Particle rotation effects in Cosserat-Maxwell boundary layer flow with non-Fourier heat transfer using a new novel approach

Document Type : Article


1 Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

2 Department of Mathematics, College of Sciences Al Zufli, Majmaah University, Majmaah, 11952, Saudi Arabia

3 - Department of Mathematics, College of Sciences Al Zufli, Majmaah University, Majmaah, 11952, Saudi Arabia. - Department of Mathematics, Faculty of Sciences, Aswan University, 81528, Aswan, Egypt


In this article we use a non-classical approach to investigate different physical effects of Cosserat-Maxwell fluid flow with non-Fourier heat transfer mechanism. Furthermore, a new numerical approach is used and outlined for computing and analyzing the behavior of such flows. In particular, continuous Galerkin-Petrov discretization scheme is embedded with shooting method to get the numerical algorithm to solve the stagnation point flow of Cosserat-Maxwell fluid with Cattaneo-Christov heat transfer. The mathematical description of the physical problem is stated in the form of partial differential equations (PDEs) which govern the flow mechanism. Further, the suitable transformations are utilized to describe the governing PDEs into their respective ordinary differential equations. Numerical experiments are performed for a specific case where there are weak concentrations of the flow near the stretching surface thereby allowing the microelement to rotate and generate vortex flow near the stretching surface. Buoyancy effects along with other interesting physical effects are calculated and numerical results are presented for various fluidic situations. Several benchmark case studies were carried out for the validation of obtained results. Moreover, the results are also validated against the results available in the limiting classical continuum case in literature and a good agreement is found.


