Empirical modeling and sensitivity analysis of pressure rise per wavelength and frictional forces for the peristaltic flow of Bingham plastic fluids: application of response surface methodology

IF 3 3区 工程技术 Q2 CHEMISTRY, ANALYTICAL
Amad ur Rehman, Zaheer Asghar, Ahmed Zeeshan, Marin Marin
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Abstract

The efficiency of mixed convection peristaltic flow can be investigated through pressure rise per wavelength \((\Delta P_{{{\uplambda }}} )\) and frictional forces (\({F}_{\uplambda }\)). The main aim of the present study is to discover the sensitivity analysis of non-Newtonian fluids using the Bingham plastic fluid model. In order to achieve this objective, we have empirically modeled the pressure rise per wavelength \((\Delta {P}_{\uplambda })\) and frictional forces (\({F}_{\uplambda }\)) as a function varying with leading parameters of problem. The flow problem is governed by three coupled nonlinear partial differential equations. They are reduced to nonlinear coupled ordinary differential equations by using the long wavelength and low Reynolds number approximations. They are solved numerically using MATLAB built-in routine bvp4c to analyze the sensitivity of pressure rise per wavelength (\(\Delta {P}_{\uplambda }\)) and frictional forces (\({F}_{\uplambda }\)). We first derive the empirical model among each of responses \(\Delta {P}_{\uplambda }\) and \({F}_{\uplambda }\) and physical parameters which govern the flow using response surface methodology. The goodness of fit of empirical model is decided on the basis of coefficient of determination (\({R}^{2}\)) obtained from the analysis of variance (ANOVA). The coefficients of determination (\({R}^{2}\)) are 99.78% both for \(\Delta {P}_{\uplambda }\) and\({F}_{\uplambda }\). The higher values of \({R}^{2}\) determine the goodness of fit of empirical model. No correlation has been developed to optimize \(\Delta {P}_{\uplambda }\) and \({F}_{\uplambda }\) in peristaltic flow for Bingham plastic fluids using RSM. The results of sensitivity analysis revealed that \(\Delta {P}_{\uplambda }\) and \({F}_{\uplambda }\) are most sensitive to flow rate (q) at all levels such as low (− 1), medium (0) and high (+ 1). The sensitivity of \(\Delta {P}_{\uplambda }\) to Bingham number (Bn) shows a distinct behavior with varying levels of flow rate (q). At low level (− 1) of flow rate (q), the sensitivity is positive, and at high level (+ 1) of flow rate (q), the sensitivity becomes negative. Conversely, the sensitivity of \({F}_{\uplambda }\) to Bingham number (Bn) at low to high level of flow rate (q).

Abstract Image

宾汉塑性流体蠕动过程中每波长压力上升和摩擦力的经验建模和敏感性分析:响应面方法的应用
混合对流蠕动流的效率可以通过每波长的压力上升((\Delta P_{{\uplambda }}} )和摩擦力(\({F}_{\uplambda }\) )来研究。本研究的主要目的是利用宾厄姆塑性流体模型发现非牛顿流体的敏感性分析。为了实现这一目标,我们根据经验将每个波长的压力上升((\Δ {P}_{\uplambda }))和摩擦力(\({F}_{\uplambda }\))建模为随问题主要参数变化的函数。流动问题由三个耦合非线性偏微分方程控制。通过使用长波长和低雷诺数近似,它们被简化为非线性耦合常微分方程。使用 MATLAB 内置例程 bvp4c 对它们进行数值求解,分析每波长压力上升(\(\Delta {P}_{\uplambda }\) )和摩擦力(\({F}_{\uplambda }\) )的敏感性。我们首先利用响应面方法在每个响应 \(\Delta {P}_{\uplambda }\) 和 \({F}_{\uplambda }\) 与控制流动的物理参数之间推导出经验模型。根据方差分析(ANOVA)得出的判定系数(\({R}^{2}\)决定经验模型的拟合度。)\(\Delta {P}_{\uplambda }\) 和 ({F}_{\uplambda }\ )的决定系数({R}^{2}/ )都是 99.78%。较高的\({R}^{2}\)值决定了经验模型的拟合度。使用 RSM 对宾汉塑性流体蠕动流中的\(\Delta {P}_{\uplambda }\) 和\({F}_{\uplambda }\) 进行优化的相关性还没有被开发出来。敏感性分析的结果表明,在低流量(-1)、中流量(0)和高流量(+1)等各个水平上,\(\Delta {P}_{\uplambda }\) 和\({F}_{\uplambda }\) 对流量(q)最为敏感。随着流速(q)水平的变化,\(\Delta {P}_{\uplambda }\) 对宾厄姆数(Bn)的敏感性表现出不同的行为。在流量(q)的低水平(- 1)时,灵敏度为正,而在流量(q)的高水平(+ 1)时,灵敏度变为负。相反,从低到高流量水平(q),\({F}_\{uplambda }\) 对宾厄姆数(Bn)的敏感性。
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来源期刊
CiteScore
8.50
自引率
9.10%
发文量
577
审稿时长
3.8 months
期刊介绍: Journal of Thermal Analysis and Calorimetry is a fully peer reviewed journal publishing high quality papers covering all aspects of thermal analysis, calorimetry, and experimental thermodynamics. The journal publishes regular and special issues in twelve issues every year. The following types of papers are published: Original Research Papers, Short Communications, Reviews, Modern Instruments, Events and Book reviews. The subjects covered are: thermogravimetry, derivative thermogravimetry, differential thermal analysis, thermodilatometry, differential scanning calorimetry of all types, non-scanning calorimetry of all types, thermometry, evolved gas analysis, thermomechanical analysis, emanation thermal analysis, thermal conductivity, multiple techniques, and miscellaneous thermal methods (including the combination of the thermal method with various instrumental techniques), theory and instrumentation for thermal analysis and calorimetry.
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