Viscoelastic Micropolar Convection Flows from an Inclined Plane with Nonlinear Temperature: A Numerical Study

Document Type : Research Paper


1 Department of Information Technology, Mathematics Section, Salalah College of Technology, Salalah -211, Oman

2 Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle - 517325, India

3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 632014, India

4 Department of Mathematics, Sir Vishveshwaraiah Institute of Science and Technology, Madanapalle – 517325, India


An analytical model is developed to study the viscoelastic micropolar fluid convection from an inclined plate as a simulation of electro-conductive polymer materials processing with nonlinear temperature. Jeffery’s viscoelastic model is deployed to describe the non-Newtonian characteristics of the fluid and provides a good approximation for polymers. Micro-structural is one of the characteristics of non-Newtonian fluid that represents certain polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller-Box implicit finite-difference technique. Extensive solutions for velocity, surface temperature, angular velocity, skin friction, heat transfer rate and wall couple stress are visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of viscous dissipation, chemical reaction and non-Newtonian effects. This particle study finds applications in different industries like reliable equipment design, nuclear plants, paint spray, thermal fabrication, water-based gel solvents, polymeric manufacturing process, gas turbines and different propulsion devices.


Main Subjects

[1] X. Huang, M.J. Gollner, Correlations for evaluation of flame spread over an inclined fuel surface, Fire Safety Science, 11 (2014) 222-233.
[2] P. Cheng, Film condensation along an inclined surface in a porous medium, International Journal of Heat and Mass Transfer, 24 (1981) 983-990.
[3] O. Anwar Bég, J. Zueco, T.B. Chang, Numerical analysis of hydromagnetic gravity-driven thin film micropolar flow along an inclined plane, Chemical Engineering Communications, 198(3) (2010) 312- 331.
[4] N.J. Balmforth et al., Viscoplastic flow over an inclined surface, Journal of Non-Newtonian Fluid Mechanics, 142 (2007) 219-243.
[5] M.B. Ashraf et al., Radiative mixed convection flow of an Oldroyd-B fluid over an inclined stretching surface, Journal of Applied Mechanics and Technical Physics, 57 (2016) 317–325.
[6] K. Pruess, Y. Zhang, A hybrid semi-analytical and numerical method for modeling wellbore heat transmission, Proc. 30th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, USA, 2005.
[7] Y. Greener, S. Middleman, Blade‐coating of a viscoelastic fluid, Polymer Engineering and Science, 14 (1974) 791-796.
[8] H.-C. Chang, E.A. Demekhin, Complex Wave Dynamics on Thin Films, Elsevier, Amsterdam, 2002.
[9]A.F. Johnson, Rheology of thermoplastic composites I, Composites Manufacturing, 6 (1995) 153-160.
[10] M.R. Ilias, N.A. Rawi, Steady aligned MHD free convection of Ferrofluids flow over an inclined plate, Journal of Mechanical Engineering, 14(2) (2017) 1-15.
[11] R. Kandasamy, N.A. bt Adnan, J.A. Abbas Abbood, M. Kamarulzaki, M. Saifullah, Electric field strength on water based aluminum alloys nanofluids flow up a non-linear inclined sheet, Engineering Science and Technology, An International Journal, 22(1) (2019) 229-236.
[12] I. Khan, S. Fatima, M.Y. Malik, T. Salahuddin, Exponentially varying viscosity of magnetohydrodynamic mixed convection Eyring-Powell nanofluid flow over an inclined surface, Results in Physics, 8 (2018) 1194-1203.
[13] D.V.V. Krishna Prasad, G.S. Krishna Chaitanya, R. Srinivasa Raju, Thermal diffusion effect on MHD mixed convection flow along a vertically inclined plate: A Casson fluid flow, AIP Conference Proceedings, 1953 (2018) 140089.
[14] MD. Shamshuddin, S.R. Mishra, T. Thumma, Chemically Reacting Radiative Casson Fluid over an inclined porous plate: A Numerical Study, Numerical Heat Transfer and Fluid Flow, Lecture Notes in Mechanical Engineering, (2019) 469-479.
[15] Ch. RamReddy, P. Naveen, D. Srinivasacharya, Influence of Non-linear Boussinesq Approximation on Natural Convective Flow of a Power-Law Fluid along an Inclined Plate under Convective Thermal Boundary Condition, Nonlinear Engineering, 8(1) (2019) 94–106.
