Effect of suction on the MHD flow in a doubly-stratified micropolar fluid over a shrinking sheet

This paper investigates the influence of suction on the flow, heat and mass transfer characteristics over a permeable shrinking sheet immersed in a doubly stratified micropolar fluid.  The model which consists of partial differential equations is converted into a set of nonlinear equations using similarity transformations and then solved using the bvp4c solver.  Numerical results obtained are presented graphically for the distributions of velocity, angular velocity, temperature and concentration profiles within the boundary layer for various values of the magnetic parameter and wall mass suction parameter.  It is visualized that the enhancement of suction parameter will increase the skin friction, heat transfer rate (local Nusselt number) and Sherwood number.  It is also found that as the magnetic parameter increase, there is an increment in the skin friction while opposite results are obtained for the local Nusselt number and Sherwood number.

double stratification
магнітне поле
micropolar fluid
mixed convection
suction effect
  1. Gad-el-Hak M.  Flow control by suction.  Structure of Turbulence and Drag Reduction. 357–360 (1990).
  2. Arunraj R., Logesh K., Balaji V., Ravichandran T., Yuvashree G. K.  Experimental investigation of lift enhancement by suction-assisted delayed separation of the boundary layer on NACA 0012 airfoil.  International Journal of Ambient Energy.  40 (3), 243–247 (2019).
  3. Miklavčič M., Wang C. Y.  Viscous flow due to a shrinking sheet.  Quarterly of Applied Mathematics.  64, 283–290 (2006).
  4. Sun J., Sun X., Huang D.  Aerodynamics of vertical-axis wind turbine with boundary layer suction –- Effects of suction momentum.  Energy.  209, 118446 (2020).
  5. Khashi'ie N. S., Arifin N. M., Pop I., Wahid N. S.  Effect of suction on the stagnation point flow of hybrid nanofluid toward a permeable and vertical Riga plate.  Heat Transfer.  50 (2), 1895–1910 (2021).
  6. Eringen A. C.  Theory of micropolar fluids.  Journal of Mathematics and Mechanics.  16 (1), 1–18 (1966).
  7. Bhattacharyya K., Mukhopadhyay S., Layek G. C., Pop I.  Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet.  International Journal of Heat and Mass Transfer.  55 (11–12), 2945–2952 (2012).
  8. Yacob N. A., Ishak A.  Micropolar fluid flow over a shrinking sheet.  Meccanica.  47, 293–299  (2012).
  9. Rosali H., Ishak A., Pop I.  Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction.  International Communications in Heat and Mass Transfer.  39 (6), 826–829 (2012).
  10. Pavlov K. B.  Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface.  Magnetohydrodynamics.  10 (4), 507–510 (1974).
  11. Chakrabarti A., Gupta A. S.  Hydromagnetic flow and heat transfer over a stretching sheet.  Quarterly of Applied Mathematics.  37, 73–78 (1979).
  12. Sandeep N., Sulochana C.  Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching/shrinking sheet with non-uniform heat source/sink.  Engineering Science and Technology, an International Journal.  18 (4), 738–745 (2015).
  13. Waqas M., Farooq M., Khan M.I., Alsaedi A., Hayat T., Yasmeen T.  Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition.  International Journal of Heat and Mass Transfer.  102, 766–772 (2016).
  14. Yahaya R. I., Arifin N. M., Mohamed Isa S. S., Rashidi M. M.  Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis.  Mathematical Methods in the Applied Sciences.  44 (13), 10578–10608 (2021).
  15. Lund L. A., Omar Z., Dero S., Khan I.  Linear stability analysis of MHD flow of micropolar fluid with thermal radiation and convective boundary condition: Exact solution.  Heat Transfer – Asian Research.  49 (1), 461–476 (2020).
  16. Lund L. A., Omar Z., Khan U., Khan I., Baleanu D., Nisar K. S.  Stability analysis and dual solutions of micropolar nanofluid over the inclined stretching/shrinking surface with convective boundary condition.  Symmetry.  12 (1), 74 (2020).
  17. Lund L. A., Omar Z., Khan I., Kadry S., Rho S., Mari I. A., Nisar K. S.  Effect of viscous dissipation in heat transfer of MHD flow of micropolar fluid partial slip conditions: Dual solutions and stability analysis.  Energies.  12 (24), 4617 (2019).
