Thermo-Solutal Chemically Reacting Micropolar Fluid Past a Permeable Stretching Porous Sheet

Abstract:

The boundary layer flow, heat and mass transfer over a permeable stretching sheet due to a chemically reacting micropolar fluid with slip and convective boundary conditions have been analyzed. Transverse magnetic field clubbed with electric field is also considered for the sake of brevity. Governing nonlinear coupled PDEs are transformed to nonlinear ODEs with the use of suitable similarity transformation. However, analytical solutions to these transformed equations are not useful therefore; numerical solution is carried out using Runge-Kutta fourth order with shooting technique. The characteristics of the embedded parameters are obtained and presented through graphs. Validation of the proposed work with earlier established results are shown in tables and these are in good agreement. From the careful observation the major outcomes are: induced magnetic field decelerates the flow, enhances the thickness of thermal boundary layer temperature whereas applied electric field decelerates the thickness of thermal boundary layer. Both electric field and slip parameter accelerates the angular momentum. Temperature and concentration magnitudes are accelerated at the sheet with an increase of slip parameter. Furthermore, Schmidt number and first order chemical reaction reduces the concentration boundary layer thickness. PACS Number: 05.45-a; 05.70-Ce.

• Periodical: Defect and Diffusion Forum (Volume 392)
• Pages: 42-59
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.392.42
• Online since: April 2019
• Authors: Mohd Shamshuddin*, Thirupathi Thumma, S.R. Mishra
• Keywords: Chemical Reaction, Convective Boundary Conditions, Mass Transfer, Micropolar Fluid, Partial Slip, Stretching Sheet

References

[1] A.C. Eringen, Theory of Micropolar fluid, J. Math. Mech. 16 (1966) 1-18.

[2] T. Ariman, M.A. Turk and N.D. Sylvester, Micro continuum Fluid Mechanics – A Review, Int. J. Eng. Sci. 11(1973) 905-930.

[3] S.K. Lakshmana Rao, Stability of micropolar fluid motions, Int. J. Eng. Sci. 8 (1970)753-762.

[4] S. Sharidan, Mathematical Modelling of g-Jitter Induced Free Convection, Universiti Teknologi Malaysia: Ph. D Thesis, (2005).

[5] N. Kishan, S. Maripala, Thermophoresis and viscous dissipation effects on Darcy-Forchheimer MHD mixed convection in a fluid saturated porous media, Adv. Appl. Sci. Res. 3(1) (2012) 60-74.

DOI: 10.14445/22315381/ijett-v10p245

[6] C. Soret, Influence de la temperature sur la distribution des sels dans leurs solutions, C. R. Acad. Sci. Paris. 91(1880) 289–291.

[7] M. Turkyilmazoglu, Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: Exact solutions, Int. J. Heat and Mass Transfer. 106 (2017) 127-134.

DOI: 10.1016/j.ijheatmasstransfer.2016.10.056

[8] T. Thirupathi, MD. Shamshuddin, Buoyancy ratio and heat source effects on MHD flow over an inclined non-linearly stretching sheet, Frontiers in Heat and Mass Transfer. 10 (2018) 1-12.

DOI: 10.5098/hmt.10.5

[9] H. Kumar, Heat transfer over a stretching porous sheet subjected to power law heat flux in presence of heat source, Thermal Sci. 15 (2011) 187-194.

DOI: 10.2298/tsci100331074k

[10] E.M.A. Elbashbeshy, D.A. Aldawody, Heat transfer over an unsteady stretching surface with variable heat flux in the presence of a heat source or sink. Computer & Mathematics with Applications. 60(10) (2010) 2806-2811.

DOI: 10.1016/j.camwa.2010.09.035

[11] M. Waqas, M. Farooq, M.I. Khan, A. Alsaedi, T. Hayat, T. Yasmeen, Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int. J. Heat Mass Transfer. 102 (2016) 766-772.

DOI: 10.1016/j.ijheatmasstransfer.2016.05.142

[12] A. Shaheen, A. Muhammad, A. Kashif, MHD flow of heat transfer analysis of micropolar fluid through a porous medium between two stretchable disks using Quasi-Linearization method, Iranian J. Chem. Eng. 36(4) (2017) 1-15.

[13] M.A.A. Mahmoud, S.E. Waheed, MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity. J. Egyptian Math Soc. 20 (2012) 20-27.

DOI: 10.1016/j.joems.2011.12.009

[14] D.H. Doh, M. Muthtamilselvan, Thermophoretic particle deposition on magnetohydrodynamic flow of micropolar fluid due to a rotating disk. Int. J. Mech. Sci. 130 (2017) 350-359.

DOI: 10.1016/j.ijmecsci.2017.06.029

[15] M. Ramzan, M. Farooq, T. Hayat, J.D. Chung, Radiative and Joule heating effect in the MHD flow of a micropolar fluid with partial slip and convective boundary condition, J. Molecular Liquids. 221 (2016) 394-400.

DOI: 10.1016/j.molliq.2016.05.091

[16] D. Pal, B. Talukdar, Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation, Central European J. Phys. 10 (2012) 1150-1167.

DOI: 10.2478/s11534-012-0063-6

[17] D. Pal, S. Biswas, Perturbation analysis of magnetohydrodynamics oscillatory flow on convective-radiative heat and mass transfer of micropolar fluid in a porous medium with chemical reaction, Eng. Sci. Tech.: An Int. J. 19 (2016) 444-462.

