合物工业中具有实际意义，并被用来解释硅酸盐熔体的某些流变行为，但并没有完全应用于岩浆流动的研究。在本文中，我们集中在有限长管的粘性加热所造成的热和机械效应。我们发现，在岩浆流在高Nahme数和典型的流速，粘性加热是负责Poietuille流的演变，在入口处的温度分布均匀，活塞流与较热的层附近的墙壁。当由粘性加热引起的温度梯度非常明显时，可能发生局部不稳定性，并且可能触发二次流。为了完整起见，本文还描述了无限长管道中的岩浆流动的恒定状态和瞬态。
英文摘要：
Viscous heating plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local temperature increase near the tube walls with a consequent decrease of the viscosity which may dramatically change the temperature and velocity profiles. These processes are mainly controlled by the Peclét number, the Nahme number, the flow rate and the thermal boundary conditions. The problem of viscous heating in fluids was investigated in the past for its practical interest in the polymer industry, and was invoked to explain some rheological behaviours of silicate melts, but was not completely applied to study magma flows. In this paper we focus on the thermal and mechanical effects caused by viscous heating in tubes of finite lengths. We find that in magma flows at high Nahme number and typical flow rates, viscous heating is responsible for the evolution from Poiseuille flow, with a uniform temperature distribution at the inlet, to a plug flow with a hotter layer near the walls. When the temperature gradients induced by viscous heating are very pronounced, local instabilities may occur and the triggering of secondary flows is possible. For completeness, this paper also describes magma flow in infinitely long tubes both at steady state and in transient phase.
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