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Entropy optimization in cubic autocatalysis chemical reactive flow of Williamson fluid subjected to viscous dissipation and uniform magnetic field

Williamson 流体在黏性耗散和均匀磁场作用下四次自催化化学反应的熵优化

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Abstract

This research elaborates magnetohydrodynamics (MHD) impact on non-Newtonian (Williamson) fluid flow by stretchable rotating disks. Both disks are rotating with different angular velocities and different stretching rates. Viscous dissipation aspect is considered for energy expression formulation. Entropy generation analysis is described via implementation of thermodynamic second law. Chemical processes (heterogeneous and homogeneous) subjected to entropy generation are introduced first time in literature. Boundary-layer approach is employed for modeling. Apposite variables are introduced for non-dimensionalization of governing systems. Homotopy procedure yields convergence of solutions subjected to computations of highly nonlinear expressions. The significant characteristics of sundry factors against thermal, velocity and solutal fields are described graphically. Besides, tabular results are addressed for engineering quantities (skin-friction coefficient, Nusselt number). The outcomes certify an increment in temperature distribution for Weissenberg (We) and Eckert (Ec) numbers.

摘要

阐述了可伸缩的旋转盘对非牛顿磁流体动力学 (MHD) 的影响。两个圆盘以不同的角速度和不同 的伸缩率旋转。在能量表达式中考虑黏性耗散, 利用热力学第二定律分析熵的生成, 文中首次介绍了 熵产生的化学过程(多相和均相)。采用边界层方法建立模型, 引入变量对控制系统进行无量纲化。通 过高度非线性表达式的计算, 得到同伦过程解的收敛性。用图解法描述了各种因素对热场、速度场和 溶质场的影响特征。此外, 以表格形式给出了工程质量包括表面摩擦系数、 Nusselt 数的计算结果。结 果证实了因 Weissenberg(We) (韦斯森伯格)和 Eckert(Ec) (埃克特)数而导致的温度梯度分布的增加。

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References

  1. BEJAN A. A study of entropy generation in fundamental convective heat transfer [J]. Journal of Heat Transfer, 1979, 101: 718–725. DOI: https://doi.org/10.1115/1.3451063.

    Article  Google Scholar 

  2. SAHIN A Z. Second law analysis of laminar viscous flow through a duct subjected to constant wall temperature [J]. Journal of Heat Transfer, 1998, 120: 76–83. DOI: https://doi.org/10.1115/1.2830068.

    Article  Google Scholar 

  3. EEGUNJOBI A S, MAKINDE O D. Entropy generation analysis in transient variable viscosity Couette flow between two concentric pipes [J]. Journal of Thermal Science and Technology, 2014, 9: 1–10. DOI: https://doi.org/10.1299/jtst.2014jtst0008.

    Article  Google Scholar 

  4. RASHIDI M M, KAVYANI N, ABELMAN S. Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties [J]. International Journal of Heat and Mass Transfer, 2014, 70: 892–917. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2013.11.058.

    Article  Google Scholar 

  5. FAROOQ S, HAYAT T, ALSAEDI A, ASGHAR S. Mixed convection peristalsis of carbon nanotubes with thermal radiation and entropy generation [J]. Journal of Molecular Liquids, 2018, 250: 451–467. DOI: https://doi.org/10.1016/j.molliq.2017.11.179.

    Article  Google Scholar 

  6. WAQAS M, FAROOQ M, KHAN M I, ALSAEDI A, HAYAT T, YASMEEN T. Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition [J]. International Journal of Heat and Mass Transfer, 2016, 102: 766–772. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.142.

    Article  Google Scholar 

  7. KHAN M I, KHAN M I, WAQAS M, HAYAT T, ALSAEDI A. Chemically reactive flow of Maxwell liquid due to variable thicked surface [J]. International Communication of Heat and Mass Transfer, 2017, 86: 231–238. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2017.06.003.

    Article  Google Scholar 

  8. HAYAT T, KHAN M I, WAQAS M, ALSAEDI A. On the performance of heat absorption/generation and thermal stratification in mixed convective flow of an Oldroyd-B fluid [J]. Nuclear Engineering and Technology, 2017, 49: 1645–1653. DOI: https://doi.org/10.1016/j.net.2017.07.027.

