MHD Slips Flow of a Micro-polar Fluid Due to Moving Plate in Porous Medium with Chemical Reaction and Thermal Radiation: A Lie Group Analysis
Tóm tắt
An attempt is made to investigation of MHD natural convection flow of a micropolar fluid due to a permeable moving plate in porous medium in the presence of chemical reaction and radiation. The Lie group analysis used to create similarity transformations and by using those transformations, the system of governing highly non-linear partial differential equations is converted into a set of non-linear coupled ordinary differential equations. The ordinary differential equations thus obtained have been solved by utilizing Keller box method. Numerical solutions for the skin-friction coefficient, Nusselt and Sherwood numbers as well as the velocity, micro-rotation, temperature and concentration are presented graphically for different parametric conditions and discussed in detail. The results show that the skin-friction coefficient reduces with greater values of micro-polar or material parameter and the heat transfer rate advances with reduction in micropolar and radiation parameters. The mass transfer rate accelerates with higher values of chemical reaction parameter.
Tài liệu tham khảo
Eringen, A.C.: Theory of micropolar fluid. J. Math. Mech. 16, 1–18 (1966)
Eringen, A.C.: Theory of thermomicrofluids. J. Math. Anal. Appl. 38, 480–496 (1972)
Ariman, T., Turk, M.A., Sylvester, N.D.: Microcontinuum fluid mechanics—a review. Int. J. Eng. Sci. 11, 905–930 (1973)
Ariman, T., Turk, M.A., Sylvester, N.D.: Applications of microcontinuum fluid mechanics. Int. J. Eng. Sci. 12, 273–293 (1974)
Eringen, A.C.: Microcontinuum Field Theories, vol. I. Springer, New York (2001)
Łukaszewicz, G.: Micropolar Fluids: Theory and Application. Birkhäuser, Basel (1999)
Singh, K., Kumar, M.: Melting heat transfer in boundary layer stagnation point flow of MHD micro-polar fluid towards a stretching/shrinking surface. Jordan J. Mech. Ind. Eng. 8, 403–408 (2014)
Haque, M.Z., Alam, M.M., Ferdows, M., Postelnicu, A.: Micropolar fluid behaviors on steady MHD free convection and mass transfer flow with constant heat and mass fluxes, joule heating and viscous dissipation. J. King Saud Univ. Eng. Sci. 24, 71–84 (2012)
Chang, Cheng-Long: Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect. Commun. Nonlinear Sci. Numer. Simul. 13, 624–636 (2008)
Zadravec, M., Hribersek, M., Skerget, L.: Natural convection of micro-polar fluid in an enclosure with boundary element method. Eng. Anal. Bound. Elem. 33, 485–492 (2009)
Alloui, Z., Vasseur, P.: Natural convection in a shallow cavity filled with a micropolar fluid. Int. J. Heat Mass Transf. 53, 2750–2759 (2010)
Cheng, Ching-Yang: Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature. Int. Commun. Heat Mass Transf. 38, 429–433 (2011)
Saleem, M., Asghar, S., Hossain, M.A.: Natural convection flow of micropolar fluid in a rectangular cavity heated from below with cold sidewalls. Math. Comput. Model. 54, 508–518 (2011)
Srinivasacharya, D., RamReddy, Ch.: Heat and mass transfer by natural convection in a doubly stratified non-Darcy micropolar fluid. Int. Commun. Heat Mass Transf. 37, 873–880 (2010)
Mishra, U., Singh, G.: Dual solutions of mixed convection flow with momentum and thermal slip flow over a permeable shrinking cylinder. Comput. Fluids 93, 107–115 (2014)
Roşca, N.C., Pop, I.: Boundary layer flow past a permeable shrinking sheet in a micropolar fluid with a second order slip flow model. Eur. J. Mech. B/Fluids 48, 115–122 (2014)
Das, K.: Lie group analysis for nanofluid flow past a convectively heated stretching surface. Appl. Math. Comput. 221, 547–557 (2013)
Uddin, M.J., Kabir, M.N., Alginahi, Y.M.: Lie group analysis and numerical solution of magneto-hydrodynamic free convective slip flow of micropolar fluid over a moving plate with heat transfer. Comput. Math Appl. 70, 846–856 (2015)
Das, K.: Slip effects on MHD mixed convection stagnation point flow of a micro-polar fluid towards a shrinking vertical sheet. Comput. Math Appl. 63, 255–267 (2012)
Mahmoud, M.A.A., Waheed, S.E.: MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity. J. Egypt. Math. Soc. 20, 20–27 (2012)
Mukhopadhyay, S.: Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation. Ain Shams Eng. J. 4, 485–491 (2013)
