RETRACTED: Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

Williamson RV . The flow of pseudoplastic materials. Industrial & Engineering Chemistry 1929 Nov 1; 21: 1108–1111.

Khan NA Khan H . A boundary layer flows of non-newtonian williamson fluid. Nonlinear Engineering 2014 Jun 1; 3: 107–115.

Hayat T Saeed Y Asad S , et al. Soret and dufour effects in the flow of williamson fluid over an unsteady stretching surface with thermal radiation. Zeitschrift für Naturforschung A 2015 Apr 1; 70: 235–243.

Salahuddin T Malik MY Hussain A , et al. MHD Flow of cattanneo–christov heat flux model for williamson fluid over a stretching sheet with variable thickness: using numerical approach. J Magn Magn Mater 2016 Mar 1; 401: 991–997.

Khan SU Shehzad SA Ali N . Interaction of magneto-nanoparticles in williamson fluid flow over convective oscillatory moving surface. Journal of the Brazilian Society of Mechanical Sciences and Engineering 2018 Apr; 40: 1–2.

Ibrahim W Gamachu D . Nonlinear convection flow of williamson nanofluid past a radially stretching surface. AIP Adv 2019 Aug 26; 9: 085026.

Nawaz S Hayat T Alsaedi A . Analysis of entropy generation in peristalsis of williamson fluid in curved channel under radial magnetic field. Comput Methods Programs Biomed 2019 Oct 1; 180: 105013.

Rashid M Ansar K Nadeem S . Effects of induced magnetic field for peristaltic flow of williamson fluid in a curved channel. Physica A: Statistical Mechanics and its Applications 2020 Sep 1; 553: 123979.

Gailitis A . On the possibility to reduce the hydrodynamic drag of a plate in an electrolyte. Appl. Magnetohydrodynamics. Rep. Inst Phys. Riga 1961; 13: 143–146.

Pantokratoras A Magyari E . EMHD free-convection boundary-layer flow from a Riga-plate. J Eng Math 2009 Jul 1; 64: 303–315.

Ahmad R Mustafa M Turkyilmazoglu M . Buoyancy effects on nanofluid flow past a convectively heated vertical Riga-plate: a numerical study. Int J Heat Mass Transfer 2017 Aug 1; 111: 827–835.

Farooq M Anjum A Hayat T , et al. Melting heat transfer in the flow over a variable thicked Riga plate with homogeneous-heterogeneous reactions. J Mol Liq 2016 Dec 1; 224: 1341–1347.

Ayub M Abbas T Bhatti MM . Inspiration of slip effects on electromagnetohydrodynamics (EMHD) nanofluid flow through a horizontal Riga plate. The European Physical Journal Plus 2016 Jun; 131: 1–9.

Kumar R Sood S Shehzad SA , et al. Radiative heat transfer study for flow of non-newtonian nanofluid past a Riga plate with variable thickness. J Mol Liq 2017 Dec 1; 248: 143–152.

Hayat T Khan M Khan MI , et al. Electromagneto squeezing rotational flow of carbon (C)-water (H2O) kerosene oil nanofluid past a Riga plate: a numerical study. PloS one 2017 Aug 16; 12: e0180976.

Parvine M Alam MM . Nano fluid flow along the Riga plate with electromagnetic field in a rotating system. In AIP Conference Proceedings, vol. 2121. 1, 070003. AIP Publishing LLC, 2019.

Abbas N Nadeem S Malik MY . Theoretical study of micropolar hybrid nanofluid over Riga channel with slip conditions. Physica A: Statistical Mechanics and its Applications 2020 Aug 1; 551: 124083.

Hayat T Saif RS Ellahi R , et al. Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions. Results Phys 2017 Jan 1; 7: 2601–2606.

Abbas Z Imran M Naveed M . Hydromagnetic flow of a carreau fluid in a curved channel with non-linear thermal radiation. Thermal Science 2019; 23: 3379–3390.