    Article  Google Scholar 

  9. KHAN M, IRFAN M, KHAN W A, AHMAD L. Modeling and simulation for 3D magneto Eyring-Powell nanomaterial subject to nonlinear thermal radiation and convective heating [J]. Results in Physics, 2017, 7: 1899–1906. DOI: https://doi.org/10.1016/j.rinp.2017.06.002.

    Article  Google Scholar 

  10. WAQAS M, HAYAT T, KHAN M I, ALSAEDI A. Numerical simulation for magneto Carreau nanofluid model with thermal radiation: A revised model [J]. Computer Methods in Applied Mechanics and Engineering, 2017, 324: 640–653. DOI: https://doi.org/10.1016/j.cma.2017.06.012.

    Article  MathSciNet  Google Scholar 

  11. WILLIAMSONRV. The flow of pseudoplastic materials [J]. Industrial and Engineering Chemistry, 1929, 21: 1108–1111. DOI: https://doi.org/10.1021/ie50239a035.

    Article  Google Scholar 

  12. HAYAT T, BASHIR G, WAQAS M, ALSAEDI A. MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer [J]. Journal of Molecular Liquids, 2016, 223: 836–844. DOI: https://doi.org/10.1016/j.molliq.2016.08.104.

    Article  Google Scholar 

  13. KHAN M, HAMID A. Influence of non-linear thermal radiation on 2D unsteady flow of a Williamson fluid with heat source/sink [J]. Results in Physics, 2017, 7: 3968–3975. DOI: https://doi.org/10.1016/j.rinp.2017.10.014.

    Article  Google Scholar 

  14. WAQAS M, KHAN M I, HAYAT T, ALSAEDI A, KHAN M I. Nonlinear thermal radiation in flow induced by a slendering surface accounting thermophoresis and Brownian diffusion [J]. The European Physical Journal Plus, 2017, 132: 280. DOI: https://doi.org/10.1140/epjp/i2017-11555-0.

    Article  Google Scholar 

  15. HAYAT T, KIYANI M Z, ALSAEDI A, KHAN M I, AHMAD I. Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction [J]. International Journal of Heat and Mass Transfer, 2018, 127: 422–429. DOI: https://doi.org/10.1016/j.molliq.2017.11.179.

    Article  Google Scholar 

  16. HAYAT T, AKRAM J, ALSAEDI A, ZAHIR H. Endoscopy and homogeneous-heterogeneous reactions in MHD radiative peristaltic activity of Ree-Eyring fluid [J]. Results in Physics, 2018, 8: 481–488. DOI: https://doi.org/10.1016/j.rinp.2017.12.056.

    Article  Google Scholar 

  17. KHAN M I, WAQAS M, HAYAT T, ALSAEDI A. A comparative study of Casson fluid with homogeneous-heterogeneous reactions [J]. Journal of Colloid and Interface Science, 2017, 498: 85–90. DOI: https://doi.org/10.1016/j.jcis.2017.03.024.

    Article  Google Scholar 

  18. KHAN M I, WAQAS M, HAYAT T, KHAN M I, ALSAEDI A. Numerical simulation of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface [J]. Journal of Molecular Liquids, 2017, 246: 259–267. DOI: https://doi.org/10.1016/j.molliq.2017.09.075.

    Article  Google Scholar 

  19. SADIQ M A, WAQAS M, HAYAT T. Importance of Darcy-Forchheimer relation in chemically reactive radiating flow towards convectively heated surface [J]. Journal of Molecular Liquids, 2017, 248: 1071–1077. DOI: https://doi.org/10.1016/j.molliq.2017.10.063.

    Article  Google Scholar 

  20. IRFAN M, KHAN M, KHAN W A. Interaction between chemical species and generalized Fourier's law on 3D flow of Carreau fluid with variable thermal conductivity and heat sink/source: A numerical approach [J]. Results in Physics, 2018, 10: 107–117. DOI: https://doi.org/10.1016/j.rinp.2018.04.036.

    Article  Google Scholar 

  21. LIAO S J. Homotopy analysis method in non-linear differential equations [M]. Heidelberg: Springer and Higher Education Press, 2012. DOI: https://doi.org/10.1007/978-3-642-25132-0.

    Book  Google Scholar 

  22. HAYAT T, KHAN M I, FAROOQ M, ALSAEDI A, WAQAS M, YASMEEN T. Impact of Cattaneo-Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface [J]. International Journal of Heat and Mass Transfer, 2016, 99: 702–710. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.016.

