Effects of heat and mass transfer on stagnation point flow of micropolar Maxwell fluid over Riga plate

Document Type : Article


1 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

2 - Mathematics and Its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam. - Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

3 Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

4 Al-Farabi Kazakh National University, av. al-Farabi 71, 050040, Almaty, Kazakhstan


In this paper, we investigated the stagnation point flow of Maxwell viscoelasticity with incompressible based micropolar fluid over a Riga plate. The mathematical model has been constructed though micropolar fluid flows over Riga plate. The implement the boundary layer approximation, the system of partial differential equations is produced through momentum equation along with micro inertia theory. Nonlinear partial differential equations are become dimensionless nonlinear ordinary differential equations through suitable similarity transformations. This system is solved numerical scheme via BVP4C method. The effects of involving physical parameters like as dimensionless parameter, Modified Hartman number, Material parameter, Slip condition σ_s, Viscoelastic parameter δ_m and Soret coefficient S_T are highlighted through graphs and numerical results. The physical quantities like as Skin friction, local Nusselt number and local Sher-wood number are highlighted through tables. R is increasing with increasing dimensionless parameter, Material parameter K and Slip condition σ_s. R is decreasing with increasing behavior of Modified Hartman number Z and viscoelastic parameter δ_m.


1. Lukaszewicz, G., Micropolar Fluids: Theory and Applications, Springer Science & Business Media (1999).
2. Eringen, A.C., Microcontinuum Field Theories: II. Fluent Media, (2) Springer Science & Business Media (2001).
3. Wang, X.L. and Zhu, K.Q. "A study of the lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing (T1516)", Tribology International, 37(6), pp. 481-490 (2004).
4. Nadeem, S., Akbar, N.S., and Malik, M.Y. "Exact and numerical solutions of a micropolar fluid in a vertical annulus", Numerical Methods for Partial Differential Equations, 26(6), pp. 1660-1674 (2010).
5. Hussain, S.T., Nadeem, S., and Haq, R.U. "Modelbased analysis of micropolar nano fluid  flow over a stretching surface", The European Physical Journal Plus, 129(8), p. 161 (2014).
6. Ellahi, R., Rahman, S.U., Nadeem, S., and Akbar, N.S. "Influence of heat and mass transfer on micropolar fluid of blood flow through a tapered stenosed arteries with permeable walls", Journal of Computational and Theoretical Nanoscience, 11(4), pp. 1156-1163 (2014).
7. Rawi, N.A., Ilias, M.R., Isa, Z.M., and Shafie, S. "GJitter induced mixed convection  flow and heat transfer of micropolar nano
fluids  flow over an inclined stretching sheet", In AIP Conference Proceedings 1775(1), p.030020, AIP Publishing (2016).
8. Abbas, N., Saleem, S., Nadeem, S., Alderremy, A.A., and Khan, A.U. "On stagnation point flow of a micro polar nanofluid past a circular cylinder with velocity and thermal slip", Results in Physics, 9, pp. 1224-1232 (2018).
9. Nadeem, S., Malik, M.Y., and Abbas, N. "Heat transfer of three dimensional micropolar fluids on Riga plate", Canadian Journal of Physics, 98(1), pp. 32-38 (2020).
10. Mollamahdi, M., Abbaszadeh, M., and Sheikhzadeh,G.A. "Analytical study of Al2O3-Cu/water micropolar hybrid nanofluid in a porous channel with expanding/ contracting walls in the presence of magnetic field", Scientia Iranica, 25(1), pp. 208-220 (2018).
11. Nayak, M.K., Zeeshan, A., Pervaiz, Z., and Makinde, O.D., "Modelling, measurement and control B", 88(1), pp. 33-41 (2019).
12. Abro, K.A. and Yildirim, A. "An analytic and mathematical synchronization of micropolar nanofluid by Caputo-Fabrizio approach", Scientia Iranica, 26(6), pp. 3917-3927 (2019).
13. Atif, S.M., Hussain, S., and Sagheer, M. "Effect of thermal radiation on MHD micropolar Carreau nanofluid with viscous dissipation, Joule heating, and internal heating", Scientia Iranica, Transactions F, Nanotechnology, 26(6), pp. 3875-3888 (2019).
14. Gailitis, A.K. and Lielausis, O.A. "On the possibility of drag reduction of a at plate in an electrolyte", Appl. Magnetohydrodyn. Trudy Inst. Fisiky AN Latvia SSR, 12, p. 143 (1961).
15. Grinberg, E. "On determination of properties of some potential fields", Applied Magnetohydrodynamics Reports of the Physics Institute, 12, pp. 147-154 (1961).
16. Pantokratoras, A. and Magyari, E. "EMHD freeconvection boundary-layer  flow from a Riga-plate", Journal of Engineering Mathematics, 64(3), pp. 303- 315 (2009).
17. Magyari, E. and Pantokratoras, A. "Aiding and opposing mixed convection  flows over the Riga-plate", Communications in Nonlinear Science and Numerical Simulation, 16(8), pp. 3158-3167 (2011).
18. Ayub, M., Abbas, T., and Bhatti, M.M. "Inspiration of slip effects on electromagnetohydrodynamics (EMHD) nano fluid flow through a horizontal Riga plate", The European Physical Journal Plus, 131(6), p. 193 (2016).
