Analysis of MHD viscous fluid flow under the influence of viscous dissipation force over vertically moving plate with innovative constant proportional Caputo derivative

In this study, magnetohydrodynamic viscous fluid is considered unsteady and incompressible, considering the effect of inclined magnetic field. Assessing the impact of viscous dissipation force in the fluid, the fractional model is proposed. This scenario has real-world applicability in a variety of scientific and technical domains and incorporates many physical phenomena. Fluid is considered as flowing over a vertically oriented plate moving about its own plane. Constant Proportional Caputo (CPC) derivative operator is obtained while developing the fractional model by transforming the governed equations into a dimensionless form. We solved these transformed equations analytically by employing the technique of Laplace transform and got solutions for momentum equation and energy equation in series form. For computational analysis we employed MATHCAD software and discussed the impact of pertinent parameters on flow. One of the important significances of this study is the use of a new kind of fractional operator, i.e., CPC with power law, and comparing the obtained results with previously published results. This research showed that for greater values of fractional parameters both velocity and temperature profiles reduce while they attain the maximum values for lower values of fractional parameters. Another important significance of this study is the use of viscous dissipation term in the mathematical model. It has also been found that viscous dissipation reduces the fluid temperature. Further, comparison graphs for temperature and velocity profiles are provided to validate our model.