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

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

Gauri Shanker Seth* Bidyasagar Kumbhakar Subharthi Sarkar

Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, INDIA

Corresponding Author Email: 
gsseth_ism@yahoo.com
Page: 
87-94
|
DOI: 
https://doi.org/10.18280/ijht.320113
| |
Published: 
31 December 2014
| Citation

OPEN ACCESS

Abstract: 

Investigation of unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, optically thick radiating and chemically reactive fluid past an infinite vertical plate with Newtonian heating is carried out considering impulsive, accelerated and oscillatory movements of the free-stream. Exact analytical solutions for fluid temperature and species concentration are obtained using Laplace transform technique whereas solution for fluid velocity is obtained numerically using INVLAP routine of MATLAB software along with Laplace tranform technique. The numerical solutions for fluid velocity, fluid temperature and species concentration are displayed graphically whereas the numerical values of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. Comparison between the present numerical results and the carlicr published results is made and there is an excellent agreement between these results.

Keywords: 

hydromagnetic natural convection, Newtonian heating, thermal radiation, chemical reaction, free-stream

1. Introduction
2. Formulation of the Problem and Its Solution
3. Numerical Solution
4. Results and Discussion
5. Conclusions
Nomenclature
  References

[1] C. C. Tseng and R. Viskanta, Heat Transfer in Thermophotovoltaics Radiation Filters, Int. J. Heat Tech., vol. 26, pp. 53-58, 2008.

[2] A. Ogulu and O. D. Makinde, Unsteady Hydromagnetic Free Convection Flow of a Dissipative and Radiating Fluid Past a Vertical Plate with Constant Heat Flux. Chem. Engng. Comm., vol. 196, pp. 454–462, 2008.

[3] S. N. Singh, Numerical Study of Combined Natural Convection, Conduction and Surface Radiation Heat Transfer in Open Top, Side Vented Cavities, Int. J. Heat Tech., vol. 26, pp. 113-121, 2008.

[4] G. S. Seth, Md. S. Ansari and R. Nandkeolyar, MHD Natural Convection Flow with Radiative Heat Transfer Past an Impulsively Moving Plate with Ramped Wall Temperature, Heat Mass Transf., vol. 47, pp. 551–561, 2011.

[5] N. Kumar, S. Gupta and T. Jain, Effects of Thermal Radiation and Mass Transfer on MHD Unsteady Flow Through a Porous Medium Bounded by Two Porous Horizontal Parallel Plates Moving in Opposite Directions, Int. J. Heat Tech., vol. 29, pp. 41-50, 2011.

[6] G. S. Seth, S. Sarkar and S. M. Hussain, Effects of Hall Current, Radiation and Rotation on Natural Convection Heat and Mass Transfer Flow Past a Moving Vertical Plate, Ain Shams Engng. J., vol. 5, pp. 489-503, 2014a.

[7] A. A. Afify, The Effect of Radiation on Free Convective Flow and Mass Transfer Past a Vertical Isothermal Cone Surface with Chemical Reaction in the Presence of a Transverse Magnetic Field. Canad. J. Phys., vol. 82, pp. 447-458, 2004.

[8] P. G. Palanimani, Effects of Chemical Reactions, Heat and Mass Transfer on Nonlinear Magnetohydrodynamic Boundary Layer Flow Over a Wedge with a Porous Medium in the Presence of Ohmic Heating and Viscous Dissipation, J. Porous Media, vol. 10, pp. 489–501, 2007.

[9] A. J. Chamkha, R. A. Mohamed and S. E. Ahmed, Unsteady MHD Natural Convection from a Heated Vertical Porous Plate in a Micropolar Fluid with Joule Heating, Chemical Reaction and Radiation Effects, Meccanica, vol. 46, pp. 399–411, 2011.

[10] R. Nandkeolyar, M. Das and P. Sibanda, Unsteady Hydromagnetic Heat and Mass Transfer Flow of a Heat Radiating and Chemically Reactive Fluid Past a Flat Porous Plate with Ramped Wall Temperature, Math. Prob. Engng., vol. 2013, Article ID: 381806, 2013.

[11] G. S. Seth, S. M. Hussain and S. Sarkar, Hydromagnetic Natural Convection Flow with Heat and Mass Transfer of a Chemically Reacting and Heat Absorbing Fluid Past an Accelerated Moving Vertical Plate with Ramped Temperature and Ramped Surface Concentration Through a Porous Medium, J. Egyp. Math. Soc., http://dx.doi.org/10.1016/j.joems.2014.03.006, 2014.

