Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy–Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface

The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

[1]  Hao Peng,et al.  Lattice Boltzmann method for thermomagnetic convection and entropy generation of paramagnetic fluid in porous enclosure under magnetic quadrupole field , 2018, International Journal of Heat and Mass Transfer.

[2]  Esmail Lakzian,et al.  Investigating the entropy generation in condensing steam flow in turbine blades with volumetric heating , 2018 .

[3]  I. Tlili,et al.  Entropy Generation Due to MHD Stagnation Point Flow of a Nanofluid on a Stretching Surface in the Presence of Radiation , 2018, Journal of Nanofluids.

[4]  Ting Zhang,et al.  Marangoni Effect in Second Grade Forced Convective Flow of Water Based Nanofluid , 2019, Journal of Advances in Nanotechnology.

[5]  Iskander Tlili,et al.  MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect , 2019, Symmetry.

[6]  Ting Zhang,et al.  Influence of Chemical Reaction on Marangoni Convective Flow of Nanoliquid in the Presence of Lorentz Forces and Thermal Radiation: A Numerical Investigation , 2019, Journal of Advances in Nanotechnology.

[7]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[8]  Ilyas Khan,et al.  Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface , 2019, Journal of Central South University.

[9]  Ebrahim Afshari,et al.  Simulation and prediction of MHD dissipative nanofluid flow on a permeable stretching surface using artificial neural network , 2016 .

[10]  Ilyas Khan,et al.  Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis , 2019, Heat Transfer-Asian Research.

[11]  Ioan Pop,et al.  Flow and heat transfer of magnetohydrodynamic three-dimensional Maxwell nanofluid over a permeable stretching/shrinking surface with convective boundary conditions , 2017 .

[12]  Min Zhang,et al.  Stagnation-point heat and mass transfer of MHD Maxwell nanofluids over a stretching surface in the presence of thermophoresis , 2016 .

[13]  Sumaira Qayyum,et al.  Entropy optimization in flow of Williamson nanofluid in the presence of chemical reaction and Joule heating , 2019, International Journal of Heat and Mass Transfer.

[14]  I. Tlili,et al.  On the MHD Casson Axisymmetric Marangoni Forced Convective Flow of Nanofluids , 2019, Mathematics.

[15]  B. Ben-Beya,et al.  Numerical simulation of entropy generation due to unsteady natural convection in a semi-annular enclosure filled with nanofluid , 2018, International Journal of Heat and Mass Transfer.

[16]  G. Ibáñez,et al.  Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions , 2017 .

[17]  A. Alsaedi,et al.  Entropy generation in dissipative flow of Williamson fluid between two rotating disks , 2018, International Journal of Heat and Mass Transfer.

[18]  Ali J. Chamkha,et al.  A numerical investigation of magneto-hydrodynamic natural convection of Cu–water nanofluid in a wavy cavity using CVFEM , 2019, Journal of Thermal Analysis and Calorimetry.

[19]  Ming Liu,et al.  Entropy generation analysis on a heat exchanger with different design and operation factors during transient processes , 2018, Energy.

[20]  Stephen U. S. Choi.  Enhancing thermal conductivity of fluids with nano-particles , 1995 .

[21]  L. Crane.  Flow past a stretching plate , 1970 .

[22]  Sohail Nadeem,et al.  Brazilian Journal of Chemical Engineering FLOW OF A WILLIAMSON FLUID OVER A STRETCHING SHEET , 2013 .

[23]  Study on Sakiadis and Blasius flows of Williamson fluid with convective boundary condition , 2015 .

[24]  Tasawar Hayat,et al.  MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer , 2016 .

[25]  T. Hayat,et al.  Inclined magnetic field and heat source/sink aspects in flow of nanofluid with nonlinear thermal radiation , 2016 .

[26]  Ting Zhang,et al.  Second grade nanofluidic flow past a convectively heated vertical Riga plate , 2019, Physica Scripta.

[27]  Muhammad Awais,et al.  MHD flow of Cattanneo–Christov heat flux model for Williamson fluid over a stretching sheet with variable thickness: Using numerical approach , 2016 .

[28]  C. Sulochana,et al.  Unsteady MHD radiative flow and heat transfer of a dusty nanofluid over an exponentially stretching surface , 2016 .

[29]  Iskander Tlili,et al.  Marangoni convective nanofluid flow over an electromagnetic actuator in the presence of first-order chemical reaction , 2019, Heat Transfer-Asian Research.

[30]  Ting Zhang,et al.  Characteristics of chemical reaction and convective boundary conditions in Powell-Eyring nanofluid flow along a radiative Riga plate , 2019, Heliyon.

[31]  Zurni Omar,et al.  Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points , 2019, Symmetry.

[32]  Najeeb Alam Khan,et al.  Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation , 2019, Symmetry.

[33]  T. Hayat,et al.  Radiative flow of Powell–Eyring nanofluid with convective boundary conditions , 2017 .

[34]  T. Hayat,et al.  Soret and Dufour Effects in the Flow of Williamson Fluid over an Unsteady Stretching Surface with Thermal Radiation , 2015 .

[35]  Gohar Ali,et al.  Entropy Generation on Nanofluid Thin Film Flow of Eyring–Powell Fluid with Thermal Radiation and MHD Effect on an Unsteady Porous Stretching Sheet , 2018, Entropy.

[36]  M. Y. Malik,et al.  MHD flow of Williamson nanofluid over a cone and plate with chemically reactive species , 2017 .

[37]  Zhe Tian,et al.  Efficiency assessment of using graphene nanoplatelets-silver/water nanofluids in microchannel heat sinks with different cross-sections for electronics cooling , 2019, International Journal of Numerical Methods for Heat & Fluid Flow.

[38]  El-Sayed M. Sherif,et al.  Significance of Double Stratification in Stagnation Point Flow of Third-Grade Fluid towards a Radiative Stretching Cylinder , 2019, Mathematics.

[39]  R. V. Williamson.  The Flow of Pseudoplastic Materials , 1929 .

[40]  Ting Zhang,et al.  Darcy-Forchheimer nanofluidic flow manifested with Cattaneo-Christov theory of heat and mass flux over non-linearly stretching surface , 2019, PloS one.

[41]  Z. Omar,et al.  Analysis of dual solution for MHD flow of Williamson fluid with slippage , 2019, Heliyon.

[42]  C. M. Khalique,et al.  Magnetohydrodynamic Darcy–Forchheimer nanofluid flow over a nonlinear stretching sheet , 2019, Physica Scripta.

[43]  I. Tlili,et al.  Nanotechnology for water purification: electrospun nanofibrous membrane in water and wastewater treatment , 2019, Journal of Water Reuse and Desalination.

[44]  Wenchang Tan,et al.  Entropy generation of electromagnetohydrodynamic (EMHD) flow in a curved rectangular microchannel , 2018, International Journal of Heat and Mass Transfer.

[45]  K. Ramadan,et al.  MHD Flow of Nanofluid Flow Across Horizontal Circular Cylinder: Steady Forced Convection , 2019, Journal of Nanofluids.

[46]  Muhammad Idrees Afridi,et al.  Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation , 2018 .

[47]  Iskander Tlili,et al.  Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet , 2019, Symmetry.

[48]  H. Blasius.  The Boundary Layers in Fluids with Little Friction , 2013 .