    Article  Google Scholar 

  23. HAYAT T, KHAN M I, FAROOQ M, YASMEEN T, ALSAEDI A. Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions [J]. Journal of Molecular Liquids, 2016, 220: 49–55. DOI: https://doi.org/10.1016/j.molliq.2016.04.032.

    Article  Google Scholar 

  24. QAYYUM S, KHAN M I, HAYAT T, ALSAEDI A, TAMOOR M. Entropy generation in dissipative flow of Williamson fluid between two rotating disks [J]. International Journal of Heat and Mass Transfer, 2018, 127: 933–942. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.034.

    Article  Google Scholar 

  25. WAQAS M, HAYAT T, ALSAEDI A. A theoretical analysis of SWCNT-MWCNT and H2O nanofluids considering Darcy-Forchheimer relation [J]. Applied Nanoscience, (2018) DOI: https://doi.org/10.1007/sl3204-018-0833-6.

  26. KHAN M I, HAYAT T, KHAN M I, ALSAEDI A. A modified homogeneous-heterogeneous reactions for MHD stagnation flow with viscous dissipation and Joule heating [J]. International Journal of Heat and Mass Transfer, 2017, 113: 310–317. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.082.

    Article  Google Scholar 

  27. HAYAT T, KHAN M I, QAYYUM S, ALSAEDI A. Entropy generation in flow with silver and copper nanoparticles [J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2018, 539: 335–346. DOI: https://doi.org/10.1016/j.colsurfa.2017.12.021.

    Article  Google Scholar 

  28. ELLAHI R, HASSAN M, ZEESHAN A, KHAN A A. The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection [J]. Applied Nanoscience, 2018, 6: 641–651. DOI: https://doi.org/10.1007/s13204-015-0481-z.

    Article  Google Scholar 

  29. KHAN M I, ULLAH S, HAYAT T, WAQAS M, KHAN M I, ALSAEDI A. Salient aspects of entropy generation optimization in mixed convection nanomaterial flow [J]. International Journal of Heat and Mass Transfer, 2018, 126: 1337–1346. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.168.

    Article  Google Scholar 

  30. MAMOURIAN M, SHIRVAN K M, ELLAHI R, RAHIMIA B. Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach [J]. International Journal of Heat and Mass Transfer, 2016, 102: 544–554. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.056.

    Article  Google Scholar 

  31. AHMAD S, KHAN M I, HAYAT T, KHAN M I. ALSAEDI A. Entropy generation optimization and unsteady squeezing flow of viscous fluid with five different shapes of nanoparticles [J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2018, 554: 197–210. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.056.

    Article  Google Scholar 

  32. ESFAHANI J A, AKBARZADEH M, RASHIDI S, ROSEN M A, ELLAHI R. Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat [J]. International Journal of Heat and Mass Transfer, 2017, 109: 1162–1171. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.006.

    Article  Google Scholar 

  33. KHAN M I, HAYAT T, ALSAEDI A, S, TAMOOR M. Entropy optimization and quartic autocatalysis in MHD chemically reactive stagnation point flow of Sisko nanomaterial [J]. International Journal of Heat and Mass Transfer, 2018, 127: 829–837. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.037.

    Article  Google Scholar 

  34. RASHIDI S, AKAR S, BOVAND S, ELLAHI R. Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still [J]. Renewable Energy, 2018, 115: 400–410. DOI: https://doi.org/10.1016/j.renene.2017.08.059.

    Article  Google Scholar 

  35. KHAN M I, WAQAS M, HAYAT T, ALSAEDI A. Magneto-hydrodynamical numerical simulation of heat transfer in MHD stagnation point flow of Cross fluid model towards a stretched surface [J]. Physics and Chemistry of Liquids, 2018, 56: 584–595. DOI: https://doi.org/10.1080/00319104.2017.1367791.

    Article  Google Scholar 

  36. HSIAO K L. To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method [J]. Energy, 2017, 130: 486–499. DOI: https://doi.org/10.1016/j.energy.2017.05.004.

    Article  Google Scholar 

  37. HAYAT T, KHAN M W A, KHAN M I, WAQAS M, ALSAEDI A. Impact of chemical reaction in fully developed radiated mixed convective flow between two rotating disk [J]. Physica B: Condensed Matter, 2018, 538: 138–149. DOI: https://doi.org/10.1016/j.physb.2018.01.068.

    Article  Google Scholar 

  38. HSIAO K L. Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects [J]. Applied Thermal Engineering, 2017, 2017: 1281–1288. DOI: https://doi.org/10.1016/j.applthermaleng.2016.08.208.

