Simultaneous effects of chemical reaction and Ohmic heating with heat and mass transfer over a stretching surface:A numerical study

doi:10.1016/j.cjche.2016.09.016

摘要/Abstract

摘要： In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number. The governing flow problem comprises of momentum, continuity, thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms, which are then, solved numerically with the help of Successive Linearization method (SLM) and Chebyshev Spectral collocation method. Numerical values of skin friction coefficient, local Nusselt number, and Sherwood number are also taken into account with the help of tables. The physical influence of the involved parameters of flow velocity, temperature and concentration distribution is discussed and demonstrated graphically. The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.

关键词: Ohmic heating, Heat and mass transfer, Chemical reaction, Successive linearization method

Abstract: In this article, we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet. The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number. The governing flow problem comprises of momentum, continuity, thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms, which are then, solved numerically with the help of Successive Linearization method (SLM) and Chebyshev Spectral collocation method. Numerical values of skin friction coefficient, local Nusselt number, and Sherwood number are also taken into account with the help of tables. The physical influence of the involved parameters of flow velocity, temperature and concentration distribution is discussed and demonstrated graphically. The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.

Key words: Ohmic heating, Heat and mass transfer, Chemical reaction, Successive linearization method

S. R. Mishra, M. M. Bhatti. Simultaneous effects of chemical reaction and Ohmic heating with heat and mass transfer over a stretching surface:A numerical study[J]. , 2017, 25(9): 1137-1142.

