Entropy generation optimization and activation energy in flow of Walters-B nanomaterial

Document Type : Article

Authors

1 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

2 - Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan. - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

10.24200/sci.2020.54593.3822

Abstract

In present research, we concentrated on the characterization of Walters-B nanofluid flow to investigate the irreversibility mechanism. Energy equation incorporated with radiation effects and heat generation phenomena. Influence of activation energy is discussed using modified Arrhenius energy term along binary chemical reaction. The consequences of thermophoresis, Brownian motion and viscous dissipation on fluids velocity, temperature of fluid particles and concentration of involved chemical species. Set of ordinary differential equations are obtained by implementing appropriate similarity variables. Governing mathematical model is solved using homotopy analysis method. Flow behavior is analyzed through Nusselt number, coefficient of drag force and mass transfer rate.

Keywords


References:
1.    Choi, S. U. S. ‘‘Enhancing Thermal Conductivity of Fluids With Nanoparticles’’, ASME-Publications-Fed, 231, pp. 99-106 (1995).
2.    Waini, I. Ishak, A. and Pop, I. ‘‘Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface’’, Int. J. Numerical Meth. Heat & Fluid Flow, (2019) 0057
3.    Sheikholeslami, M. ‘‘Numerical approach for MHD Al   O   -water nanofluid transportation inside a permeable medium using innovative computer method’’, Comp. Meth. Appl. Mech. Eng. 344, pp. 306-318 (2019)
4.    Aly E. H., ‘‘Dual exact solutions of graphene--water nanofluid flow over stretching/shrinking sheet with suction/injection and heat source/sink: Critical values and regions with stability’’, Powder Tech. 342 pp. 528-544 (2019)
5.    Rafiq, T. Mustafa, M. and Khan J. A., ‘‘Numerical study of Bödewadt slip flow on a convectively heated porous disk in a nanofluid’’, Phys. Scr. (2019) ab1549.
6.    Hsiao, K. L. ‘‘Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature’’, Int. J. Heat and Mass Transf., 112, pp. 983—990 (2017).
7.    Turkyilmazoglu, M.  ‘‘MHD natural convection in saturated porous media with heat generation/absorption and thermal radiation: closed-form solutions’’, Archi. Mech., 71, pp. 49-64 (2019).
8.    Ramzan, M. Bilal, M. and Chung, J. D. ‘‘Effects of thermal and solutal stratification on jeffrey magneto-nanofluid along an inclined stretching cylinder with thermal radiation and heat generation/absorption’’, Int. J. Mech. Sci., 132, pp. 317-324 (2017).
9.    Hsiao, K. L. ‘‘To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-nanofluid with parameters control method’’, Energy, 130 (2017) 486-499
10.    Mustafa, M. Khan, J. A. Hayat, T. et al. ‘‘Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy’’, Int. J. Heat and Mass Transf. 108, pp. 1340-1346 (2017).
11.    Hsiao, K. L. ‘‘Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet’’, Appl. Therm. Eng., 98, pp. 850--861(2016).
12.    Bejan, A. “A study of entropy generation in fundamental convective heat transfer”, ASME J. Heat Transfer, 101 (4), pp. 718-725 (1979).
13.    Bejan, A. Kestin, J. “Entropy generation through heat and fluid flow”, J. Appl. Mech., 50 (1983).
14.    Liu, Y. Jian, Y. and Tan, W. “Entropy generation of electromagnetohydrodynamic (EMHD) flow in a curved rectangular microchannel”, Int. J. Heat Mass Transf., 127, pp. 901-913 (2018).
15.    Qayyum. S. Khan, M. I. Hayat, T. et al., “Entropy generation in dissipative flow of Williamson fluid between two rotating disks”, Int. J. Heat Mass and Transf., 127,pp. 933-942 (2018).
