Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

doi:10.1016/j.cjche.2020.08.005

中国化学工程学报 ›› 2021, Vol. 29 ›› Issue (3): 17-25.DOI: 10.1016/j.cjche.2020.08.005

• Special Issue on Frontiers of Chemical Engineering Thermodynamics • 上一篇下一篇

Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

M. Ijaz Khan¹, Seifedine Kadry², Yuming Chu^3,4, M. Waqas⁵

1 Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad 38000, Pakistan;
2 Department of Mathematics and Computer Science, Beirut Arab University, Beirut, Lebanon;
3 Department of Mathematics, Huzhou University, Huzhou 313000, China;
4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China;
5 NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad 44000, Pakistan

收稿日期:2020-05-09 修回日期:2020-08-16 出版日期:2021-03-28 发布日期:2021-05-13
通讯作者: Yuming Chu
基金资助:
The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, and 11601485).

Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

M. Ijaz Khan¹, Seifedine Kadry², Yuming Chu^3,4, M. Waqas⁵

1 Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad 38000, Pakistan;
2 Department of Mathematics and Computer Science, Beirut Arab University, Beirut, Lebanon;
3 Department of Mathematics, Huzhou University, Huzhou 313000, China;
4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China;
5 NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad 44000, Pakistan

Received:2020-05-09 Revised:2020-08-16 Online:2021-03-28 Published:2021-05-13
Contact: Yuming Chu
Supported by:
The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, and 11601485).

摘要/Abstract

摘要： The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating disks. Electrical conducting flow is considered and saturated through Darcy–Forchheimer relation. Both the disks are rotating with different angular frequencies and stretches with different rates. Here graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase liquid. Joule heating, heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy expression. Furthermore, binary chemical reaction with activation energy is considered. The total entropy rate is calculated in the presence of heat transfer irreversibility, fluid friction irreversibility, Joule heating irreversibility, porosity irreversibility and chemical reaction irreversibility through thermodynamics second law. The nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting method. Characteristics of sundry flow variables on the entropy generation rate, velocity, concentration, Bejan number, temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid nanoparticles. The engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through tables. It is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion parameter. Also entropy generation rate is more against the higher Brinkman number.

关键词: Darcy–Forchheimer porous medium, Titanium dioxide and graphene oxide nanoparticles, Second order velocity slip, Convective boundary condition, Activation energy, Heat generation/absorption

Abstract: The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating disks. Electrical conducting flow is considered and saturated through Darcy–Forchheimer relation. Both the disks are rotating with different angular frequencies and stretches with different rates. Here graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase liquid. Joule heating, heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy expression. Furthermore, binary chemical reaction with activation energy is considered. The total entropy rate is calculated in the presence of heat transfer irreversibility, fluid friction irreversibility, Joule heating irreversibility, porosity irreversibility and chemical reaction irreversibility through thermodynamics second law. The nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting method. Characteristics of sundry flow variables on the entropy generation rate, velocity, concentration, Bejan number, temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid nanoparticles. The engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through tables. It is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion parameter. Also entropy generation rate is more against the higher Brinkman number.

Key words: Darcy–Forchheimer porous medium, Titanium dioxide and graphene oxide nanoparticles, Second order velocity slip, Convective boundary condition, Activation energy, Heat generation/absorption

M. Ijaz Khan, Seifedine Kadry, Yuming Chu, M. Waqas. Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation[J]. 中国化学工程学报, 2021, 29(3): 17-25.

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Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

Modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

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