The main theme of the current work is to investigate the flow and heat transport characteristics of non-Newtonian Williamson fluid in an inclined micro-channel along with entropy generation analysis. The significance of the thermal radiation, convective boundary condition, and multiple slip effects is explored. The entropy generation of the system has been analyzed by adopting the 2nd law of thermodynamics. The rheological expressions of the Williamson fluid model are also taken into account. The nonlinear system is tackled by using the finite element method. An appropriate comparison has been made with previously published results in the literature as a limiting case of the considered problem. The comparison confirmed an excellent agreement. Detailed discussion of the significance of effective parameters on Bejan number, entropy generation rate, temperature and velocity is presented through graphs. The numerical results portray that the entropy generation and Bejan number have escalating behavior to the higher value of angle of inclination. Furthermore, the Bejan number changing its behavior at two points for different values of Reynolds’ number.
WilliamsonRV. The flow of pseudoplastic materials. Industrial & Engineering Chemistry1929; 21: 1108–1111.
2.
NadeemSHussainSTLeeC. Flow of a Williamson fluid over a stretching sheet. Brazilian journal of chemical engineering2013; 30: 619–625.
3.
HayatTKiyaniMZAlsaediA,et al.Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction. Int J Heat Mass Transfer2018; 127: 422–429.
4.
RazaJMebarek-OudinaFMahantheshB. Magnetohydrodynamic flow of nano Williamson fluid generated by stretching plate with multiple slips. Multidiscipline Modeling in Materials and Structures2019; 4: 871–894.
5.
RajuCSSandeepNAliME,et al.Heat and mass transfer in 3-d mhd Williamson-Casson fluids flow over a stretching surface with non-uniform heat source/sink. Thermal Science2019; 23: 281–293.
6.
HumanePPPatilVSPatilAB. Chemical reaction and thermal radiation effects on magnetohydrodynamics flow of Casson–Williamson nanofluid over a porous stretching surface. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering2021; 09544089211025376.
7.
BejanA. Entropy generation minimization: the new thermodynamics of finite size devices and finite time processes. J Appl Phys1996; 79: 1191–1218.
8.
SrinivasacharyaDBinduKH. Entropy generation in a micropolar fluid flow through an inclined channel with slip and convective boundary conditions. Energy2015; 91: 72–83.
9.
SrinivasacharyaDBinduKH. Entropy generation in a micropolar fluid flow through an inclined channel. Alexandria Eng J2016; 55: 973–982.
10.
GireeshaBJSrinivasaCTShashikumarNS,et al.Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering2019; 233: 1173–1184. 0954408919849987.
11.
MadhuMShashikumarNSMahantheshB,et al.Heat transfer and entropy generation analysis of non-Newtonian flu flow through vertical microchannel with convective boundary condition. Applied Mathematics and Mechanics2019; 40: 1285–1300.
12.
ShashikumarNSGireeshaBJMahantheshB,et al.Entropy generation analysis of magneto-nanoliquids embedded with aluminium and titanium alloy nanoparticles in microchannel with partial slips and convective conditions. International Journal of Numerical Methods for Heat & Fluid Flow2018; 29: 3638–3658.
13.
RashadAMArmaghaniTChamkhaAJ,et al.Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: effects of a heat sink and source size and location. Chinese journal of physics2018; 56: 193–211.
14.
ShashikumarNSPrasannakumaraBCArchanaM,et al.Thermodynamics analysis of a Casson nanofluid flow through a porous microchannel in the presence of hydrodynamic slip: a model of solar radiation. Journal of Nanofluids2019; 8: 63–72.
15.
ZeeshanAHassanMEllahiR,et al.Shape effect of nanosize particles in unsteady mixed convection flow of nanofluid over disk with entropy generation. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering2017; 231: 871–879.
16.
BashaHTSivarajR. Entropy generation of peristaltic Eyring–Powell nanofluid flow in a vertical divergent channel for biomedical applications. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering2021; 235: 1575–1586.
17.
TuckermanDBPeaseRFW. High-performance heat sinking for VLSI. IEEE Electron Device Lett1981; 2: 126–129.
18.
SwiftGMiglioriAWheatleyJ. Construction of and measurements with an extremely compact cross-flow heat exchanger. Heat Transfer Eng1985; 6: 39–47.
19.
IbáñezGLópezAPantojaJ,et al.Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation. Int J Heat Mass Transfer2016; 100: 89–97.
