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Chemically reacting fluid flow induced by an exponentially accelerated infinite vertical plate in a magnetic field and variable temperature via LTT and FEM. (English) Zbl 1474.76104

Summary: In this research paper, we found both numerical and analytical solutions for the effect of chemical reaction on unsteady, incompressible, viscous fluid flow past an exponentially accelerated vertical plate with heat absorption and variable temperature in a magnetic field. The flow problem is governed by a system of coupled non-linear partial differential equations with suitable boundary conditions. We have solved the governing equations by an efficient, accurate, powerful finite element method (FEM) as well as Laplace transform technique (LTT). The evaluation of the numerical results are performed and graphical results for the velocity, temperature and concentration profiles within the boundary layer are discussed. Also, the expressions for the skin-friction, Nusselt number and the Sherwood number coefficients have been derived and discussed through graphs and tabular forms for different values of the governing parameters.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76V05 Reaction effects in flows
76M10 Finite element methods applied to problems in fluid mechanics
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[1] M. M. Rashidi, N. Vishnu Ganesh, A. K. Abdul Hakeem, B. GangaBuoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation, J. Mol. Liq. 198(2014), 234-238.
[2] M. M. Rashidi, M. Ali, N. Freidoonimehr, F. Nazari,Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm, Energy55(2013), 497-510.
[3] M. M. Rashidi, Behnam Rostami, Navid Freidoonimehr, Saeid Abbasbandy,Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects, Ain Shams Eng. J.5(2014), 901-912.
[4] M. M. Rashidi, Esmaeel Erfani,A new analytical study of MHD stagnation-point flow in porous media with heat transfer, Comput. Fluids40(2011), 172-178. · Zbl 1245.76160
[5] M. M. Rashidi,The modified differential transform method for solving MHD boundary-layer equations, Comput. Phys. Commun.180(2009), 2210-2217. · Zbl 1197.76156
[6] M. M. Rashidi, T. Hayat, E. Erfani, S. A. Mohimanian Pour, A. A. Hendi,Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk, Commun. Nonlinear Sci. Numer. Simul.16(2011), 4303-4317. · Zbl 1419.76712
[7] O. A. B´eg, M. J. Uddin, M. M. Rashidi, N. Kavyani,Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects, J. Eng. Thermophys.23(2014), 79-97.
[8] N. Freidoonimehr, M. M. Rashidi, Shohel Mahmud,Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid, Int. J. Therm. Sci.87(2015), 136-145.
[9] Mohammad Hossein Abolbashari, Navid Freidoonimehr, Foad Nazari, M. M. Rashidi,Entropy analysis for an unsteady MHD flow past a stretching permeable surface in nano-fluid, Powder Technol.267(2014), 256-267.
[10] Saeed Dinarvand, Ahmad Doosthoseini, Ensiyeh Doosthoseini, M. M. Rashidi,Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces, Nonlinear Anal. Real World Appl.11 (2010), 1159-1169. · Zbl 1253.76129
[11] A. M. Abd-Alla, S. M. Abo-Dahab, R. D. Al-Simery,Effect of rotation on peristaltic flow of a micropolar fluid through a porous medium with an external magnetic field, J. Magn. Magn. Mater.348(2013), 33-43.
[12] M. Hatami, Dengwei Jing, Dongxing Song, M. Sheikholeslami, D. D. Ganji,Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM, J. Magn. Magn. Mater.396(2015), 275-282.
[13] M. M. Rashidi, Mohammad Nasiri, Marzieh Khezerloo, Najib Laraqi,Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls, J. Magn. Magn. Mater.401(2016), 159-168.
[14] M. M. Rashidi, S. Johnson, Z. Yang,Theoretical study of moving magnetic beads on an inclined plane and its application in the ratchet separation technique, J. Magn. Magn. Mater. 398(2016), 13-19.
[15] S. Rashidi, J. A. Esfahani,The effect of magnetic field on instabilities of heat transfer from an obstacle in a channel, J. Magn. Magn. Mater.391(2015), 5-11.
