Local nonsimilarity solutions for mixed convective flow over a stretching sheet in the presence of chemical reaction and hall current

Authors

  • M. O. Lawal Adeyemi College of Education, Ondo
  • S. O. Ajadi Obafemi Awolowo University

Abstract

This paper presents the combined eects of buoyancy forces, pressure gradient, heat source, thermal radiation, chemical reaction and Hall current on the heat and mass transfer of Newtonian uid over a stretching sheet subjected to a non-linear stretching velocity. The governing nonlinear partial differential equations were reduced to a system of coupled nonlinear ordinary differential equations by using an established local non-similarity transformation. The resulting equations are then solved numerically using the Midpoint Method with Richardson Extrapolation Enhancement scheme and implemented on the MAPLE 18 platform. The result reveals that axial and transverse velocity proles increase as Hall current parameter increases; though the increase is more pronounced for the transverse velocity. The magnetic eld strength was observed to reduce concentration, axial and transverse velocity proles but increases the temperature proles. It was also observed that increasing the nonlinear velocity parameter led to increases in the axial and transverse velocity proles whereas it reduces the temperature and concentration proles. In line with the physics of the problem, an increase in chemical reaction parameter reduces the concentration and the in uence of Hall current parameter on both axial and transverse velocities are of great signicance. The study concluded that the combined eects of thermophysical parameters such as chemical reaction, Hall current, thermal radiation.

Author Biography

S. O. Ajadi, Obafemi Awolowo University

Mathematics Department

References

B. C. Sakiadis, Boundary-layer Equations for Two-dimensional and Axisymmetric Flow, Boundary-layer Behaviour on Continuous Solid Surface I, AICHE J, 7, 26-28, 1961.

B. C. Sakiadis, Boundary-layer Behaviour on Continuous Flat Surface, Boundary-layer Behaviour on Continuous Solid Surface II, AICHE J, 7, 221-225, 1961.

J. A. Dantzig and C. L. Tucker, Modeling in in Materials Processing, Cambridge University Press. 1900.

A. S. P. Devi and R. Kandasamy, Eects of heat and mass transfer on MHD laminar boundary layer flow over a wedge with suction or injection, Journal of Energy Heat and Mass Transfer, 2, 167, 2001.

P. Dulal and M. Hiranmoy, Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a no-isothermal wedge, Applied Mathematics and Combustion, 212, 194-208, 2009.

T. Fang and J. Zhang, Flow between two stretchable disks - An Exact solution of the Navier-Stokes equation International Communication in Heat and Mass Transfer, 35, 892-895, 2008.

A. D. Fitt and C. P. Please, Asymptotic analysis of the flow of shear-thinning foodstus in annular scraped heat heat exchangers, J. Engineering Mathematics, 39, 345-366, 1900.

T. Haga and S. Suzuki, A downward melt drag single roll caster for casting semisolid slurry, J. Materials Processing Technology, 157, 695-700, 2004.

B. G. Hildebrand, S. G. Sterling and M. A. Price, An evaluation of three material models used in the nite element simulation of a sheet stretching process, J. Materials Processing Technology, 103, 57-64, 2000.

C. Y. Wang, Liquid lm on an unsteady stretching sheet, Quarterly of Applied Mathematics, 48(4), 601-610, 1990.

P. K. Kundu, I. M. Cohen and D. R. Dowling, Fluid Mechanics. Fifth edition, Elsevier, The Boulevard, Langford lane Kidlington, Oxford, UK, 369-375, 2012.

T. Watanabe and I. Pop, Thermal boundary layers in magnetohydrodynamics flow over a flat plate in the presence of a transverse magnetic eld, Acta Mech, 105, 233-238, 1994.

N. G. Kafoussias and N. D. Nanousis, Magnetohydrodynamic laminar boundary layer flow over a wedge with suction or injection, Can. J. Phys., 75, 787-792, 1997.

A. S. P. Devi and R. Kandasamy Eects of heat and mass transfer on MHD laminar boundary layer flow over a wedge with suction or injection, Journal of Energy Heat and Mass Transfer, 2, 167, 2001.

R. Muthucumaraswamy, Eect of a chemical reaction on a moving isothermal vertical surface with suction, Acta Ciencia Indica, 155, 65-70, 2002.