20.
MadhuMShashikumarNSGireeshaBJ,et al.Second law analysis of Powell–Eyring fluid flow through an inclined microchannel with thermal radiation. Phys Scr2019; 94: 125205.
21.
MakindeODEegunjobiAS. Entropy analysis of thermally radiating magnetohydrodynamic slip flow of Casson fluid in a microchannel filled with saturated porous media. J Porous MEdia2016; 19: 799–810.
22.
ShashikumarNSGireeshaBJMahantheshB,et al.Brinkman-Forchheimer flow of SWCNT and MWCNT magneto-nanoliquids in a microchannel with multiple slips and Joule heating aspects. Multidiscipline Modeling in Materials and Structures2018; 14: 769–786.
23.
KhanZHMakindeODAhmadR,et al.Numerical study of unsteady MHD flow and entropy generation in a rotating permeable channel with slip and Hall effects. Commun Theor Phys2018; 70: 641.
24.
ShamsabadiHRashidiSEsfahaniJA. Entropy generation analysis for nanofluid flow inside a duct equipped with porous baffles. J Therm Anal Calorim2019; 135: 1009–1019.
25.
MaXSheikholeslamiMJafaryarM,et al.Solidification inside a clean energy storage unit utilizing phase change material with copper oxide nanoparticles. J Cleaner Prod2020; 245: 118888.
MadhuMMahantheshBShashikumarNS,et al.Performance of second law in Carreau fluid flow by an inclined microchannel with radiative heated convective condition. International Communications in Heat and Mass Transfer2020; 117: 104761.
28.
AgrawalPDadheechPKJatRN,et al.Lie similarity analysis of MHD flow past a stretching surface embedded in porous medium along with imposed heat source/sink and variable viscosity. Journal of Materials Research and Technology2020; 9: 10045–10053.
29.
MahantaGShawS. 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition. Alexandria Eng J2015; 54: 653–659.
30.
HayatTWaqasMShehzadSA,et al.Stretched flow of Carreau nanofluid with convective boundary condition. Pramana2016; 86: 3–17.
31.
HussainZMuhammadT. Simultaneous influence of Hall and wall characteristics in peristaltic convective carbon–water flow subject to Soret and Dufour effects. Arabian Journal for Science and Engineering2021; 46: 2033–2046.
32.
MuhammadTAlsaediAShehzadSA,et al.A revised model for Darcy-Forchheimer flow of Maxwell nanofluid subject to convective boundary condition. Chinese Journal of Physics2017; 55: 963–976.
33.
ShehzadSAMadhuMShashikumarNS,et al.Thermal and entropy generation of non-Newtonian magneto-Carreau fluid flow in microchannel. J Therm Anal Calorim2021; 143: 2717–2727.
34.
EegunjobiASMakindeOD. Combined effect of buoyancy force and Navier slip on entropy generation in a vertical porous channel. Entropy2012; 14: 1028–1044.
35.
NavierCLM. Sur les lois du mouvement des fluides. Mem Acad Royale des Sci1827; 6: 389–440.
36.
EegunjobiASMakindeOD. Effects of Navier slip on entropy generation in a porous channel with suction/injection. Journal of Thermal Science and Technology2012; 7: 522–535.
37.
DasSJanaRN. Entropy generation due to MHD flow in a porous channel with Navier slip. Ain Shams Engineering Journal2014; 5: 575–584.
38.
PrasannakumaraBCShashikumarNSVenkateshP. Boundary layer flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet embedded in a porous medium. Nonlinear Engineering2017; 6: 179–190.
39.
HayatTMuhammadTShehzadSA,et al.On magnetohydrodynamic flow of nanofluid due to a rotating disk with slip effect: a numerical study. Comput Methods Appl Mech Eng2017; 315: 467–477.
40.
MuhammadTAlamriSZWaqasH,et al.Bioconvection flow of magnetized Carreau nanofluid under the influence of slip over a wedge with motile microorganisms. J Therm Anal Calorim2021; 143: 945–957.
41.
MuhammadTWaqasHKhanSA,et al.Significance of nonlinear thermal radiation in 3D Eyring–Powell nanofluid flow with Arrhenius activation energy. J Therm Anal Calorim2021; 143: 929–944.
42.
MakindeODEegunjobiAS. Effects of convective heating on entropy generation rate in a channel with permeable walls. Entropy2013; 15: 220–233.