1. Eringen, A.C. Theory of micropolar uids", J. Math.Mech., 16, pp. 1{18 (1966).2. Uddin, Z., Kumar, M., and Harmand, S. Inuenceof thermal radiation and heat generation absorptionon MHD het transfer ow of a micropolaruid past awedge with hall and ion slip currents", Thermal Sci.,18, p. S489 (2014).3. Mukhopadhyay, S. and Bhattacharyya, K. Unsteadyow of a Maxwell
uid over a stretching surface inpresence of chemical reaction", J.E. Math. Soc., 20(3),pp. 229{234 (2012).4. Abel, M.S., Tawade, J.V., and Nandeppanavar, M.M.MHD
ow and heat transfer for the upper-convectedMaxwell uid over a stretching sheet", Meccanica, 1,pp. 25{38 (2013).5. Shah, S., Hussain, S., and Sagheer, M. MHD e ectsand heat transfer for the UCM uid along withJoule heating and thermal radiation using Cattaneo-Christov heat
ux model", AIP Adv., 6, p. 085103(2016).6. Renardy, M. High Weissenberg number boundarylayers for the upper convected Maxwell uid", J. Non-Newtonian Fluid Mech., 68, pp. 125{133 (1997).7. Olaru, I. A study of the cooling systems and uid owsimulation in metal cutting processing", IOP Conf.Ser. Mater. Sci. Eng., 227, p. 012086 (2017).8. Abel, M.S. and Mahesha, N. Heat transfer in MHDviscoelastic uid ow over a stretching sheet with
variable thermal conductivity non-uniform heat sourceand radiation", Appl. Mathematical Model., 32(10),pp. 1965{1983 (2008).9. Guilmineau, E. Computational study of
ow arounda simpli ed car body", J. Wind Engin. and IndustrialAerodynamics, 6(7), pp. 1207{1217 (2008).10. Levenspiel, O. Chemical reaction engineering",
Chem. Res., 38(11), pp. 4140{4143 (1999).11. Rana, S., Nawaz, M., and Qureshi, I.H. Numericalstudy of hydrothermal characteristics in nano uidusing KKL model with Brownian motion", Sci. Iran.,26(3), pp. 1931{1943 (2019).12. Atif, S.M., Hussain, S., and Sagheer, M. E ectof thermal radiation on MHD micropolar Carreaunanouid with viscous dissipation, Joule heating, andinternal heating", Sci. Iran., Transaction F., Nanotechnology,26(6), pp. 3875{3888 (2019).13. Eringen, A.C. Theory of thermomicro uid", J. Math.Anal. Appl., 138, pp. 480{496 (1972).14. Das, K. Slip e ects on MHD mixed convectionstagnation point ow of a micropolar
uid towards ashrinking vertical sheet", Comput. Math. Appl., 63(1),pp. 255{267 (2012).15. Ibrahim, W. and Zemedu, C. MHD nonlinear mixedconvection ow of micropolar nanouid over nonisothermalsphere", Math. Prob. Eng., 2020(1), p.4735650 (2020).16. Ashraf, M. and Batool, K. MHD ow and heattransfer of a micropolar uid over a stretchable disk",J. Theor. Appl. Mech., 51(1), pp. 25{38 (2013).17. Tripathy, R.S., Dash, G.C., Mishra, S.R., et al.Numerical analysis of hydromagnetic micropolar uidalong a stretching sheet embedded in porous mediumwith non-uniform heat source and chemical reaction",Eng. Sci. Technol. Int. J., 19, pp. 1573{1581 (2016).18. Yasin, M.M., Ishak, A., and Pop, I. MHD stagnationpoint
ow and heat transfer with e ects of viscousdissipation joule heating and partial velocity slip", Sci.Rep., 5, p. 17848 (2015).19. Lian-Cun, Z., Xin-Xin, Z., and Chun-Qing. L. Heattransfer for power law non-Newtonian uids", Chin.Phys. Lett., 23(12), p. 3301 (2006).20. Cattaneo, C. Sulla conduzione del calore", Atti Sem.Mat. Fis, Univ. Modena., 3(1) pp. 83{101 (1948).21. Christov, C.I. On frame indi erent formulation ofthe Maxwell-Cattaneo model of nite-speed heat conduction",Mech. Res. Commun., 36(4), pp. 481{486(2009).22. Mahapatra, T.R., Nandy, S.K., and Gupta, A.S. Magnetohydrodynamicstagnation-point ow of a powerlaw
uid towards a stretching surface", Int. J. Non-LinearMech., 44, pp. 124{129 (2009).23. Sadeghy, K., Hajibeygi, H., and Taghavi, S.M.Stagnation-point ow of upper-convected Maxwell
uids", Int. J. Non-Lin. Mech., 41(10), pp. 1242{1247(2006).24. Kumari, M. and Nath, G. Steady mixed convectionstagnation-point ow of upper convected Maxwelluids with magnetic eld", Int. J. Non-Lin. Mech.,44(10), pp. 1048{1055 (2009).25. Han, S., Zheng, L., Li, C., et al. Coupled owand heat transfer in viscoelastic uid with Cattaneo-Christov heat ux model", Appl. Math. Letters, 38,pp. 87{93 (2014).26. Sheikholeslami, M., Ganji, D.D., Li, Z., et al. Numerical
simulation of thermal radiative heat transfere ects on Fe3O4-ethylene glycol nanouid EHD
ow ina porous enclosure", Sci. Iran., 26(3), pp. 1405{1414(2019).1234 M.B. Hafeez et al./Scientia Iranica, Transactions B: Mechanical Engineering 28 (2021) 1223{123527. Ismael, M.A. and Ghalib, H.S. Double di usive naturalconvection in a partially layered cavity with inner
solid conductive body", Sci. Iran., B., 25(5), pp. 2643{2659 (2018).28. Gha arpasand, O. Unsteady double-di usive naturalconvection with Soret and Dufour e ects inside a twosidedlid-driven skewed enclosure in the presence ofapplied magnetic eld", Sci. Iran., B., 25(3), pp.1215{1235 (2018).29. Gha arpasand, O. E ect of alternating magnetic eld on unsteady MHD mixed convection and entropygeneration of ferro uid in a linearly heated two-sided
cavity", Sci. Iran., 24(3), pp. 1108{1125 (2017).30. Alinia, M., Gorji-Bandpy, M., Ganji, D.D., et al.Two-phase natural convection of SiO2-water nanouid in an inclined square enclosure", Sci. Iran., 21(5),pp. 1643{1654 (2014).31. Sheikhzadeh, G.A., Heydari, R., Hajialigol, N., et al.
Heat and mass transfer by natural convection arounda hot body in a rectangular cavity", Sci. Iran., 20(5),pp. 1474{1484 (2013).32. Amini, Y., Emdad, H., and Farid, M. Fluid-tructureinteraction analysis of a piezoelectric exible plate in acavity lled withuid", Sci. Iran., 23(2), pp. 559{565(2016).33. Arefmanesh, A., Mahmoodi, M., and Nikfar, M.E ect of position of a square-shaped heat source onbuoyancy-driven heat transfer in a square cavity lledwith nano uid", Sci. Iran., 21(3), pp. 1129{1142(2014).34. Kaneez, H., Alebraheem, J., Elmoasry, A., et al.Numerical investigation on transport of momenta and
energy in micropolar uid suspended with dusty, monoand hybrid nano-structures", AIP Adva., 10(4), p.045120 (2020).35. Fatunmbi, E.O. and Okoya, S.S. Heat transferin boundary layer magneto-micropolar uids withtemperature-dependent material properties over astretching sheet", Adv. Mater. Sci. Eng., p. 5734979(2020).36. Srinivasacharya, D. and Mendu, D.S. Free convectionin MHD micropolar uid with radiation and chemicalreaction e ects", Chem. Ind. Chem. Eng. Q., 20(2),pp. 183{195 (2014).37. Raftari, B. and Yildirim, A. The application of homotopy
perturbation method for MHD ows of UCMuids above porous stretching sheets", Comput. Math.Appl., 59(10), pp. 3328{3337 (2010).38. Mushtaq, A., Mustafa, M., Hayat, T., et al. Buoyancye ects in stagnation-point ow of Maxwell uid utilizingnon-Fourier heat ux approach", Plos One, 13(7),p. e0200325 (2018).39. Khan, M.S. and Khan, M.I. A novel numerical algorithmbased on Galerkin-Petrov time-discretizationmethod for solving chaotic nonlinear dynamical systemsnonlinear dynamics", Nonlinear Dyn., 91(3), pp.1555{1569 (2018).40. Abel, M.S., Tawade, J.V., and Nandeppanavar, M.M.MHD
ow and heat transfer for the upper convectedMaxwell uid over a stretching sheet", Mecc., 47, pp.385{393 (2012).41. Megahed, A.M. Variable uid properties and variableheat ux e ects on the ow and heat transfer in a non-Newtonian Maxwell uid over an unsteady stretchingsheet with slip velocity", Chin. Phys. B., 22, p. 094701(2012).42. Mustafa, M., Hayat, T., and Alsaedi, A. Rotating owof Maxwell uid with variable thermal conductivity anapplication to non-Fourier heat
ux theory", Int. J.Heat Mass Transf., 106, pp. 142{148 (2017).