    Article  Google Scholar 

  39. HAYAT T, SHAH F, KHAN M I, KHAN M I, ALSAEDI A. Entropy analysis for comparative study of effective Prandtl number and without effective Prandtl number via ψAl2O3-H2O and ψAl2O3-C2H6O2 nanoparticles [J]. Journal of Molecular Liquids, 2018, 266: 814–823. DOI: https://doi.org/10.1016/j.molliq.2018.06.029.

    Article  Google Scholar 

  40. HSIAO K L. Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature [J]. International Journal of Heat and Mass Transfer, 2017, 112: 983–990. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.042.

    Article  Google Scholar 

  41. HAYAT T, SHAH F, KHAN M I, ALSAEDI A. Framing the performance of heat absorption/generation and thermal radiation in chemically reactive Darcy-Forchheimer flow [J]. Results in Physics, 2017, 7: 3390–3395. DOI: https://doi.org/10.1016/j.rinp.2017.08.052.

    Article  Google Scholar 

  42. HSIAO K L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet [J], Applied Thermal Engineering, 2016, 98: 850–861. DOI: https://doi.org/10.1016/j.applthermaleng.2015.12.138.

    Article  Google Scholar 

  43. JAVED M, FAROOQ M, AHMAD S, ANJUM A. Melting heat transfer with radiative effects and homogeneous-heterogeneous reaction in thermally stratified stagnation flow embedded in porous medium [J]. Journal of Central South University, 2018, 25: 2701–2711. DOI: https://doi.org/10.1007/sll771-018-3947-9.

    Article  Google Scholar 

  44. KHAN M I, WAQAS M, HAYAT T, ALSAEDI A. Chemically reactive flow of micropolar fluid accounting viscous dissipation and Joule heating [J]. Results in Physics, 2017, 7: 3706–3715. DOI: https://doi.org/10.1016/j.rinp.2017.09.016.

    Article  Google Scholar 

  45. ZHAO C H, WANG X P, YAO X F, TIAN M H. A background refinement method based on local density for hyperspectral anomaly detection [J]. Journal of Central South University, 2018, 25: 84–94. DOI: https://doi.org/10.1007/sl1771-018-3719-6.

    Article  Google Scholar 

  46. ALSAEDI A, KHAN M I, HAYAT T. Recent progresses about statistical declaration and probable error for surface drag force of chemically reactive squeezing flow with temperature dependent thermal conductivity [J]. Journal of Theoretical and Computational Chemistry, 2017, 16: 1750064. DOI: https://doi.org/10.1142/S021963361750064X.

    Article  Google Scholar 

  47. HAYAT T, IMTIAZ M, ALSAEDI A. Effects of homogeneous-heterogeneous reactions in flow of Powell-Eyring fluid [J]. Journal of Central South University, 2015, 22: 3211–3216. DOI: https://doi.org/10.1007/s11771-015-2858-2.

    Article  Google Scholar 

  48. KHAN M I, WAQAS M, HAYAT T, ALSAEDI A. Soret and Dufour effects in stretching flow of Jeffrey fluid subject to Newtonian heat and mass conditions [J]. Results in Physics, 2017, 7: 4183–4188. DOI: https://doi.org/10.10l6/j.rinp.2017.10.011.

    Article  Google Scholar 

  49. HUSSAIN T, SHEHZAD S A, ALSAEDI A, HAYAT T, RAMZAN M. Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model [J]. Journal Central South University, 2015, 22: 1132–1140. DOI: https://doi.org/10.1007/s11771-015-2625-4.

    Article  Google Scholar 

  50. HAYAT T, KHAN M I, WAQAS M, ALSAEDI A. Magnetohydrodynamic stagnation point flow of third-grade liquid toward variable sheet thickness [J]. Neural Computing Applications, 2018, 30: 2417–2423. DOI: https://doi.org/10.1007/s00521-016-2827-1.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    M. Ijaz Khan, Sania Javed & M. Waqas

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

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  1. M. Ijaz Khan
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Ijaz Khan, M., Javed, S., Hayat, T. et al. Entropy optimization in cubic autocatalysis chemical reactive flow of Williamson fluid subjected to viscous dissipation and uniform magnetic field. J. Cent. South Univ. 26, 1218–1232 (2019). https://doi.org/10.1007/s11771-019-4082-y

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