The roll-coating analysis of viscous nanofluid using lubrication approximation theory over a flat porous sheet is investigated. We considered water-based copper (Cu) nanoparticles to discuss the roll-coating analysis. The rate of fluid entering at the roll surface is assumed equal to the rate of fluid leaving on the web surface. The resulting differential equation developed under lubrication approximation and closed-form expressions is obtained for velocity and pressure gradient. The effects of entering velocity, Reynolds number, geometric parameter, and nanoparticle volume fraction with different models on physical quantities such as pressure, pressure gradient, velocity, force, power input are calculated. Some of these effects are presented graphically. It is noted that increasing nanoparticle volume fraction increases the pressure gradient, pressure distribution and has negligible effect on the velocity profile. Model II has a greater effect on pressure and pressure gradient than model I and has an inverse effect on force and power factor.

中文翻译：

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含Cu-水纳米粒子的粘性纳米流体卷筒涂层评估的理论分析

研究了使用润滑近似理论在平坦多孔片上对粘性纳米流体进行辊涂分析。我们考虑了水基铜 (Cu) 纳米粒子来讨论辊涂分析。假定流体进入辊表面的速率等于流体离开卷筒表面的速率。所得微分方程在润滑近似和闭式表达式下得到了速度和压力梯度。计算了不同模型的进入速度、雷诺数、几何参数和纳米粒子体积分数对压力、压力梯度、速度、力、功率输入等物理量的影响。其中一些效果以图形方式呈现。注意到增加纳米颗粒体积分数会增加压力梯度，压力分布，对速度分布的影响可以忽略不计。与模型 I 相比，模型 II 对压力和压力梯度的影响更大，并且对力和功率因数具有相反的影响。