[16] P. Rana, R. Bhargava, O.A. Beg, Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium, Computers and Mathematics with Applications, 61 (2012) 25816-2832.
[17] M. Ramzan, M. Bilal, J.D. Chung, Effects of MHD homogeneous-hetrogeneous reactions on third grade fluid with Cateneo-Christov heat flux, Journal of Molecular Liquids, 223 (2016) 1284-1290.
[18] M. Ramzan, M. Bilal, J.D. Chung, MHD stagnation point Cattaneo–Christov heat flux in Williamson fluid flow with homogeneous–heterogeneous reactions and convective boundary condition—A numerical approach, Journal of Molecular Liquids, 225 (2017) 856-862.
[19] M. Ramzan, M. Bilal, J.D. Chung, Influence of homogeneous-heterogeneous reactions on MHD 3D Maxwell fluid flow with Cattaneo-Christov heat flux and convective boundary condition, Journal of Molecular Liquids, 230 (2017) 415-422.
[20] M. Ramzan, M. Bilal, J.D. Chung, Radiative flow of Powell-Eyring magneto-nanofluid over a stretching cylinder with chemical reaction and double stratification near a stagnation point, PLoS ONE, 12(1) (2017) e170790.
[21] M. Ramzan, M. Bilal, J.D. Chung, Soret and Dufour effects on three dimensional Upper-Convected Maxwell fluid with chemical reaction and non-Linear radiative heat flux, International Journal of Chemical Reactor Engineering, 15(3) (2017) 20160136.
[22] M. Ramzan, M. Bilal, S. Kanwal, Effects of variable thermal conductivity and nonlinear thermal radiative flow past Eyring Powell nanofluid with chemical reaction, Communications in Theoretical Physics, 67(6) (2017) 723.
[23] M. Ramzan, M. Bilal, J.D. Chung, Radiative Williamson nanofluid flow over a convectively heated Riga plate with chemical reaction-A numerical approach, Chinese Journal of Physics, 55(4) (2017) 1663-1673.
[24] M.D. Shamshuddin, P.V. Satya Narayana, Primary and Secondary flows on unsteady MHD free convective micropolar fluid flow past an inclined plate in a rotating system: a Finite Element Analysis, Fluid Dynamics and Materials Processing, 14(1) (2018) 57-86.
[25] N. Manzoor, K. Maqbool, O.A. Bég, S. Shaheen, Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer, Heat Transfer - Asian Research,48(2) (2019) 556-581.
[26] V.R. Prasad, S. Abdul Gaffar, E. Keshava Reddy, O. Anwar Bég, Numerical study of non-Newtonian boundary layer flow of Jeffreys fluid past a vertical porous plate in a non-Darcy porous medium, Internatioanl Journal of Computer  Mathematics, Engineering Science & Mechanics, 15(4) (2014) 372-389.
[27] S. Abdul Gaffar, V. Ramachandra Prasad, O. Anwar Bég, Md. Hidayathullah Khan, K. Venkatadri, Effects of ramped wall temperature and concentration on viscoelastic Jeffrey’s fluid flows from a vertical permeable cone, Journal of the Brazilian Society of Mechanical Sciences and Engineering,40 (2018) 441-459.
[28] K. Ahmad, A. Ishak, Magnetohydrodynamic (MHD) Jeffrey fluid over a stretching vertical surface in a porous medium, Propulsion and Power Research, 6(4) (2017) 269-276.
[29] A.C. Eringen, Simple microfluids, International Journal of Engineering Science, 2 (1964) 205-217.
[30] A.C. Eringen, Theory of micropolar fluids, Journal of Mathematics & Mechanics, 16 (1966) 1-18.
[31] A.C. Eringen, Theory of thermo-micropolar fluids, Journal of Mathematical Analysis Applications, 38 (1972) 480–496.
[32] S.R. Mishra, M. Mainul Hoque, B. Mohanty, N.N. Anika, Heat transfer effect on MHD flow of a micropolar fluid through porous medium with uniform heat source and radiation, Nonlinear Engineering, 8(1) (2019) 65–73.
[33] I. Pazanin, M. Radulovic, Asymptotic Approximation of the nonsteady Micropolar fluid flow through a circular pipe, Mathematical Problems in Engineering, 2018 (2018) Article ID 6759876, 16p.
[34] M. Nazeer, N. Ali, T. Javed, Z. Asghar, Natural convection through spherical particles of a micropolar fluid enclosed in a trapezoidal porous container, The European Physical Journal Plus, 133 (2018) 423.
[35] O.K. Koriko, I.L. Animasaun, A.J. Omowaye, T. Oreyeni, The combined influence of nonlinear thermal radiation and thermal stratification on the dynamics of micropolar fluid along a vertical surface, Multidiscipline Modeling in Materials and Structures, 15(1) (2019) 133-155.
[36] R. Mehmood, S. Nadeem, S. Masood, Effects of transverse magnetic field on a rotating micropolar fluid between parallel plates with heat transfer, Journal of Magnetism and Magnetic Materials, 401 (2016) 1006-1014.