[16] S. Rashidi, M. Dehghan, R. Ellahi, M. Riaz, M. T. Jamal-Abad,Study of stream wise transverse magnetic fluid flow with heat transfer around an obstacle embedded in a porous medium, J. Magn. Magn. Mater.378(2015), 128-137.
[17] B. I. Olajuwon, J. I. Oahimire, M. A. Waheed,Convection heat and mass transfer in a hydromagnetic flow of a micropolar fluid over a porous medium, Theoret. Appl. Mech.,41(2) (2014), 93-117. · Zbl 1458.76049
[18] R. Muthucumaraswamy, C. Santhana Lakshmi,Mass and Heat transfer effects on MHD fluid flow of an exponentially accelerated isothermal vertical plate with variable mass diffusion, Adv. Appl. Fluid Mech.18(2015), 31-49. · Zbl 1332.76016
[19] K. Das,Exact solution of MHD free convection flow and mass transfer near a moving vertical plate in presence of thermal radiation, Afr. J. Math. Phy.8(2010), 29-41. · Zbl 1197.76048
[20] K. E. Sathappan, M. Muthucumaraswamy,Radiation effects on exponentially accelerated vertical plate with uniform mass diffusion, Int. J. Automotive Mech. Eng.3(2011), 341-349.
[21] K. Jonah Philliph, M. C. Raju, A. J. Chamkha, S. V. K. Varma,MHD rotating heat and mass transfer free convective flow past an exponentially accelerated isothermal plate with fluctuating mass diffusion, Int. J. Industrial Math.6(2014) Article ID IJIM-00478, 10.
[22] R. Muthucumarswamy, Tina Lal, D. Ranganayakulu,Effects of rotation on MHD flow past an accelerated isothermal vertical plate with heat and mass transfer, Theoret. Appl. Mech. 37(2010), 189-202. · Zbl 1299.76307
[23] U. S. Rajput, S. Kumar,Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer, Int. J. Appl. Math. Mech.8(1) (2012), 66-85.
[24] Rudra Kanta Deka, Ashish Paul,Transient free convective MHD flow past an infinite vertical cylinder, Theoret. Appl. Mech.40(2013), 385-402. · Zbl 1299.76070
[25] V. Rajesh, S. V. K. Varma,Radiation and mass transfer effects on MHD free convection flow past an exponentially accelerated vertical plate with variable temperature, ARPN J. Eng. Appl. Sci.4(2009), 20-26.
[26] M. Sheikholeslami, M. M. Rashidi,Ferro-fluid heat transfer treatment in the presence of variable magnetic field, The European Physical J. Plus.130(2015), 115.
[27] M. Sheikholeslami, M. M. Rashidi, D. D. Ganji,Numerical investigation of magnetic nanofluid forced convective heat transfer in existence of variable magnetic field using two phase model, J. Mol. Liq.212(2015), 117-126.
[28] M. Sheikholeslami, K. Vajravelu, M. M. Rashidi,Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field, Int. J. Heat and Mass Transf.92 (2016), 339-348.
[29] M. Sheikholeslami, D. D. Ganji, M. M. Rashidi,Ferro-fluid flow and heat transfer in a semi annulus enclosure in the presence of magnetic source considering thermal radiation, J. Taiwan Inst. Chem. Eng.47(2015), 6-17.
[30] S. Sivaiah, R. Srinivasa Raju,Finite element solution of heat and mass transfer flow with Hall current heat source and viscous dissipation, Appl. Math. Mech. (English Edition).34 (2013), 559-570. · Zbl 1376.76026
[31] Siva Reddy Sheri, R. Srinivasa Raju,Soret effect on unsteady MHD free convective flow past a semi-infinite vertical plate in the presence viscous dissipation, Int. J. Comput. Methods Eng. Sci. Mech.16(2015), 132-141. · Zbl 1359.76344
[32] R. S. Raju, K. Sudhakar, M. Rangamma,The effects of thermal radiation and Heat source on an unsteady MHD free convection flow past an infinite vertical plate with thermal diffusion and diffusion thermo, J. Inst. Eng. (India): Series C.94(2013), 175-186.
