粘弹性流体通过球体的无界流的共轭传热
Conjugate heat transfer in the unbounded flow of a viscoelastic fluid past a sphere
摘要：
本文研究了简化PTT流体在Stokes区（$Re = 0.01$）流过无界球时的共轭传热。问题的数值求解与有限体积法假设轴对称，没有自然对流和恒定的物理性质。球体以恒定和均匀的速率产生热量，并且在固体-流体界面处存在或不存在热接触电阻的情况下，对Deborah（$0 \leq De \leq 100$）、Prandtl（$10^0 \leq Pr \leq 10^5$）、Brinkman（$0 \leq Br \leq 100$）和电导率比（$0.1 \leq κ\leq 10$）的范围进行分析。阻力系数随$De$的增大而单调减小，而球表面和尾流中的应力随$De$的增大先增大后减小。对于所测试的两种溶剂粘度比（$β$ = 0.1和0.5），观察到负尾流，对于弹性更大的流体，负尾流更强烈。在没有粘性耗散的情况下，平均努塞尔数在初始增加之后开始随着$De$而减小。传热增强相对于一个等效的牛顿流体观察到的整个范围内的测试条件。球的温度降低，变得更加均匀，当它的导热系数增加有关的流体的传导性，虽然小的变化，观察到的努塞尔数。界面处的接触热阻增加了球体的平均温度，而不会显著影响球体内部的温度分布的形状。当考虑粘性耗散时，随着$Br$的增加，在传热过程中观察到显著的变化。总的来说，与牛顿流体相比，简化的PTT流体可以增强热传递，但是增加$De$不一定改善热交换。
英文摘要：
This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime ($Re = 0.01$). The problem is numerically solved with the finite-volume method assuming axial symmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah ($0 \leq De \leq 100$), Prandtl ($10^0 \leq Pr \leq 10^5$), Brinkman ($0 \leq Br \leq 100$) and conductivity ratios ($0.1 \leq κ\leq 10$), in the presence or absence of thermal contact resistance at the solid-fluid interface. The drag coefficient shows a monotonic decrease with $De$, whereas the stresses on the sphere surface and in the wake first increase and then decrease with $De$. A negative wake was observed for the two solvent viscosity ratios tested ($β$ = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with $De$ after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as $Br$ increases. Overall, a simplified PTT fluid can enhance heat transfer compared to a Newtonian fluid, but increasing $De$ does not necessarily improve heat exchange.
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