@article{41695209ef914ed392c3251c10a92a25,

title = "Unsteady mhd mixed convection flow of non-newtonian casson hybrid nanofluid in the stagnation zone of sphere spinning impulsively",

abstract = "In the present analysis, an unsteady MHD mixed convection flow is scrutinized for a non-Newtonian Casson hybrid nanofluid in the stagnation zone of a rotating sphere, resulting from the impulsive motion of the angular velocity of the sphere and the velocity of the free stream. A set of linearized equations is derived from the governing ones, and these differential equations are solved numerically using the hybrid linearization–differential quadrature method. The surface shear stresses in the x-and y-directions and the surface heat transfer rate are improved due to the Casson βo, mixed convection α, rotation γ and magnetic field M parameters. In addition, as nanoparticles, the solid volume fraction (parameter φ) increases, and the surface shear stresses and the rate of heat transfer are raised. A comparison between earlier published data and the present numerical computations is presented for the limiting cases, which are noted to be in very good agreement.",

keywords = "Casson, Hybrid nanofluid, Magnetohydrodynamic, Mixed convection, Rotating sphere",

author = "essam elzahar and Mahdy, {Abd El Nasser} and Rashad, {Ahmed M.} and Wafaa Saad and laila morad",

note = "Funding Information: The impact of thermal radiation on the time-dependent MHD flow and heat transfer of a laminar incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluid (Ag-TiO2) wi2 thin the stagnation region of a rotating sphere has been addressed in the present paper. Non-similar transformations and the hybrid linearization– differential quadrature method in a MATLAB environment have been applied to solve the flow governing equations. Some of the significant notes are listed as follows: 1. The heat transfer rate and surface shear stress in x-and y-direction are enhanced by increasing the magnetic field, Casson, mixed convection and the sphere rotation pa-rameters. parameters. 2. The velocity profile in x-direction, temperature profile and surface shear stresses in x- 2. The velocity profile in x-direction, temperature profile and surface shear stresses in and y-direction are enhanced by the increase in the thermal radiation, unlike the rate x-and y-direction are enhanced by the increase in the thermal radiation, unlike the of heat transfer and the velocity profile in y-direction, which is decreased by boosting rate of heat transfer and the velocity profile in y-direction, which is decreased by the thermal radiation parameter. boostiSurfaceng the tshearhstrermaessesl raindiax-tandion paray-direction,meter. the velocity distribution in x-direction and Steumrfpaecera stuhreeardissttrreisbsuetsi oinn oxf-haynbdriyd-dniarneoctfliounid, t(hAeg -vTeilOo2c/itHy 2dOis)tirsibgurteiaotne rinasxc-odmirpecatrieodn atondth teembapseerfalutuidre. distribution of hybrid nanofluid (Ag-TiO2/H2O) is greater as com-4. pBaortehdv teol othciet ybadsies tfrluibiudt. ions in y-direction and the temperature distribution in non- 4. Both velocity distributions i′ n y-direction and the temperature distri′ bution in non-Newtonian hybrid nanofluid are greater than in Newtonian hybrid nanofluid, unlike the velocity distribution ′(, ) where it is noticed that the ′ of non-Newtonian hy-brid nanofluid is smaller than Newtonian fluid. Author Contributions: Conceptualization, A.E.N.M., A.M.R. and W.S.; methodology, E.R.E.-Z., A.E.N.M., A.M.R., W.S. and L.F.S.; formal analysis, A.E.N.M., A.M.R. and W.S.; investigation, E.R.E.-A.E.N.M., A.M.R., W.S. and L.F.S..; formal analysis, A.E.N.M., A.M.R. and W.S.; investigation, E.R.E.-Z., A.E.N.M., A.M.R., W.S. and L.F.S.; resources, A.E.N.M., A.M.R. and W.S., .; writing—original draft preparation, E.R.E.-Z., A.E.N.M., A.M.R., W.S. and L.F.S.; writing—review and editing, E.R.E.-Z., A.M., A.M.R., W.S. and L.F.S.; supervision, A.E.N.M. and A.M.R. ; project administration, A.E.N.M. and A.M.R.; funding acquisition, A.M.R., E.R.E.-Z. and L.F.S. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors acknowledge that this publication was supported by the Deanship oAfcSkcnieonwtilfeicdRgmeseenartcsh: TahteP aruintcheorSsa tatcakmnobwinleAdbgde uthlaaztitzhUisn pivuebrlsicitayt,ioAnl kwhaasrjs,uSpaupdoritAedra bbyiat.he Deanship of Scientific Research at Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia. Conflicts of Interest: The authors declare no conflict of interest. Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = may,

day = "26",

doi = "https://doi.org/10.3390/FLUIDS6060197",

language = "English",

volume = "6",

journal = "Fluids",

issn = "2311-5521",

publisher = "MDPI Multidisciplinary Digital Publishing Institute",

number = "6",

}