[33] F. Garoosi, G. Bagheri, M. M. Rashidi,Two phase simulation of natural convection and mixed convection of the nanofluid in a square cavity, Powder Technol.275(2015), 239-256.
[34] O. Anwar B´eg, S. Rawat, J. Zueco, L. Osmond, R. S. R. Gorla,Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and Hall currents, Theoret. Appl. Mech.41(2014), 1-35. · Zbl 1458.76063
[35] J. Anand Rao, S. Sivaiah, R. Srinivasa Raju,Chemical Reaction effects on an unsteady MHD free convection fluid flow past a semi-infinite vertical plate embedded in a porous medium with Heat Absorption, J. Appl. Fluid Mech.5(2012), 63-70.
[36] J. Anand Rao, R. Srinivasa Raju, S. Sivaiah,Finite Element Solution of heat and mass transfer in MHD Flow of a viscous fluid past a vertical plate under oscillatory suction velocity, J. Appl. Fluid Mech.5(2012), 1-10.
[37] J. Anand Rao, R. Srinivasa Raju, S Sivaiah,Finite Element Solution of MHD transient flow past an impulsively started infinite horizontal porous plate in a rotating fluid with Hall current, J. Appl. Fluid Mech.5(2012), 105-112.
[38] M. V. Ramana Murthy, R. Srinivasa Raju, J. Anand Rao,Heat and Mass transfer effects on MHD natural convective flow past an infinite vertical porous plate with thermal radiation and Hall Current, Procedia Eng. J.127(2015), 1330-1337.
[39] V. S. Rao, L. A. Babu, R. S. Raju,Finite Element Analysis of Radiation and mass transfer flow past semi-infinite moving vertical plate with viscous dissipation, J. Appl. Fluid Mech.6 (2013), 321-329.
[40] Siva Reddy Sheri, R. Srinivasa Raju,Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation, Meccanica51(5) (2015), 1057-1068. · Zbl 1337.76075
[41] R. Srinivasa Raju,Combined influence of thermal diffusion and diffusion thermo on unsteady hydromagnetic free convective fluid flow past an infinite vertical porous plate in presence of chemical reaction, J. Inst. Engineers (India): Series C (2016) (In Press).
[42] R. Srinivasa Raju, B. Mahesh Reddy, M. M. Rashidi, R. S. R. Gorla,Application of finite element method to unsteady MHD free convection flow past a vertically inclined porous plate including thermal diffusion and diffusion thermo effects, J. Porous Media (2016) (In Press).
[43] R. Srinivasa Raju, G. Jithender Reddy, J. Anand Rao, M. M. Rashidi, Rama Subba Reddy Gorla,Analytical and Numerical study of unsteady MHD free convection flow over an exponentially moving vertical plate with heat absorption, Int. J. Thermal Sci.107(2016), 303-315.
[44] R. B. Hetnarski,An algorithm for generating some inverse Laplace transforms of exponential form, ZAMP26(1975), 249-253. · Zbl 0313.44001
[45] R. Bhargava, P. Rana,Finite element solution to mixed convection in MHD flow of micropolar fluid along a moving vertical cylinder with variable conductivity, Int. J. Appl. Math. Mech. 7(2011), 29-51. · Zbl 1426.76223
[46] Y-Y. Lin, S-P. Lo,Finite element modeling for chemical mechanical polishing process under different back pressures, J. Mat. Proc. Tech.140(2003), 646-652.
[47] W. Dettmer, D. Peric,A computational framework for fluid-rigid body interaction: finite element formulation and applications, Comp. Meth. Appl. Mech. Engg.195(2006), 1633-1666. · Zbl 1123.76029
[48] A. Hansbo, P. Hansbo,A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Comp. Meth. Appl. Mech. Engg.193(2004), 3523-3540. · Zbl 1068.74076
[49] K. J. Bathe,Finite Element Procedures, Prentice-Hall, New Jersy, 1996. · Zbl 1326.65002
[50] J. N. Reddy,An Introduction to the Finite Element Method, McGraw-Hill, New York, 1985. CHEMICALLY REACTING FLUID FLOW INDUCED BY AN EXPONENTIALLY...83
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