Soret effect on transient magnetohydrodynamic nanofluid flow past a vertical plate through a porous medium with second order chemical reaction and thermal radiation

Soret effect on transient magnetohydrodynamic nanofluid flow past a vertical plate through a porous medium with second order chemical reaction and thermal radiation

Amit KumarRamayan Singh Gauri Shanker Seth Rajat Tripathi 

Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India

Indian Institute of Technology, Indian School of Mines, Dhanbad 826004, Jharkhand, India

Corresponding Author Email: 
rajat17mnnit@gmail.com
Page: 
1430-1437
|
DOI: 
https://doi.org/10.18280/ijht.360435
Received: 
3 January 2017
| |
Accepted: 
6 February 2018
| | Citation

OPEN ACCESS

Abstract: 

In the present article, an investigation on the impact of Soret effect on unsteady magnetohydrodynamic natural convection flow of a viscous, electrically conducting and incompressible nanofluid over a vertical plate through a medium filled with porous materials with the consideration of a second order chemical reaction, has been investigated. Three kinds of water-based nanofluids, comprising of aluminum oxide (AL2O3), titanium oxide (TIO2) and silver (Ag) as nanoparticles, are chosen for this analysis. Governing equations accompanied by the boundary and initial conditions are changed into non-dimensional form and then they are solved by Crank-Nicolson type finite difference scheme. The impact of relevant flow parameters on nanofluid velocity, nanofluid temperature and species concentration are depicted graphically with comprehensive discussions whereas numerical findings for coefficient of skin friction, wall temperature gradient i.e. Nusselt number and wall concentration gradient are depicted in tabular form. It has been observed that Soret effect has the ability to enhance the species concentration. The investigation we have performed here, has various scientific and industrial applications.

Keywords: 

nanofluid, Soret effect, MHD, chemical reaction, porous medium

1. Introduction
2. Mathematical Formulation
3. Numerical Solution
4. Wall Velocity Gradient, Wall Temperature Gradient and Concentration Gradient in the Vicinity of the Plate
5. Results and Discussion
6. Conclusion
Nomenclature
  References

[1] Choi SUS. (1995). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the ASME International Mechanical Engineering Congress and Exposition 66: 99-105.

[2] Selvakumar RD, Dhinakaran S. (2016). Effective viscosity of nanofluids: a modified Krieger–Dougherty model based on particle size distribution (PSD) analysis. Journal of Molecular Liquids 225: 20-27. https://doi.org/10.1016/j.molliq.2016.10.137

[3] Heris SZ, Esfahany MN, Etemad SG. (2007). Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube. J. Heat Fluid Flow 28: 203-210. https://doi.org/10.1016/j.ijheatfluidflow.2006.05.001 

[4] Fotukian SM, Nasr Esfahany M. (2010). Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube. I. J. Commun. Heat Mass Transf. 37: 214-219. https://doi.org/10.1016/j.icheatmasstransfer.2009.10.003

[5] Turkyilmazoglu M. (2012). Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. Chem. Eng. Sci. 84: 182–187. https://doi.org/10.1016/j.ces.2012.08.029

[6] Sheikholeslami M, Bandpy M.G, Ellahi R, Zeeshan A. (2014). Simulation of MHD CuO water nanofluid flow and convective heat transfer considering Lorentz forces. J. Magn. Magn. Mater. 369: 69–80. 

[7] Sandeep N, Reddy MG. (2017). Heat transfer of nonlinear radiative magnetohydrodynamic Cu-water nanofluid flow over two different geometries. Journal of Molecular Liquids 225: 87-94. https://doi.org/10.1016/j.molliq.2016.11.026

[8] Takhar HS, Gorla RSR, Soundalgekar VM. (1996). Short communication radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate. Int. J. Numer. Methods Heat Fluid Flow 6: 77-83. https://doi.org/10.1108/09615539610113118

[9] Das S, Jana RN. (2015). Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate. Alexandria Engineering Journal 54: 5-64. https://doi.org/10.1016/j.aej.2015.01.001

[10] Ogulu A, Makinde OD. (2008). Unsteady hydromagnetic free convection flow of a dissipative and radiating fluid past a vertical plate with constant heat flux. Chem. Eng. Comm. 196: 454-462. https://doi.org/10.1080/00986440802484531

[11] Mahmoud MAA. (2009). Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature dependent viscosity. Canad. J. Chem. Eng. 87: 47–52. https://doi.org/10.1002/cjce.20135