[12] J. H. Merkin, Natural Convection Boundary Layer Flow on a Vertical Surface with Newtonian Heating, Int. J. Heat Fluid Flow, vol. 15, pp. 392–398, 1994.

[13] D. Lesnic, D. B. Ingham and I. Pop, Free Convection Boundary Layer Flow Along a Vertical Surface in a Porous Medium with Newtonian Heating, Int. J. Heat Mass Transf., vol. 42, pp. 2621–2627, 1999.

[14] R. C. Chaudhary and P. Jain, Unsteady Free Convection Boundary Layer Flow Past an Impulsively Started Vertical Plate with Newtonian Heating, Rom. J. Phys., vol. 51, pp. 911-925, 2006.

[15] M. Z. Salleh, R. Nazar and I. Pop, Mixed Convection Boundary Layer Flow Over a Horizontal Circular Cylinder with Newtonian Heating, Heat Mass Transf., vol. 46, pp. 1411–1418, 2010.

[16] M. Narahari and B. K. Dutta, Effects of Thermal Radiation and Mass Diffusion on Free Convection Flow Near a Vertical Plate with Newtonian Heating, Chem. Engng. Comm., vol. 199, pp. 628-643, 2012.

[17] V. Rajesh, Effects of Mass Transfer on Flow Past an Impulsively Started Infinite Vertical Plate with Newtonian Heating and Chemical Reaction, J. Engng. Phys. Thermophys., vol. 85, pp. 205–211, 2012.

[18] A. Hussanan, Md. I. Anwar, F. Ali, I. Khan and S. Shafie, Natural Convection Flow Past an Oscillating Plate with Newtonian Heating, Heat Transf. Res., vol. 45, pp. 119-135, 2014.

[19] G. S. Seth and S. Sarkar, Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate with Newtonian Heating, J. Nature Sci. Sustain. Tech., vol. 8, pp. 83-97, 2014.

[20] M. J. Lighthill, The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity, Proc. R. Soc. Lond. A, vol. 224, pp. 1-23, 1954.

[21] C. C. Lin, Motion in the Boundary Layer with a Rapidly Oscillating External Flow, Proc. 9th Int. Congress Appl. Mech.Brussels, vol. 4, pp. 155-167, 1957.

[22] Z. U. A. Warsi, Motion in a Three-dimensional Boundary Layer with a Rapidly Oscillating External Flow, J. Phys. Soc. Japan, vol. 19, pp. 121-124, 1964.

[23] S. A. S. Messiha, Laminar Boundary Layers in Oscillating Flow Along an Infinite Flat Plate with Variable Suction, Math. Proc. Cambridge Phil. Soc., vol. 62, pp. 329-337, 1966.

[24] V. M. Soundalgekar, Free Convection Effects on the Oscillatory Flow Past an Infinite, Vertical, Porous Plate with Constant Suction II, Proc. R. Soc. Lond. A, vol. 333, pp. 37-50, 1973.

[25] A. Raptis and C. P. Perdikis, Oscillatory Flow Through a Porous Medium by the Presence of Free Convective Flow, Int. J. Engng. Sci., vol. 23, pp. 51-55, 1985.

[26] Y. J. Kim, Unsteady MHD Convective Heat Transfer Past a Semi-infinite Vertical Porous Moving Plate with Variable Suction, Int. J. Engng. Sci., vol. 38, pp. 833-845, 2000.

[27] R. S. R. Gorla, Unsteady Mixed Convection Due to Time-dependent Free-stream Velocity, Heat Mass Transf., vol. 39, pp. 639-644, 2003.

[28] S. Das, C. Mandal and R. N. Jana, Unsteady Mixed Convection Flow Past a Vertical Plate with Newtonian Heating, Int. J. Energy Tech., vol. 6, pp. 1-9, 2014.

[29] K. R. Cramer and S. I. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw Hill Book Company, New York, 1973.

[30] K. J. Hollenbeck, INVLAP.M: A Matlab Function for Numerical Inversion of Laplace Transforms by the De Hoog Algorithm, http://www.isva.dtu.dk/staff/karl/invlap.htm, 1998.