参考文献

[1] P.D. McCormack, L.J. Crane, Physical Fluid Dynamics, Academic Press, New York, 1973.
[2] L.J. Grubka, K.M. Bobba, Heat transfer characteristics of a continuous, stretching surface with variable temperature, J. Heat Transf. 107(1) (1985) 248-250.
[3] S.J. Liao, I. Pop, Explicit analytic solution for similarity boundary layer equations, Int. J. Heat Mass Transf. 47(1) (2004) 75-85.
[4] R. Nazar, N. Amin, I. Pop, Unsteady boundary layer flow due to a stretching surface in a rotating fluid, Mech. Res. Commun. 31(1) (2004) 121-128.
[5] S. Nadeem, R.U. Haq, N.S. Akbar, Z.H. Khan, MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alex. Eng. J. 52(4) (2013) 577-582.
[6] N.S. Akbar, S. Nadeem, R.U. Haq, Z.H. Khan, Numerical solutions of Magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet, Indian J. Phys. 87(11) (2013) 1121-1124.
[7] N.S. Akbar, Z.H. Khan, R.U. Haq, S. Nadeem, Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet, Appl. Math. Mech. 35(7) (2014) 813-820.
[8] N.S. Akbar, A. Ebaid, Z.H. Khan, Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet, J. Magn. Magn. Mater. 382(2015) 355-358.
[9] M.M. Bhatti, M.M. Rashidi, Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet, J. Mol. Liq. 221(2016) 567-573.
[10] M.M. Bhatti, T. Abbas, M.M. Rashidi, A new numerical simulation of MHD stagnationpoint flow over a permeable stretching/shrinking sheet in porous media with heat transfer, Iran. J. Sci. Technol. Trans. A Sci. (2016) 1-7.
[11] H.I. Andersson, J.B. Aarseth, B.S. Dandapat, Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Transf. 43(1) (2000) 69-74.
[12] H.S. Takhar, A.J. Chamkha, G. Nath, Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species, Int. J. Eng. Sci. 38(12) (2000) 1303-1314.
[13] S.R. Mishra, G.C. Dash, M. Acharya, Free convective flow of visco-elastic fluid in a vertical channel with Dufour effect, World Appl. Sci. J. 28(9) (2013) 1275-1280.
[14] S.A. Devi, R. Kandasamy, Effects of chemical reaction, heat and mass transfer on nonlinear MHD laminar boundary-layer flow over a wedge with suction or injection, Int. Commun. Heat Mass Transf. 29(5) (2002) 707-716.
[15] S. Baag, S.R. Mishra, G.C. Dash, M.R. Acharya, Numerical investigation on MHD micropolar fluid flow toward a stagnation point on a vertical surface with heat source and chemical reaction, J. King Saud Univ. Eng. Sci. 29(1) (2017) 75-83.
[16] S. Jena, S.R. Mishra, G.C. Dash, Chemical reaction effect on MHD Jeffery fluid flow over a stretching sheet through porous media with heat generation/absorption, Int. J. Appl. Comput. Math. (2016) 1-14.
[17] R.S. Tripathy, G.C. Dash, S.R. Mishra, S. Baag, Chemical reaction effect on MHD free convective surface over a moving vertical plate through porous medium, Alex. Eng. J. 54(3) (2015) 673-679.
[18] R.S. Tripathy, G.C. Dash, S.R. Mishra, M.M. Hoque, Numerical analysis of hydromagnetic micropolar fluid along a stretching sheet embedded in porous medium with non-uniform heat source and chemical reaction, Eng. Sci. Technol. 19(3) (2016) 1573-1581.
[19] M. Pirmohammadi, M. Ghassemi, Effect of magnetic field on convection heat transfer inside a tilted square enclosure, Int. Commun. Heat Mass Transf. 36(7) (2009) 776-780.
[20] M.F. El-Amin, Combined effect of viscous dissipation and Joule heating on MHD forced convection over a non-isothermal horizontal cylinder embedded in a fluid saturated porous medium, J. Magn. Magn. Mater. 263(3) (2003) 337-343.
[21] E.M. AboEldahab, Radiation effect on heat transfer in an electrically conducting fluid at a stretching surface with a uniform free stream, J. Phys. D. Appl. Phys. 33(24) (2000) 3180.
[22] G.C. Dash, R.S. Tripathy, M.M. Rashidi, S.R. Mishra, Numerical approach to boundary layer stagnation-point flow past a stretching/shrinking sheet, J. Mol. Liq. 221(2016) 860-866.
[23] D. Pal, H. Mondal, Hydromagnetic non-Darcy flow and heat transfer over a stretching sheet in the presence of thermal radiation and Ohmic dissipation, Commun. Nonlinear Sci. Numer. Simul. 15(5) (2010) 1197-1209.
[24] B. Mohanty, S.R. Mishra, H.B. Pattanayak, Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet through porous media, Alex. Eng. J. 54(2) (2015) 223-232.
[25] S.R. Mishra, G.C. Dash, P.K. Pattnaik, Flow of heat and mass transfer on MHD free convection in a micropolar fluid with heat source, Alex. Eng. J. 54(3) (2015) 681-689.
[26] K. Bhattacharyya, Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet, Int. Commun. Heat Mass Transf. 38(7) (2011) 917-922.
[27] M.M. Bhatti, A. Shahid, M.M. Rashidi, Numerical simulation of fluid flow over a shrinking porous sheet by successive linearization method, Alex. Eng. J. 55(1) (2016) 51-56.
[28] M.M. Bhatti, T. Abbas, M.M. Rashidi, M.E.S. Ali, Numerical simulation of entropy generation with thermal radiation on MHD Carreau nanofluid towards a shrinking sheet, Entropy 18(6) (2016) 200.
[29] M.M. Bhatti, M.M. Rashidi, Entropy generation with nonlinear thermal radiation in MHD boundary layer flow over a Permeable shrinking/stretching sheet:Numerical solution, J. Nanofluids 5(4) (2016) 543-548.
[30] M.M. Bhatti, M.M. Rashidi, Numerical simulation of entropy generation on MHD Nanofluid towards a stagnation point flow over a stretching surface, Int. J. Appl. Comput. Math. (2016) 1-15.
[31] T. Zhu, W. Ye, Origin of Knudsen forces on heated microbeams, Phys. Rev. E 82(3) (2010) 036308.
[32] T. Zhu, W. Ye, J. Zhang, Negative Knudsen force on heated microbeams, Phys. Rev. E 84(5) (2011) 056316.
[33] H. Liu, K. Xu, T. Zhu, W. Ye, Multiple temperature kinetic model and its applications to micro-scale gas flows, Comput. Fluids 67(2012) 115-122.
[34] T. Zhu, W. Ye, Theoretical and numerical studies of noncontinuum gas-phase heat conduction in micro/nano devices, Numer. Heat Transf. B Fundam. 57(3) (2010) 203-226.
[35] J. Qing, M.M. Bhatti, M.A. Abbas, M.M. Rashidi, M.E.S. Ali, Entropy generation on MHD Casson nanofluid flow over a porous stretching/shrinking surface, Entropy 18(4) (2016) 123.
[36] M.M. Bhatti, T. Abbas, M.M. Rashidi, M.E.S. Ali, Z. Yang, Entropy generation on MHD Eyring-Powell nanofluid through a permeable stretching surface, Entropy 18(6) (2016) 224.
[37] R. Sharma, Effect of viscous dissipation and heat source on unsteady boundary layer flow and heat transfer past a stretching surface embedded in a porous medium using element free Galerkin method, Appl. Math. Comput. 219(3) (2012) 976-987.
[39] C.H. Chen, Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat Mass Transf. 33(5-6) (1998) 471-476.