The study of viscous dissipation in the context of unsteady incompressible magnetohydrodynamic viscous fluid flow over a moving plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. The fractional mathematical model is proposed by considering the effect of viscous dissipation force of the flowing fluid. For this purpose, fluid is assumed to be lying over a vertical plate that is moving in its own plane. The governing equations are transformed into the dimensionless form and developed fractional model with a new operator Constant Proportional Caputo Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for energy and momentum balances developed in terms of series. The validation of the present model comparison graphs is plotted for temperature. The sensitivity of different input parameters on output response are analyzed and displayed the sensitivity results in tabular and graphical form and found that the permeable parameter is most sensitive to skin friction coefficient, and the Eckert number is most sensitive parameter among others to Nusselt Number. The novelty of present work is to develop a correlation between input parameters and output responses by using Response Surface Methodology (RSM). As no such correlation has been developed for optimization of mass and heat flux of MHD viscous fluid flow with Constant Proportional Caputo derivative by using RSM. By using this correlation, we have performed sensitivity analysis for output responses.

中文翻译：

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利用响应面法以恒比例 Caputo 导数优化 MHD 粘性流体的质量和热通量：灵敏度分析

在移动板上的非定常不可压缩磁流体动力粘性流体流动背景下的粘性耗散研究是流体动力学和传热领域一个复杂而重要的课题。该场景结合了多种物理现象，在各个工程和科学领域都有实际应用。考虑流动流体粘性耗散力的影响，提出了分数式数学模型。为此，假设流体位于在其自身平面内移动的垂直板上。控制方程被转换为无量纲形式，并使用新算子“常数比例卡普托导数”开发了分数模型。我们使用拉普拉斯变换技术来解析无量纲控制方程的解。能量和动量平衡的转换解决方案是按级数开发的。本模型的验证比较图是针对温度绘制的。分析了不同输入参数对输出响应的敏感性，并以表格和图形形式显示敏感性结果，发现渗透性参数对皮肤摩擦系数最敏感，埃克特数是对努塞尔数最敏感的参数。目前工作的新颖之处在于通过使用响应面方法（RSM）来开发输入参数和输出响应之间的相关性。由于尚未开发出这样的相关性来通过使用 RSM 来优化 MHD 粘性流体流动的质量和热通量以及恒定比例 Caputo 导数。通过使用这种相关性，我们对输出响应进行了敏感性分析。