[12] Das S, Jana RN, Chamkha AJ. (2015). Unsteady free convection flow past a vertical plate with heat and mass fluxes in the presence of thermal radiation. Journal of Applied Fluid Mechanics 8: 845-854. https://doi.org/10.18869/acadpub.jafm.73.238.23265

[13] Seth GS, Tripathi R, Sharma R. (2015). Natural convection flow past an exponentially accelerated vertical ramped temperature plate with hall effects and heat absorption. International Journal of Heat and Technology 33: 139-144. https://doi.org/10.18280/ijht.330321

[14] Seth GS, Kumbhakar B, Sarkar S. (2014). Unsteady hydromagnetic natural convection flow with heat and mass transfer of a thermally radiating and chemically reactive fluid past a vertical plate with Newtonian heating and time dependent free-stream. International Journal of Heat and Technology 32: 87-94.

[15] Ahmed N. (2012). Heat and mass transfer in Hartmann flow with Soret effect in presence of a constant heat source. Turk. J. Phys. 36: 446–460. https://doi.org/10.3906/fiz-1109-20 

[16] Hussanan A, Salleh MZ, Khan I, Tahar RM, Ismail Z. (2015). Soret effects on unsteady magnetohydrodynamic mixed convection heat-and-mass-transfer flow in a porous medium with Newtonian heating. Maejo Int. J. Sci. Technol. 9: 224–245. https://doi.org/10.14456/mijst.2015.17

[17] Seth GS, Kumbhakar B, Sarkar S. (2015). Soret and Hall effects on unsteady MHD free convection flow of radiating and chemically reactive fluid past a moving vertical plate with ramped temperature in rotating system. Int. J. of Engg, Sci. and Tech. 7: 94-108. https://doi.org/10.4314/ijest.v7i2.8

[18] Zhao J, Zheng L, Zhang X. Liu F. (2016). Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects. Int. J. of Heat and Mass Transf. 103: 203–210.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.07.057

[19] Reddy PS, Chamkha AJ. (2016). Soret and Dufour effects on unsteady MHD heat and mass transfer from a permeable stretching sheet with thermophoresis and non-uniform heat generation/absorption. Journal of Applied Fluid Mechanics 9: 2443–2455.  https://doi.org/10.18869/acadpub.jafm.68.236.25171

[20] Saritha K, Rajasekhar MN, Reddy BS. (2017). Heat and mass transfer of laminar boundary layer flow of non-Newtonian power law fluid past a porous flat plate with Soret and DuFour effects. Physical Science International Journal 11: 1–13. https://doi.org/10.9734/PSIJ/2016/26957

[21] Bég OA, Bakier AY, Prasad VR. (2009). Numerical study of free convection magnetohydrodynamic heat and mass transfer from a stretching surface to a saturated porous medium with Soret and Dufour effects. Computational Materials Science 46: 57–65. https://doi.org/10.1016/j.commatsci.2009.02.004

[22] Abdel-wahed MS, Abdel-AAL SM. (2016). Soret and DuFour effects on MHD stagnation point flow and heat transfer impinging on stretching sheet with Chemical reaction and transpiration. European Journal of Scientific Research 137: 63–73.  

[23] Das UN, Deka R, Soundalgekar VM. (1994). Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction. Forschung im Ingenieurwesen 60: 284–287.

[24] Seth GS, Sarkar S. (2015). Hydromagnetic natural convection flow with induced magnetic field and nth order chemical reaction of a heat absorbing fluid past an impulsively moving vertical plate with ramped temperature. Bulgarian Chemical Communications 47: 66-79. https://doi.org/10.1016/j.joems.2014.03.006  

[25] Venkateswarlu S, Kumar GV, Durga Prasad P, Varma SVK. (2017). Effect of Dufour number and chemical reaction on MHD free convection flow of Jeffrey fluid past a vertical permeable moving plate. Int. J. of Pure and App. Math. 113: 169-177.   

[26] Rosseland S. (1931). Astrophysik und atom-theoretische Grundlagen, Springer-Verlag, Berlin.  

[27] Carnahan B, Luther HA, Wilkes JO. (1969). Applied Numerical Methods, New York, John Wiley.

[28] Antia H.M. (1991). Numerical methods for scientists and engineers. New Delhi: Tata McGraw-Hill Publishing Co Ltd.