19. Ramzan, M., Bilal, M., and Chung, J.D. "Radiative Williamson nanofluid  flow over a convectively heated Riga plate with chemical reaction - A numerical approach", Chinese Journal of Physics, 55(4), pp. 1663-1673 (2017).
20. Zaib, A., Haq, R.U., Chamkha, A.J., and Rashidi, M.M. "Impact of partial slip on mixed convective  flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles", International Journal of Numerical Methods for Heat and Fluid Flow, 29(5), pp. 1647-1662 (2018).
21. Rasool, G. and Zhang, T. "Characteristics of chemical reaction and convective boundary conditions in Powell-Eyring nanofluid flow along a radiative Riga plate", Heliyon, 5(4), e01479 (2019).
22. Bhatti, M.M., Zeeshan, A., Ellahi, R., and Shit, G.C. "Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium", Advanced Powder Technology, 29(5), pp. 1189-1197 (2018).
23. Nayak, M.K., Shaw, S., Makinde, O.D., and Chamkha, A.J. "Effects of homogenous-heterogeneous reactions on radiative NaCl-CNP nanofluid flow past a convectively heated vertical Riga plate", Journal of Nanofluids, 7(4), pp. 657-667 (2018).
24. Mehmood, R., Nayak, M.K., Akbar, N.S., and Makinde, O.D. "Effects of thermal-diffusion and diffusion-thermo on oblique stagnation point flow of couple stress Casson fluid over a stretched horizontal Riga plate with higher order chemical reaction", Journal of Nanofluids, 8(1), pp. 94-102 (2019).
25. Nayak, M.K., Shaw, S., Makinde, O.D., and Chamkha, A.J. "Investigation of partial slip and viscous dissipation effects on the radiative tangent hyperbolic nanofluid  flow past a vertical permeable Riga plate with internal heating: Bungiorno model", Journal of Nanofluids, 8(1), pp. 51-62 (2019).
26. Riaz, A., Ellahi, R., Bhatti, M.M., and Marin, M. "Study of heat and mass transfer on eyring-powell fluid model propagating peristaltically through a rectangular complaint channel", Heat Transfer Research, 50(16), pp. 1539-1560 (2019). DOI: 10.1615/HeatTransRes.2019025622.
27. Khan, A.A., Bukhari, S.R., Marin, M., and Ellahi, R. "Effects of chemical reaction on third-grade MHD fluid flow under the in
uence of heat and mass transfer with variable reactive index", Heat Transfer Research, 50(11), pp. 1061-1080 (2019).
28. Hiemenz, K. "Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder", Dinglers Polytech. J., 326, pp. 321- 324 (1911).
29. Howarth, L. "The boundary layer in three dimensional flow-Part II The flow near a stagnation point", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 42(335), pp. 1433-1440, (1951).
30. Ishak, A., Jafar, K., Nazar, R., and Pop, I. "MHD stagnation point  flow towards a stretching sheet", Physica A: Statistical Mechanics and Its Applications, 388(17), pp. 3377-3383 (2009).
31. Van Gorder, R.A. and Vajravelu, K. "Hydromagnetic stagnation point  flow of a second grade fluid over a stretching sheet", Mechanics Research Communications, 37(1), pp. 113-118 (2011).
32. Fang, T., Chia-fon, F.L., and Zhang, J. "The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer", International Journal of Non-Linear Mechanics, 46(7), pp. 942-948 (2011).
33. Nadeem, S., Abbas, N., and Khan, A.U. "Characteristics of three dimensional stagnation point flow of hybrid nanofluid past a circular cylinder", Results in Physics, 8, pp. 829-835 (2018).
34. Nadeem, S. and Abbas, N. "On both MHD and slip effect in Micropolar hybrid nanofluid past a circular cylinder under stagnation point region", Canadian Journal of Physics, 97(4), pp. 392-399 (2018).
35. Iacopini, S. and Piazza, R. "Thermophoresis in protein solutions", EPL (Europhysics Letters), 63(2), p. 247 (2003).
36. Putnam, S.A., Cahill, D.G., andWong, G.C. "Temperature dependence of thermodiffusion in aqueous suspensions of charged nanoparticles", Langmuir, 23(18), pp. 9221-9228 (2007).
37. Braibanti, M., Vigolo, D., and Piazza, R. "Does thermophoretic mobility depend on particle size", Physical Review Letters, 100(10), p. 108303 (2008).
38. Khan, A.A., Usman, H., Vafai, K., and Ellahi, R. "Study of peristaltic  flow of magnetohydrodynamics Walter's B fluid with slip and heat transfer", Scientia Iranica, 23(6), pp. 2650-2662 (2016).
39. Niranjan, H., Sivasankaran, S., and Bhuvaneswari, M. "Chemical reaction, Soret and Dufour effects on MHD mixed convection stagnation point  flow with radiation and slip condition", Scientia Iranica, Transactions B, Mechanical Engineering, 24(2), p. 698 (2017).
40. Ijaz, N., Zeeshan, A., Bhatti, M.M., and Ellahi, R."Analytical study on liquid-solid particles interaction in the presence of heat and mass transfer through a wavy channel", Journal of Molecular Liquids, 250, pp. 80-87 (2018).
41. Nayak, M.K., Hakeem, A.K., and Makinde, O.D. "Influence of Catteneo-Christov heat  flux model on mixed convection flow of third grade nanofluid over an inclined stretched Riga plate", In Defect and Diffusion Forum, 387, pp. 121-134, Trans Tech Publications Ltd (2018).