### AIMS Mathematics

2021, Issue 6: 5942-5976. doi: 10.3934/math.2021352
Research article Special Issues

# Analysis and modeling of fractional electro-osmotic ramped flow of chemically reactive and heat absorptive/generative Walters'B fluid with ramped heat and mass transfer rates

• Received: 19 January 2021 Accepted: 08 March 2021 Published: 30 March 2021
• MSC : 26A33, 35R11, 76D05

• In this contemporary era, fractional derivatives are widely used for the development of mathematical models to precisely describe the dynamics of real-world physical processes. In the field of fluid mechanics, analysis of thermal performance and flow behavior of non-Newtonian fluids is a topic of interest for a variety of researchers due to their significant applications in several industries, engineering operations, devices, and thermal equipment. The primary focus of this article is to investigate the effectiveness of jointly imposed time-controlled (ramped) boundary conditions in the electro-osmotic flow of a chemically reactive and radiative Walters' B fluid along with concentration and energy distributions. In Particular, the concept of using piece-wise time-dependent mass, motion, and energy conditions simultaneously for any non-Newtonian fluid is extensively explored in this work. The flow is developed due to the motion of the bounding vertical wall, which is suspended in a porous material subject to heat injection/absorption and uniform magnetic influences. Atangana-Baleanu derivative of order $\psi$ is incorporated to establish the fractional form of ordinary modeled equations. Laplace transform method is adapted in light of some unit-less quantities to procure the exact solutions of the under observation model. Several graphical delineations are produced to comprehensively analyze the key characteristics of many physical and thermal parameters. To highlight the significance of operating surface conditions, solutions are compared for time-dependent and constant boundary conditions in every graph. Furthermore, the role of the fractional parameter, time-dependent conditions, and different other involved parameters in heat transfer, mass transfer, and flow rates is characterized by determining the expressions for Nusselt and Sherwood number and coefficient of skin friction. The numerical outcomes are organized in several tables to deeply scrutinize the noteworthy variations in the behavior of the aforementioned physical quantities. The graphical study reveals that the parameter $E_s$ accounting for electro-osmotic effects decelerates the flow of fluid. At the atomic level, such electro-osmotic flows are useful in the separation processes of the liquids. The fractional parameter $\psi$ attenuates thicknesses of boundary layers for the evolution of time $t$ but, it exhibits an opposite role for smaller values of $t$. It is also noted that the direct correspondence between velocity and time at the boundary for time duration $t < 1$ plays a supportive part to effectively control the flow. The exercise tolerance level of cardiac patients is anticipated by following a ramped velocity based protocol. The fractional models are more effective than ordinary models for restricting the boundary shear stress. The occurrence of a chemical reaction leads to improving the mass transfer rate. Additionally, augmentation in heat transfer rate due to the ramped heating technique indicates the significance of this technique in cooling processes. The findings of this work are helpful for clear and comprehensive understanding of electro-osmotic flow of Walters' B fluid in a fractional framework together with chemically reacted mass transfer and thermally radiative heat transfer phenomena subject to wall ramping technique.

Citation: Asifa, Poom Kumam, Talha Anwar, Zahir Shah, Wiboonsak Watthayu. Analysis and modeling of fractional electro-osmotic ramped flow of chemically reactive and heat absorptive/generative Walters'B fluid with ramped heat and mass transfer rates[J]. AIMS Mathematics, 2021, 6(6): 5942-5976. doi: 10.3934/math.2021352

### Related Papers:

• In this contemporary era, fractional derivatives are widely used for the development of mathematical models to precisely describe the dynamics of real-world physical processes. In the field of fluid mechanics, analysis of thermal performance and flow behavior of non-Newtonian fluids is a topic of interest for a variety of researchers due to their significant applications in several industries, engineering operations, devices, and thermal equipment. The primary focus of this article is to investigate the effectiveness of jointly imposed time-controlled (ramped) boundary conditions in the electro-osmotic flow of a chemically reactive and radiative Walters' B fluid along with concentration and energy distributions. In Particular, the concept of using piece-wise time-dependent mass, motion, and energy conditions simultaneously for any non-Newtonian fluid is extensively explored in this work. The flow is developed due to the motion of the bounding vertical wall, which is suspended in a porous material subject to heat injection/absorption and uniform magnetic influences. Atangana-Baleanu derivative of order $\psi$ is incorporated to establish the fractional form of ordinary modeled equations. Laplace transform method is adapted in light of some unit-less quantities to procure the exact solutions of the under observation model. Several graphical delineations are produced to comprehensively analyze the key characteristics of many physical and thermal parameters. To highlight the significance of operating surface conditions, solutions are compared for time-dependent and constant boundary conditions in every graph. Furthermore, the role of the fractional parameter, time-dependent conditions, and different other involved parameters in heat transfer, mass transfer, and flow rates is characterized by determining the expressions for Nusselt and Sherwood number and coefficient of skin friction. The numerical outcomes are organized in several tables to deeply scrutinize the noteworthy variations in the behavior of the aforementioned physical quantities. The graphical study reveals that the parameter $E_s$ accounting for electro-osmotic effects decelerates the flow of fluid. At the atomic level, such electro-osmotic flows are useful in the separation processes of the liquids. The fractional parameter $\psi$ attenuates thicknesses of boundary layers for the evolution of time $t$ but, it exhibits an opposite role for smaller values of $t$. It is also noted that the direct correspondence between velocity and time at the boundary for time duration $t < 1$ plays a supportive part to effectively control the flow. The exercise tolerance level of cardiac patients is anticipated by following a ramped velocity based protocol. The fractional models are more effective than ordinary models for restricting the boundary shear stress. The occurrence of a chemical reaction leads to improving the mass transfer rate. Additionally, augmentation in heat transfer rate due to the ramped heating technique indicates the significance of this technique in cooling processes. The findings of this work are helpful for clear and comprehensive understanding of electro-osmotic flow of Walters' B fluid in a fractional framework together with chemically reacted mass transfer and thermally radiative heat transfer phenomena subject to wall ramping technique.

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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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