[37] M. Ramzan, J.D. Chung, N. Ullah, Partial slip effect in the flow of MHD micropolar nanofluid flow due to a roztating disk – A numerical approach, Results in Physics, 7 (2017) 3557-3566.
[38] M. Ramzan, N. Ullah, J.D. Chung, D. Lu, U. Farooq, Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction, Scientific Reports, 7 (2017) 12901. 
[39] A. Maceiras, P. Martins, High-temperature polymer based magnetoelectric nanocomposites, European Polymer Journal, 64 (2015) 224-228.
[40] P.M. Xulu, P. Filipcsei, M. Zrinyi, Preparation and responsive properties of magnetically soft poly (N-isopropylacrylamide) gels, Macromolecules, 33(5) (2000) 1716-1719.
[41] O.A. Bég, Numerical methods for multi-physical magnetohydrodynamics, New Developments in Hydrodynamics Research, M. J. Ibragimov and M. A. Anisimov, Eds., Nova Science, New York, September, 2012, p 1-112.
[42] S. Abdul Gaffar, V. Ramachandra Prasad E. Keshava Reddy, MHD free convection flow of non-Newtonian Eyring-Powell fluid from vertical surface in porous media with Hall/Ionslip currents and Ohmic dissipation, Alexandria Engineering Journal, 55 (2016) 875-905.
[43] S. Abdul Gaffar, V. Ramachandra Prasad, E. Keshava Reddy, Computational Study of MHD free  convection flow of non-Newtonian Tangent Hyperbolic fluid from a vertical surface in porous media with Hall/Ionslip current and Ohmic dissipation, International Journal of Applied and Computational Mathematics, 3(2) (2017) 859-890.
[44] O.A.Beg, S. Abdul Gaffar, V. Ramachandra Prasad, M.J. Uddin, Computational solutions for non-isothermal, nonlinear magneto-convection in porous media with hall/ionslip currents and ohmic dissipation, Engineering Science and Technology, An International Journal, 19(1) (2016) 377-394.
[45] M.T. Shaw, Introduction to Polymer Rheology, Wiley, New York, 2012.
[46] O.A. Bég, R. Bhargava, M.M. Rashidi, Numerical Simulation in Micropolar Fluid Dynamics, Lambert, Saarbrucken, Germany, 2011.
[47] O.A. Bég, V. R. Prasad, B. Vasu, N. Bhaskar Reddy, Q. Li, R. Bhargava, Free convection heat and mass transfer from an isothermal  sphere to a micropolar regime with Soret/Dufour effects, International Journal of Heat and Mass Transfer, 54 (2011) 9-18.
[48] S. Abdul Gaffar, O.A. Bég, V. R. Prasad, Mathematical modelling of natural convection in a third grade viscoelastic micropolar fluid from an isothermal inverted cone, Iranian Journal of Science and Technology Transactions of Mechanical Engineering, (2018)
[49] A. Subba Rao, Prasad, V.R., O.A. Bég, Rashidi, M., Free convection heat and mass transfer of a nanofluid past a horizontal cylinder embedded in a non-Darcy porous medium, Journal of Porous Media, 21(3) (2018) 279-294.
[50] B. Vasu, Rama S. R. Gorla, O.A. Bég, P.V.S. N. Murthy, V.R. Prasad, A. Kadir, Unsteady flow of a nanofluid over a sphere with non-linear Boussinesq approximation, AIAA Journal of Thermophysics Heat Transfer, (2018) 13p.
[51]S.A. Gaffar, V.R. Prasad, B.R. Kumar, O.A. Bég, Computational modelling and solutions for mixed convection boundary layer flows of nanofluid from a non-isothermal wedge, Journal of Nanofluids, 7 (2018) 1-9. 
[52] J.R. Lloyd, E.M., Sparrow, Combined forced and free convection flow on vertical surfaces. International Journal Heat Mass Transfer,13(2) (1970) 434-438.
[53] S.G. Rochelle, J. Peddieson, Viscoelastic boundary-layer flows past wedges and cones, International Journal of Engineering Science, 18 (1980) 713–726.
[54] R.S.R. Gorla, H.S. Takhar, Boundary layer flow of micropolar fluid on rotating axisymmetric surfaces with a concentrated heat source, Acta Mechanica, 105 (1994) 1–10.
[55] R.S.R. Gorla, A. Slaouti, H.S. Takhar, Free convection in micropolar fluids over a uniformly heated vertical plate, International Journal of Numerical Methods for Heat & Fluid Flow, 8 (1988) 504-518.
[56] M. Norouzi, M. Davoodi, O.A. Bég, MD. Shamshuddin, Theoretical study of Oldroyd-B visco-elastic fluid flow through curved pipes with slip effects in polymer flow processing, International Journal of Applied Computational Mathematics, 4 (2018) 108.
[57] H.B. Keller, Numerical methods in boundary-layer theory, Annual Review of Fluid Mechanics, 10 (1978) 417-433.