Aman, F., Ishak, A., Pop, I.: Magnetohydrodynamic stagnation-point flow towards a stretching/shrinking sheet with slip effects. Int. Commun. Heat Mass Transf. 47, 68–72 (2013)
Bourantas, G.C., Loukopoulos, V.C.: MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. Int. Commun. Heat Mass Transf. 79, 930–944 (2014)
EL-Kabeir, S.M.M., Chamkha, A.J., Rashad, A.M.: Heat and mass transfer by MHD stagnation-point flow of a power-law fluid towards a stretching surface with radiation, chemical reaction and Soret and Dufour effects. Int J Chem React Eng 8, 1–18 (2010)
Rashad, A.M., Chamkha, A.J., Abdou, M.M.M.: MHD free convective heat and mass transfer of a chemically-reacting fluid from radiate stretching surface embedded in a saturated porous medium. Int. J. Chem. React. Eng. 9, 1–15 (2011)
Das, K., Jana, S., Kundu, P.K.: Thermophoretic MHD slip flow over a permeable surface with variable fluid properties. Alex. Eng. J. 54, 35–44 (2015)
Siddiqa, S., Faryad, A., Begum, N., Hossain, M.A., Gorla, R.S.R.: Periodic magneto-hydrodynamic natural convection flow of a micropolar fluid with radiation. Int. J. Therm. Sci. 111, 215–222 (2017)
Turkyilmazoglu, M.: Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: Exact solutions. Int. J. Heat Mass Transf. 106, 127–134 (2017)
Chamkha, A.J., Rashad, A.M.: Heat and mass transfer from truncated cones with variable wall temperature and concentration in the presence of chemical reaction effects. Int. J. Numer. Methods Heat Fluid Flow 22(3), 357–376 (2012)
Rashad, A.M., Chamkha, A.J., EL-Kabeir, S.M.M.: Effects of radiation and chemical reaction on heat and mass transfer by natural convection in a micropolar fluid saturated porous medium with streamwise temperature and species concentration variations. Heat Transf. Res. 45(8), 795–815 (2014)
Chamkha, A.J., EL-Kabeir, S.M.M., Rashad, A.M.: Unsteady coupled heat and mass transfer by mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface in the presence of radiation and chemical reaction. Prog. Comput. Fluid Dyn. 15(3), 186–196 (2015)
Mallikarjuna, B., Rashad, A.M., Chamkha, Ali J., Hariprasad Raju, S.: Chemical reaction effects on MHD convective heat and mass transfer flow past a rotating vertical cone embedded in a variable porosity regime. Afrika Matematika 27(3), 646–665 (2016)
Mabood, F., Ibrahim, S.M., Rashidi, M.M., Shadloo, M.S., Lorenzini, G.: Non-heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation. Int. J. Heat Mass Transf. 93, 674–682 (2016)
Mohamed, R.A., Abo-Dahab, S.M.: Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation. Int. J. Therm. Sci. 48, 1800–1813 (2009)
Das, K.: Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference. Int. J. Heat Mass Transf. 54, 3505–3513 (2011)
Singh, K., Kumar, M.: Effects of thermal radiation on mixed convection flow of a micro-polar fluid from an unsteady stretching surface with viscous dissipation and heat generation/absorption. Int. J. Chem. Eng. 2016(4), 1–10 (2016)
Siddheshwar, P.G., Manjunath, S.: Unsteady convective diffusion with heterogeneous chemical reaction in a plane-Poiseuille flow of a micropolar fluid. Int. J. Eng. Sci. 38, 765–783 (2000)
Kandasamy, R., Muhaimin, Hashim, I., Ruhaila, : Thermophoresis and chemical reaction effects on non-Darcy mixed convective heat and mass transfer past a porous wedge with variable viscosity in the presence of suction or injection. Nucl. Eng. Des. 238, 2699–2705 (2008)
Magyari, E., Chamkha, A.J.: Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface: The full analytical solution. Int. J. Therm. Sci. 49, 1821–1828 (2010)
Das, K.: Influence of thermophoresis and chemical reaction on MHD micropolar fluid flow with variable fluid properties. Int. J. Heat Mass Transf. 55, 7166–7174 (2012)
Singh, K., Kumar, M.: The effect of chemical reaction and double stratification on MHD free convection in a micropolar fluid with heat generation and Ohmic heating. Jordan J. Mech. Ind. Eng. 9(4), 279–288 (2015)
Singh, K., Kumar, M.: Influence of chemical reaction on heat and mass transfer flow of a micropolar fluid over a permeable channel with radiation and heat generation. J. Thermodyn. 2016, 1–10 (2016)
Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, New York (1984)