DOI: 10.1016/j.jestch.2015.09.003

[18] P.K. Rout, S.N. Sahoo, G.C. Dash, S.R. Mishra, Chemical reaction effect on MHD free convection flow in a micropolar fluid, Alexandria Eng. J. (2016). https://doi.org/10.1016/j.aej.2016.04.033.

DOI: 10.1016/j.aej.2016.04.033

[19] S. Siva Reddy, MD. Shamshuddin, Heat and mass transfer on the MHD flow of a micropolar fluid in the presence of viscous dissipation and chemical reaction, Procedia Eng. 127 (2015) 885-892.

DOI: 10.1016/j.proeng.2015.11.426

[20] K. Gangadhar, K.L. Narayana, P.S. Kumar, B.R. Kumar, MHD micropolar fluid flow over a stretching permeable sheet in the presence of thermal radiation and thermal slip flow: a numerical study, IOP conf. Series: Material Sci. Eng., 263, Article ID: 062010, 2017. https://doi/org/10.1088/1757-899X/263/6/062010.

DOI: 10.1088/1757-899x/263/6/062010

[21] K. Suneetha, S.M. Ibrahim, G.V. Ramana Reddy, Radiation and heat source effect on MHD flow over a permeable stretching sheet through porous stratum with chemical reaction, Multidiscipline Modelling in Materials and Structures. (2018). https://doi.org/10/1108/MMMS-122017-0159.

DOI: 10.1108/mmms-12-2017-0159

[22] K.P. Priyadarsan, S. Panda, Effect of variable fluid properties on MHD mixed convection flow of second-grade fluid over a linear Heated stretching sheet with a convective boundary condition, Proc. Natl. Acad. Sci., India-Section A Phys. Sci. (2018). https://doi.org/10.1007/s40010-018-0559-6.

DOI: 10.1007/s40010-018-0559-6

[23] E.O. Fatunmbi, A. Adeniyan, Heat and mass transfer in MHD micropolar fluid flow over a stretching sheet with velocity and thermal slip conditions, Open J. Fluid Dynamics. 8 (2018) 195-215.

DOI: 10.4236/ojfd.2018.82014

[24] D. Srinivasacharya, K. Himabindu, Effect of Slip and convective boundary conditions on entropy generation in a porous channel due to micropolar fluid flow, Int. J. Nonlinear Sci. Numer. Simult. 19(1) (2018) 11-24.

DOI: 10.1515/ijnsns-2016-0056

[25] S.R. Mishra, M.M. 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 Eng. (2018). https://doi.org/10.1515/nIeng-2017-0126.

DOI: 10.1515/nleng-2017-0126

[26] S.R. Mishra, I. Khan, Q.M. Al-mdallal, T. Asifa, Free convective micropolar fluid flow and heat transfer over a shrinking sheet with heat source, Case studies in Thermal Eng. 11 (2018) 113-119.

DOI: 10.1016/j.csite.2018.01.005

[27] MD. Shamshuddin, S.R. Mishra, O. Anwar Beg, A. Kadir, Unsteady reactive radiative micropolar flow, heat and mass transfer from an inclined plate with Joule heating: A model for electro-conductive polymer processing, Proc. IMechE Part C: J. Mech. Eng. Sci. (2018). https://doi.org/10.1177/094406218768837.

DOI: 10.1177/0954406218768837

[28] J.A. Shercliff, A text book of magnetohydrodynamics, Pergamon Press, New York, (1965).

[29] G.S. Guram, A.C. Smith, Stagnation point flows of micropolar fluids with strong and weak interactions, Computers and Mathematics with Applications. 6 (1980) 231-233.

DOI: 10.1016/0898-1221(80)90030-9

[30] G. Ahmadi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Sci. 14 (1976) 639-646.

DOI: 10.1016/0020-7225(76)90006-9

[31] J. Peddieson, An application of the micropolar fluid model to the calculation of turbulent shear flow, Int. J. Eng. Sci. 10 (1972) 23-32.

DOI: 10.1016/0020-7225(72)90072-9

[32] V.K. Stokes, Theories of Fluids with Microstructure, Springer, New York, (1984).

[33] B. Mohanty, S.R. Mishra, H.B. Pattnaik, Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet, Alexandria Eng. J. 54(2) (2015) 223-232.

DOI: 10.1016/j.aej.2015.03.010

[34] T. Thirupathi, S.R. Mishra, Effect of Viscous Dissipation and Joule Heating on MHD Jeffery Nanofluid Flow with and Without Multi Slip Boundary Conditions, J. Nanofluids 7(3) (2018) 516–526.

DOI: 10.1166/jon.2018.1469

[35] MD. Shamshuddin, S.R. Mishra, O. Anwar Beg and A. Kadir, Lie Symmetry Analysis and numerical solutions for Thermo-solutal chemically reacting radiative micropolar flow from an inclined porous plate, Heat Transfer Asian Reaserch. 47(7) (2018) 918-940. https://doi.org/10.1002/htj.21358.

DOI: 10.1002/htj.21358

[36] M.J. Uddin O. Anwar Beg, M.N. Uddin, A.I.M. Ismail, Numerical solutions of thermo-solutal mixed convective slip flow from a radiative plate with convective boundary conditions, Journal of Hydrodynamics. 28(3) (2016) 451-461.

DOI: 10.1016/s1001-6058(16)60649-2

[37] T. Hayat, A. Shafiq, A. Alsaedi, S.A. Shahzad, Unsteady MHD flow over exponentially stretching sheet with slip conditions, Appl. Math. Mech. 37(2) (2016) 193-208.

DOI: 10.1007/s10483-016-2024-8