R. L. V. R. Devi, T. Poornima, N. B. Reddy and S. Venkataramana, Radiation and mass transfer eects on MHD Boundary Layer Flow due to an exponentially stretching sheet with heat source, IJEIT, 3(8), 33-38, 2014.

K. Gangadhar and R. N. Bhaskar, Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a moving Vertical Plate in a Porous Medium with Suction, Journal of Applied Fluid Mechanics, 6(1), 107-114, 2013.

K. Bhattacharyya Eects of heat source/sink on MHD flow and heat transfer over a shrinking sheet with mass suction, Chemical Engineering Research Bulletin, 15, 12-17, 2011.

T. S. Reddy, O. S. P. Reddy, M. C. Raju and S. V. K. Varma MHD free convection heat and mass transfer flow through a porous medium bounded by a vertical surface in presence of Hall current, Advances in Applied Science Research, 3(6), 3482-3490, 2012.

O. D. Makinde, K. Zimba and O. A. Beg Numerical Study of Chemically-Reacting Hydromagnetic Boundary Layer Flow with Soret/Dufour Eects and a Convective surface Boundary Condition, Int. J. of Thermal and Environmental Engineering, 4(1), 89-98, 2012.

S. Shateyi and M. Gerald, Hall Effect on MHD flow and heat transfer over an unsteady stretching permeable surface in the presence of thermal radiation and heat Source/Sink, Journal of Applied Mathematics, 2008, 1-12, 2014.

B. M. Rao , G. V. Reddy, M.C. Raju, S.V.K. Varma, MHD Transient free convection and chemically reactive flow past a porous vertical plate with radiation and temperature gradient dependent heat source in slip

ow regime, IOSR Journal of Applied Physics (IOSR-JAP), 3(6), 22-32, 2013.

E. O. Fatunmbi, S. S. Okoya and O. D. Makinde, Convective heat transfer analysis of hydromagnetic micropolar fluid flow past an inclined nonlinear stretching sheet with variable thermophysical properties, Diusion Foundations, ISSN: 2296-3642, 26, 63-77, 2020.

Ishak A., Nazar R. and Pop I. Heat transfer over an unsteady stretching permeable surface with prescribe wall temperature, Nonlinear Analysis: Real World applications, 10, 2909-2913, 2009.

Khan, S., Karim, I. and Biswas, H. A. (2012), `Heat generation, thermal radiation and chemical reaction eects on MHD mixed convection

ow over an unsteady stretching permeable surface', International Journal of Basic and Applied Science, 1(2), 350 - 364.

W. J. Minkowycz and E. M. Sparrow, `Numerical Solution scheme for Local Non-similarity Boundary Layer Analysis ', Numerical Heat Transfer, 1, 69 - 85, 1978.

E. M. Sparrow, H. Quack and C. J. Boerner, Local Non-similarity Boundary Layer Solutions, American Institute of Aeronautics and Astronatics Journal, 8(11), 1936-1942, 1970.

E. M. Sparrow and H. S. Yu, Local Non-similarity Thermal Boundary Layer Solutions, Journal of Heat Transfer, 93, 328-334, 1971.

Mohamad, R., Kandasamy, R. and Ismoen, M. (2015), Local Non-similarity Solution for MHD Mixed convectin Flow of a Nanofluid Past a Permeable Vertical Plate in the Presence of Thermal Radiation Eects, Journal of Applied and Computational Mathematics, 4(6), 1-9.

W. Ibrahim and O. D. Makinde, Magnetohydrodynamic stagnation point flow and heat transfer of casson nano fluid past a stretching sheet with slip and convective boundary condition, Journal of Aerospace Engineering, 292, 04015037-1-11, 2016.

T. E. Akinbobola and S. S. Okoya, The flow of second grade

uid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink, Journal of the Nigerian Mathematical Society, 34, 331-342, 2015.

E. O. Fatunmbi and S. S. Okoya, Heat transfer in boundary layer magneto-micropolar fluids with temperature-dependent material properties over a Stretching sheet, Advances in Materials Science and Engineering, Article ID 5734979, 2020, 1-11, 2020.

Downloads

Published

2021-01-08

How to Cite

LAWAL, M. O., & Ajadi, S. O. (2021). Local nonsimilarity solutions for mixed convective flow over a stretching sheet in the presence of chemical reaction and hall current. Journal of the Nigerian Mathematical Society, 39(3), 353–388. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/578

Issue

Section

Articles