Unsteady MHD Chemically Reacting and Radiating Mixed Convection Slip Flow Past a Stretching Surface in a Porous Medium

Abstract:

This paper studies the effects of combined buoyancy forces, thermal radiation, chemical reaction, velocity slip, magnetic field and porous medium permeability on unsteady mixed convection flow of electrically conducting fluid past a stretching sheet embedded in a porous medium. Appropriate governing equations are procured and also reduced to set of nonlinear coupled ordinary differential equations by means of suitable similarity transformations. The boundary valued problem is numerically tackled using the fourth-fifth order Runge-Kutta-Fehlberg integration approach with shooting outline. Various controlling parameters effects on the fluid velocity, temperature and kinds concentration profiles together with local skin friction, Nusselt number and Sherwood number are presented diagrammatically and deliberated upon quantitatively. It is found that buoyancy forces increment enhance both heat and mass transfer rate while thermal and concentration boundary layer denseness diminished.

• Periodical: Defect and Diffusion Forum (Volume 377)
• Pages: 200-210
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.377.200
• Online since: September 2017
• Authors: Adetayo Samuel Eegunjobi*, Oluwole Daniel Makinde, Srinivas Jangili
• Keywords: Chemical Reaction, Mixed Convection, Porous Media, Slip Condition, Thermal Radiation

References

[1] B. C. Sakiadis, Boundary layer behaviour on continuous solid surfaces: I. Boundary layer equations for two-dimensional and axisymmetric flow, AIChE Journal 7(1) (1961) 26-28.

DOI: 10.1002/aic.690070108

[2] T. Fang, Similarity solutions for a moving-flat plate thermal boundary layer, Acta Mech., 163 (2003) 161-172.

DOI: 10.1007/s00707-003-0004-y

[3] V. M. Soundalgekar, H. S. Takhar, U. N. Das, R. K. Deka, A. Sarmah, Effect of variable viscosity on boundary layer flow along a continuously moving plate with variable surface temperature, Heat Mass Transf., 40 (2004) 421-424.

DOI: 10.1007/s00231-003-0439-7

[4] O. D. Makinde, Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating, Appl. Math. Mech., 33(12) (2012) 1545–1554.

DOI: 10.1007/s10483-012-1642-8

[5] O. D. Makinde, A. Ogulu, The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chem. Eng. Comm., 195(12) (2008) 1575-584.

DOI: 10.1080/00986440802115549

[6] M. Ferdows, S. M. Chapal, A. A. Afify, Boundary layer flow and heat transfer of a nanofluid over a permeable unsteady stretching sheet with viscous dissipation, J. Eng. Thermophy., 23(3) (2014) 216–228.

DOI: 10.1134/s1810232814030059

[7] E. M. Abo-Eldahab, M. S. Elgendy, Radiation effect on convective heat transfer in an electrically conducting fluid at a stretching surface with variable viscosity and uniform free stream, Phy. Scr., 62 (2000) 321-325.

DOI: 10.1238/physica.regular.062a00321

[8] M. Madhu, N. Kishan, A. J. Chamkha, Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects, Prop. Power Res., 6(1) (2017) 31–40.

DOI: 10.1016/j.jppr.2017.01.002

[9] Y. Zhang, M. Zhang, Y. Bai, Unsteady flow and heat transfer of power-law nanofluid thin film over a stretching sheet with variable magnetic field and power-law velocity slip effect, J. Taiwan Inst. Chem. Eng., 70 (2017) 104–110.

DOI: 10.1016/j.jtice.2016.10.052

[10] O.D. Makinde, W.A. Khan, J.R. Culham, MHD variable viscosity reacting flow over a convectively heated plate in a porous medium with thermophoresis and radiative heat transfer, Int. J. Heat Mass Transf., 93 (2016) 595–604.

DOI: 10.1016/j.ijheatmasstransfer.2015.10.050

[11] M. Gnaneswara Reddy, K. Venugopal Reddy, O.D. Makinde: Hydromagnetic peristaltic motion of a reacting and radiating couple stress fluid in an inclined asymmetric channel filled with a porous medium. Alexandria Engineering Journal (2016).