  18. Lund L. A., Omar Z., Khan I., Baleanu D., Sooppy Nisar K.  Triple solutions and stability analysis of micropolar fluid flow on an exponentially shrinking surface.  Crystals.  10 (4), 283 (2020).
  19. Abbas N., Nadeem S., Malik M. Y.  On extended version of Yamada–Ota and Xue models in micropolar fluid flow under the region of stagnation point.  Physica A.  542, 123512 (2020).
  20. Nadeem S., Amin A., Abbas N.  On the stagnation point flow of nanomaterial with base viscoelastic micropolar fluid over a stretching surface.  Alexandria Engineering Journal.  59 (3), 1751–1760 (2020).
  21. Bouhal T., Fertahi S., Agrouaz Y., El Rhafiki T., Kousksou T., Jamil A.  Numerical modeling and optimization of thermal stratification in solar hot water storage tanks for domestic applications: CFD study.  Solar Energy.  157, 441–455 (2017).
  22. Chang C. L., Lee Z. Y.  Free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid.  Mechanics Research Communications.  35 (6), 421–427 (2008).
  23. Srinivasacharya D., Upendar M.  Effect of double stratification on MHD free convection in a micropolar fluid.  Journal of the Egyptian Mathematical Society.  21 (3), 370–378 (2013).
  24. Mishra S. R., Pattnaik P. K., Dash G. C.  Effect of heat source and double stratification on MHD free convection in a micropolar fluid.  Alexandria Engineering Journal.  54 (3), 681–689 (2015).
  25. Khashi'ie N. S., Arifin N. M., Nazar R., Hafidzuddin E. H., Wahi N., Pop I.  Mixed convective flow and heat transfer of a dual stratified micropolar fluid induced by a permeable stretching/shrinking sheet.  Entropy.  21 (12), 1162 (2019).
  26. Khan M. I., Tamoor M., Hayat T., Alsaedi A.  MHD boundary layer thermal slip flow by nonlinearly stretching cylinder with suction/blowing and radiation.  Results in Physics.  7, 1207–1211 (2017).
  27. Khan A. A., Zaimi K., Sufahani S. F., Ferdows M.  MHD Flow and Heat Transfer of Double Stratified Micropolar Fluid over a Vertical Permeable Shrinking/Stretching Sheet with Chemical Reaction and Heat Source.  Journal of Advanced Research in Applied Sciences and Engineering Technology.  21 (1), 1–14 (2020).
  28. Khashi'ie N. S., Arifin N. M., Rashidi M. M., Hafidzuddin E. H., Wahi N.  Magnetohydrodynamics (MHD) stagnation point flow past a shrinking/stretching surface with double stratification effect in a porous medium.  Journal of Thermal Analysis and Calorimetry.  139, 3635–3648 (2020).
  29. Khashi'ie N. S., Arifin N. M., Hafidzuddin E. H., Wahi N.  Thermally stratified flow of Cu-Al2O3/water hybrid nanofluid past a permeable stretching/shrinking circular cylinder.  Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 63 (1), 154–163 (2019).
  30. Khashi'ie N. S., Hafidzuddin E. H., Arifin N. M., Wahi N.  Stagnation point flow of hybrid nanofluid over a permeable vertical stretching/shrinking cylinder with thermal stratification effect.  CFD Letters.  12 (2), 80–94 (2020).
  31. Guram G. S., Smith A. C.  Stagnation flows of micropolar fluids with strong and weak interactions.  Computers & Mathematics with Applications.  6 (2), 213–233 (1980).
  32. Jena S. K., Mathur M. N.  Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate.  International Journal of Engineering Science. 19 (11), 1431–1439 (1981).
  33. Ahmadi G.  Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate.  International Journal of Engineering Science.  14 (7), 639–646 (1976).
  34. Peddieson Jr. J.  An application of the micropolar fluid model to the calculation of a turbulent shear flow.  International Journal of Engineering Science.  10 (1), 23–32 (1972).
  35. Daniel Y. S., Daniel S. K.  Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method.  Alexandria Engineering Journal.  54 (3), 705–712 (2015).
  36. Takhar H. S., Agarwal R. S., Bhargava R., Jain S.  Mixed convection flow of a micropolar fluid over a stretching sheet.  Heat and Mass Transfer.  34, 213–219 (1998).