16.    Akbarzadeh, M. Rashidi, S. Karimi, N. “Convection of heat and thermodynamic irreversibilities in two-phase, turbulent nanofluid flows in solar heaters by corrugated absorber plates”, Adv. Powder Techn., 29, pp. 2243-2254 (2018).
17.    Bizhaem, H. K. Abbassi, A. “Numerical study on heat transfer and entropy generation of developing laminar nanofluid flow in helical tube using two-phase mixture model”, Adv. Powder Techn., 28 (9) pp. 2110-2125 (2017).
18.    Pal, S. K. Bhattacharyya, S. and Pop, I. “Effect of solid-to-fluid conductivity ratio on mixed convection and entropy generation of a nanofluid in a lid-driven enclosure with a thick wavy wall”, Int. J. Heat and Mass Transf., 127, pp. 885-900 (2018).
19.    Sheikholeslami, M. Ganji, D.D. “Entropy generation of nanofluid in presence of magnetic field using lattice Boltzmann method”, Physica A, 417, pp. 273-286 (2015).
20.    Wang, Y. Chen, Z. and Ling, X., “Entropy generation analysis of particle suspension induced by Couette flow,” Int. J. Heat Mass Transf., 90 pp. 499-504 (2015).
21.    Hayat, T. Khan, M. I. Qayyum, S. et al., “Entropy generation for flow of Sisko fluid due to rotating disk”, J. Mol. Liq., 264, pp. 375-385 (2018).
22.    Liao, S. J. “Homotopy analysis method in non-linear differential equations” (Springer and Higher Education Press, Heidelberg, 2012).
23.    Noeiaghdam, S. Zarei, E. and Kelishami, H. B. “Homotopy analysis transform method for solving Abel's integral equations of the first kind”, Ain Shams Eng. J. 7. pp. 483-495 (2016).
24.    Hayat, T. Mustafa, M. and Asghar, S. “Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction”, Nonlinear Analysis: Real World Appl. 11 (4), pp. 3186-3197 (2010).
25.    Rahman, S. Hayat, T. Muneer, M. et al. “Global existence of solutions for MHD third grade flow equations saturating porous medium”, Comput. Math. Appl., 76, pp. 2360-2374 (2018).
26.    Jabeen, S. Hayat, T. Alsaedi, A. et al. “Consequences of activation energy and chemical reaction in radiative flow  of tangent hyperbolic nanoliquid”, Scientia Iranica, (2019) DOI: 10.24200/SCI.2019.52726.2860.
27.    Imtiaz, M. Kiran, A. Hayat, T. et al. “Axisymmetric flow by a rotating disk with Cattaneo--Christov heat flux”, J. Braz. Soc. Mec. Sci. Eng., 41, pp. 149 (2019).
28.    Hayat, T. Ahmad, S. Khan, M. I et al. “Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source”, Physica B: Cond. Matt., 537, pp. 116-126 (2018).
29.    Abbasbandy, S. Mustafa, M. “Analytical and numerical approaches for Falkner--Skan flow of MHD Maxwell fluid using a non-Fourier heat flux model”, Int. J. Num. Meth. Heat & Fluid Flow, 28, pp.1539-1555 (2018).
30.    Turkyilmazoglu, M. “Convergence accelerating in the homotopy analysis method: a new approach”, Adv. Appl. Math. Mech., 10, pp. 1-24 (2018).
31.    Hayat, T. Qayyum, S. Khan, M. I. et al. “Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating”, Phys. Fluids, 30 (2018) 017101.
32.    Qayyum, S. Hayat, T. Jabeen, S. “Entropy generation in nanofluid flow of Walters-B fluid with homogeneous-heterogeneous reactions”, Math. Meth. Appl. Sci. pp. 1—16 (2020).
33.    Hsiao, K. L. “Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects”, Appl. Therm. Eng., 112, pp. 1281-1288 (2017).
34.    Turkyilmazoglu, M. “Multiple analytic solutions of heat and mass transfer of magnetohydrodynamic slip flow for two types of viscoelastic fluids Over a stretching surface”, J. Heat Transfer, 134(7), pp. 071701 (2012)
35.    Turkyilmazoglu, M. “An effective approach for approximate analytical solutions of the damped Duffing equation”, Phy. Scrip. 86(1), pp. 015301 (2012).