DOI: 10.1016/j.aej.2016.04.010

[12] Gnaneswara Reddy Machireddy: Influence of thermal radiation, viscous dissipation and Hall current on MHD convection flow over a stretched vertical flat plate. Ain Shams Engineering Journal (2014) 5, 169–175.

DOI: 10.1016/j.asej.2013.08.003

[13] H. A. Attia, Axisymmetric stagnation point flow towards a stretching surface in the presence of a uniform magnetic field with heat generation, Tamkang J. Sci. Eng., 10(1) (2007) 11–16.

[14] J. Zhu, L. Zheng, X. Zhang, Hydrodynamic plane and axisymmetric slip stagnation-point flow with thermal radiation and temperature jump, J. Mech. Sci. Tech., 25(7) (2011) 1837–1844.

DOI: 10.1007/s12206-011-0423-y

[15] O. D. Makinde, Computational modelling of MHD unsteady flow and heat transfer over a flat plate with Navier slip and Newtonian heating. Brazilian Journal of Chemical Engineering, 29(1), (2012) 159-166.

DOI: 10.1590/s0104-66322012000100017

[16] F.M. Hayd, I.A. Hassanien, Magnetohydrodynamic and constant suction/ injection effects of axisymmetric stagnation point flow and mass transfer for power-law fluids, Indian J. Pure Appl. Math., 17(1) (1986) 108–120.

[17] M. Miklavcic, C.Y. Wang, Viscous flow due to a shrinking sheet, Q. Appl. Math., 64(2) (2006) 283–290.

[18] T. Fang, Boundary layer flow over a shrinking sheet with power-law velocity, Int. J. Heat Mass Transf., 51 (25/26) (2008) 5838–5843.

DOI: 10.1016/j.ijheatmasstransfer.2008.04.067

[19] S. R. Pop, T. Grosan, I. Pop, Radiation effects on the flow near the stagnation point of a stretching sheet, Tech. Mech., 25 (2004) 100–106.

[20] D. Pal, G. Mandal, Influence of thermal radiation on mixed convection heat and mass transfer stagnation-point flow in nanofluids over stretching/shrinking sheet in a porous medium with chemical reaction, Nucl. Eng. Des., 273(1) (2014) 644–652.

DOI: 10.1016/j.nucengdes.2014.01.032

[21] A. Muhammad, O. D. Makinde, Thermodynamics analysis of unsteady MHD mixed convection with slip and thermal radiation over a permeable surface, Defect and Diffusion Forum, 374 (2017) 29-46.

DOI: 10.4028/www.scientific.net/ddf.374.29

[22] O. D. Makinde, Computational modelling of nanofluids flow over a convectively heated unsteady stretching sheet, Current Nanoscience, 9 (2013) 673-678.

DOI: 10.2174/15734137113099990068

[23] O. D. Makinde, Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation, Meccanica, 47 (2012) 1173-1184.

DOI: 10.1007/s11012-011-9502-5

[24] O. D. Makinde, Chemically reacting hydromagnetic unsteady flow of a radiating fluid past a vertical plate with constant heat flux, Zeitschriftf¨urNaturforschung, 67 (2012) 239-247.

DOI: 10.5560/zna.2012-0014

[25] A. Raptis, Radiation and free convection flow through a porous medium, Int. Commun Heat Mass Transf., 25 (2009)289-295.

DOI: 10.1016/s0735-1933(98)00016-5

[26] S. Rosseland, Theoretical Astrophysics. Oxford University, New York, NY, USA, (1936).

[27] M. N. Ozisik, Radiation transfer and interactions with conduction and convection, Wiley-Inter-Science Publication, USA, (1973).

[28] P. Dulal, P. S. Hiremalh, Computational modelling of heat transfer over an unsteady stretching surface embedded in a porous medium. Meccanica, 45(3), 415-524, (2009).

DOI: 10.1007/s11012-009-9254-7

[29] W. Ibrahim, B. Shanker, Unsteady MHD boundary layer flow and heat transfer due to stretching sheet in the presence of heat source or sink by quasi linearization technique. Int J Appl Math Mech., 8(7), 18–30, (2012).

DOI: 10.1016/j.compfluid.2012.08.019

[30] T. Y. Na, Computational Methods in Engineering Boundary Value Problem, Academic Press, (1979).