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首页> 外文期刊>International Journal of Heat and Mass Transfer >Effect of temperature-dependent consistency index on the exiting sheet thickness in the calendering of power-law fluids
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Effect of temperature-dependent consistency index on the exiting sheet thickness in the calendering of power-law fluids

机译：幂律流体压延中温度相关稠度指数对出口板厚度的影响

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摘要

In this work we treat theoretically the calendering process of inelastic (power-law fluid) sheets of finite initial thickness, taking into account that the consistency index of the fluid is a well-defined function of the temperature. We predict the influence of the temperature-dependent consistency index on the exiting sheet thickness in the calendering process. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the exiting sheet thickness represents an eigenvalue of the mathematical problem. When the above variables were obtained, the exiting sheet thickness in the calendering process was determined, considering the influence of the temperature variations in the process. The mentioned governing equations contain four dimensionless parameters: the Graetz number, Gz, a geometrical aspect ratio, p, the power law index of the fluid, n, and a parameter that takes into account the effect of the variable consistency index as a function of the temperature and e, defined as the ratio of the Nahme-Griffith number, Na, to the Graetz number. Using the limit of ∈ 1, the dimensionless exiting sheet thickness of the calendering process have been obtained as a function of the involved dimensionless parameters. The numerical results show that the inclusion of temperature-dependent consistency index effect modifies the dimensionless exiting sheet thickness in about 6.91%.
机译：在这项工作中，我们从理论上处理初始厚度有限的非弹性（幂律流体）片材的压延过程，要考虑到流体的稠度指数是温度的明确函数。我们预测压延过程中与温度有关的稠度指数对现有板材厚度的影响。基于润滑理论，对质量，动量和能量平衡方程进行了无量纲化，并使用扰动和数值技术对速度，压力和温度场进行了求解，其中出口板的厚度代表了数学问题的特征值。当获得上述变量时，考虑到过程中温度变化的影响，确定压延过程中的出纸厚度。提到的控制方程式包含四个无因次参数：Graetz数Gz，几何长宽比p，流体的幂律指数n和考虑变量一致性指数作为变量的函数的参数。温度和e，定义为Nahme-Griffith数Na与Graetz数之比。使用ε 1的极限，已获得压延过程的无量纲出纸厚度，这是所涉及的无量纲参数的函数。数值结果表明，包含温度相关的稠度指数效应可以使无量纲的出纸厚度改变约6.91％。

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