An entropy approach of Williamson nanofluid flow with Joule heating and zero nanoparticle mass flux
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An entropy approach of Williamson nanofluid flow with Joule heating and zero nanoparticle mass flux K. Loganathan1,2 · S. Rajan1 Received: 12 December 2019 / Accepted: 4 February 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The important focus of this research is to investigate the features of MHD radiative Williamson nanofluid flow caused by a stretchable surface entrenched in a porous medium with Joule heating, convective heating and passive controls of nanoparticles. The heat flux is modelled based on the Christov–Cattaneo heat flux theory. Nanofluid contains thermophoresis and Brownian motion effects. Additionally, the entropy generation of Williamson nanofluid is calculated via the second law of thermodynamics. The governing partial differential equations are modified into nonlinear ordinary differential systems by applying appropriate similarity transformations. Homotopy progress is used to solve the nonlinear ordinary differential systems. Outcomes of magnetic field, Weissenberg number, radiation, Eckert number, Brownian motion, Bejan number and entropy generation of different parameters are discussed in detail. Moreover, skin friction, heat and mass transfer rates are evaluated. The comparison of skin friction and Nusselt number is validated, and the results have been reported. Keywords Williamson nanofluid · Christov–Cattaneo heat flux · Porous medium · Zero nanoparticle mass flux · Entropy generation · Homotopy analysis scheme List of symbols â Stretching rate (s−1) Bi Biot number Be Bejan number Br Brinkman number B0 Constant magnetic field (kgs=2 A−1) C Concentration (kgm−3) Cr Chemical reaction parameter cp Specific heat (J kg−1 K−1) C∞ Ambient concentration (kgm−3) Cw Fluid wall concentration (kgm−3) Cf Skin friction coefficient DB Brownian diffusion coefficient (m2 s−1) DT Thermophoretic diffusion coefficient (m2 s−1) EG Entropy generation parameter Ec Eckert number f (𝜂) Velocity similarity function * K. Loganathan [email protected] 1
Department of Mathematics, Erode Arts and Science College, Erode, Tamilnadu 638009, India
Department Mathematics, Faculty of Engineering, Karpagam Academy of Higher Education, Coimbatore, Tamilnadu 641021, India
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fw Suction/injection parameter hf Convective heat transfer coefficient (W m−1 K−1) k Thermal conductivity (W m−1 K−1) KP Porous parameter L Auxiliary linear operator Le Lewis number M Hartmann number N Nonlinear operator Nb Brownian motion parameter Nt Thermophoresis parameter Nu Nusselt number Pr Prandtl number Q0 Dimensional heat generation/absorption coefficient q̂ Heat flux (W m−2) Rd Radiation parameter Re Reynolds number Sh Sherwood number S Heat generation parameter T Temperature (K) T∞ Ambient temperature (K) Tf Convective surface temperature (K) û w Velocity of the sheet (m s−1) û , v̂ Velocity components in (̂x, ŷ ) directions (m s−1) v̂ w > 0 Suction velocity v̂ w < 0 Injection velocity
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We Weissenberg number x̂ , ŷ Cartesian c
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