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首页> 外文期刊>International Journal of Heat and Mass Transfer >Thermal instability in a plane channel with internal heating and horizontal Poiseuille throughflow
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Thermal instability in a plane channel with internal heating and horizontal Poiseuille throughflow

机译：具有内部加热和水平Poiseuille通流的平面通道中的热不稳定性

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摘要

The effect of a basic Poiseuille throughflow on the thermal instability of a horizontal fluid layer bounded by two plane parallel walls is studied. An unstable thermal stratification is studied, entirely due to a uniform internal heat generation in the fluid, whereas the thermal boundary conditions do not impress any temperature difference across the fluid layer. Two cases are investigated: a symmetric case where both boundaries are perfectly conducting; a non-symmetric case where the lower boundary is adiabatic and the upper boundary is perfectly conducting. A linear stability analysis is carried out and the eigenvalue problem is solved numerically for arbitrary oblique rolls, and by a symbolic weighted residual method in the special case of longitudinal roils. The main result is that the basic Poiseuille flow does not influence the thermoconvective instability at the onset of the least stable modes, i.e. the longitudinal rolls. Thus, the critical conditions are just the same as for a fluid at rest in the basic state. Although the focus is on the thermoconvective instability, it is proved that, even in the presence of the internal heat generation, Squire's theorem holds for the hydrodynamic instability of the plane Poiseuille flow.
机译：研究了基本Poiseuille通流对由两个平面平行壁为边界的水平流体层的热不稳定性的影响。对不稳定的热分层进行了研究，这完全是由于流体内部产生的热量均匀，而热边界条件并没有在流体层上产生任何温差。研究了两种情况：两个边界都完美传导的对称情况；非对称情况，下边界是绝热的，上边界是完美传导的。进行了线性稳定性分析，并通过符号加权残差法在纵向轧辊的特殊情况下对任意倾斜轧辊进行了特征值问题的数值求解。主要结果是，在最不稳定的模态（即纵向辊）开始时，基本泊瓦斯流不会影响热对流不稳定性。因此，临界条件与基本状态下的静止流体相同。尽管重点放在热对流不稳定性上，但事实证明，即使在内部产生热量的情况下，Squire定理也适用于平面Poiseuille流的流体动力不稳定性。

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