Rasool G Zhang T . Characteristics of chemical reaction and convective boundary conditions in powell-eyring nanofluid flow along a radiative Riga plate. Heliyon 2019 Apr 1; 5: e01479.

Abbas Z Imran M Naveed M . Time-dependent flow of thermally developed viscous fluid over an oscillatory stretchable curved surface. Alexandria Eng J 2020 Dec 1; 59: 4377–4390.

Imran M Abbas Z Naveed M , et al. Impact of joule heating and melting on time-dependent flow of nanoparticles due to an oscillatory stretchable curved wall. Alexandria Eng J 2021 Aug 1; 60: 4097–4113.

Khan M Salahuddin T Yousaf MM , et al. Variable diffusion and conductivity change in 3d rotating williamson fluid flow along with magnetic field and activation energy. International Journal of Numerical Methods for Heat & Fluid Flow 2019 Aug 2; 30(5).

Ramzan M Bilal M Chung JD , et al. Impact of generalized Fourier's And Fick's Laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions. Phys Fluids 2017 Sep 14; 29: 093102.

Nawaz M Rafiq S Qureshi IH , et al. Combined effects of partial slip and variable diffusion coefficient on mass and heat transfer subjected to chemical reaction. Phys Scr 2020 Feb 7; 95: 035222.

Reddy DB Reddy KS Triveni B , et al. Variable mass diffusion and temperature dependent heat source/sink effects on MHD Casson fluid through a stretching sheet. InAIP Conference Proceedings 2020 Jul 28 (Vol. 2246, No. 1, p. 020102). AIP Publishing LLC.

Jabeen I Farooq M Mir NA . Variable mass and thermal properties in three-dimensional viscous flow: application of darcy law. Journal of Central South University 2019 May; 26: 1271–1282.

Khan NS Kumam P Thounthong P . Computational approach to dynamic systems through similarity measure and homotopy analysis method for renewable energy. Crystals (Basel) 2020 Dec; 10: 1086.

Khan NS Ali L Ali R , et al. A novel algorithm for the computation of systems containing different types of integral and integro-differential equations. Heat Transfer 2021 Jun; 50: 3065–3078.

Ali L Khan NS Ali R , et al. Novel insights into the computational techniques in unsteady MHD second-grade fluid dynamics with oscillatory boundary conditions. Heat Transfer 2021 May; 50: 2502–2524.

Khan NS Shah Q Sohail A , et al. Lorentz forces effects on the interactions of nanoparticles in emerging mechanisms with innovative approach. Symmetry (Basel) 2020 Oct; 12: 1700.

Khan NS Shah Q Sohail A . Dynamics with cattaneo–christov heat and mass flux theory of bioconvection oldroyd-B nanofluid. Adv Mech Eng 2020 Aug 1; 12: 168781402093046.

Khan NS Usman AH Sohail A , et al. A framework for the magnetic dipole effect on the thixotropic nanofluid flow past a continuous curved stretched surface. Crystals (Basel) 2021 Jun; 11: 645.

Imran M Abbas Z Naveed M . Flow of eyring-powell liquid due to oscillatory stretchable curved sheet with modified Fourier and Fick's Model. Applied Mathematics and Mechanics 2021; 42: 1461–1478.

Naveed M Imran M Abbas Z . Curvilinear flow of micropolar fluid with cattaneo–christov heat flux model due to oscillation of curved stretchable sheet. Zeitschrift für Naturforschung A 2021 Jun 25; 76(9).

Khan NS Kumam P Thounthong P . Magnetic field promoted irreversible process of water based nanocomposites with heat and mass transfer flow. Sci Rep 2021 Jan 18; 11: 1–25.

Khan NS Shah Q Sohail A , et al. Rotating flow assessment of magnetized mixture fluid suspended with hybrid nanoparticles and chemical reactions of species. Sci Rep 2021 May 28; 11: 1–8.

Usman AH Khan NS Humphries UW , et al. Computational optimization for the deposition of bioconvection thin oldroyd-B nanofluid with entropy generation. Sci Rep 2021 Jun 2; 11: 1–23.