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MHD Double Diffusive Natural Convection Flow Over Exponentially Accelerated Inclined Plate

Published online by Cambridge University Press:  05 August 2016

G. S. Seth ,
R. Tripathi ,
R. Sharma  and
A. J. Chamkha
G. S. Seth*
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
R. Tripathi
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
R. Sharma
Affiliation:
Department of Applied MathematicsIndian School of MinesDhanbad, India
A. J. Chamkha
Affiliation:
Mechanical Engineering DepartmentPrince Mohammad Bin Fahd UniversityAl-Khobar, Kingdom of Saudi Arabia
*
*Corresponding author ([email protected])
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Abstract

An investigation of unsteady MHD double diffusive natural convection flow of a viscous, incompressible, electrically conducting, heat absorbing, radiating and chemically-reactive fluid past an exponentially accelerated moving inclined plate in a fluid-saturated porous medium, when the temperature of the plate and the concentration at the surface of the plate have ramped profiles, is carried out. Exact solutions for the fluid velocity, fluid temperature and the species concentration, under Boussinesq approximation, are obtained in closed form by the Laplace transform technique. The expressions for the shear stress, rate of heat transfer and the rate of mass transfer at the plate are also derived. Numerical evaluations of the fluid velocity, fluid temperature and the species concentration are performed and displayed graphically whereas those of the shear stress, rate of heat transfer and the rate of mass transfer at the plate are presented in tabular form for various values of the pertinent flow parameters.

Keywords

Thermal radiationChemical reactionRamped temperatureRamped surface concentration
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 1 , February 2017 , pp. 87 - 99
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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References

1. Hossain, M. A. and Mandal, A. C., “Mass transfer effects on the unsteady hydromagnetic free convection flow past an accelerated vertical porous plate,” Journal Physics D: Applied Physics, 18, pp. L63–L69 (1985).CrossRefGoogle Scholar
2. Jha, B. K., “MHD free-convection and mass-transform flow through a porous medium,” Astrophysics and Space Science, 175, pp. 283–289 (1991).Google Scholar
3. Ibrahim, F. S., Hassanien, I. A. and Bakr, A. A., “Unsteady magnetohydrodynamic micropolar fluid flow and heat transfer over a vertical porous plate through a porous medium in the presence of thermal and mass diffusion with a constant heat source,” Canadian Journal of Physics, 82, pp. 775–790 (2004).Google Scholar
4. Eldabe, N.T.M., EIbashbeshy, E.M.A., Hasanin, W.S.A. and Elsaid, E. M., “Unsteady motion of MHD viscous incompressible fluid with heat and mass transfer through porous medium near a moving vertical plate,” International Journal of Energy and Technology, 3, pp. 1–11 (2011).Google Scholar
5. Gorla, R. S. R. and Chamkha, A. J., “Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid,” Journal of Modern Physics, 2, pp. 62–71 (2011).Google Scholar
6. Gorla, R. S. R. and Chamkha, A. J., “Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a non-Newtonian nanofluid,” International Journal of Microscale and Nanoscale thermal Fluid transport Phenomena, 2, pp. 211–227 (2011).Google Scholar
7. Cogley, A. C., Gilles, S. E. and Vincenti, W. G., “Differential approximation for radiative transfer in a non-grey gas near equilibrium,” AIAA Journal, 6, pp. 551–553 (1968).Google Scholar
8. Howell, J. R., Siegel, R. and Menguc, M. P., Thermal Radiation and Heat Transfer, 5 th ed. CRC Press, New York. (2010).CrossRefGoogle Scholar
9. Takhar, H. S., Gorla, R. S. R. and Soundalgekar, V. M., “Short communication radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate,” International Journal of Numerical Methods for Heat and Fluid Flow, 6, pp. 77–83 (1996).Google Scholar
10. Azzam, G.E.A., “Radiation effects on the MHD mixed free forced convective flow past a semi-infinite moving vertical plate for high temperature differences,” Physica Scripta, 66, pp. 71–76 (2002).CrossRefGoogle Scholar
11. Mbeledogu, I.U. and Ogulu, A., “Heat and mass transfer of an unsteady MHD natural convection flow of a rotating fluid past a vertical porous flat plate in the presence of radiative heat transfer,” International Journal of Heat and Mass Transfer, 50, pp. 1902–1908 (2006).Google Scholar
12. Palani, G. and Abbas, I.A., “Free Convection MHD Flow with Thermal Radiation from an Impulsively-Started Vertical Plate,” Nonlinear Analysis: Modelling and Control, 14, pp. 73–84 (2009).Google Scholar
13. Prakash, J., Bhanumathi, D., Kumar, A. G. V. and Varma, S. V. K., “Diffusion-Thermo and radiation effects on unsteady MHD flow through porous medium past an impulsively started infinite vertical plate with variable temperature and mass diffusion,” Transport in Porous Media, 96, pp. 135–151 (2013).CrossRefGoogle Scholar
14. Hussanan, A., Ismail, Z., Khan, I., Hussein, A. G. and Shafie, S., “Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating,” European Physical Journal Plus, 129, 46 (2014).Google Scholar
15. Vedavathi, N., Ramakrishna, K. and Reddy, K. J., “Radiation and Mass Transfer Effects on Unsteady MHD Convective Flow past an Infinite Vertical Plate with Dufour and Soret Effects,” Ain Shams Engineering Journal, 6, pp. 363–371 (2015).Google Scholar
16. Vajravelu, K. and Nayfeh, J., “Hydromagnetic Convection at a Cone and a Wedge,” International Communication in Heat and Mass Transfer, 19, pp. 701–710 (1992).Google Scholar
17. Chamkha, A.J. and Khaled, A.R.A., “Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption,” Heat and Mass Transfer, 37, pp. 117–123 (2001).Google Scholar
18. Chamkha, A.J., “Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption,” International Journal of Engineering Science, 42, pp. 217–230 (2004).CrossRefGoogle Scholar
19. Alam, M. S., Rahman, M. M. and Sattar, M. A., “MHD free convective heat and mass transfer flow past an inclined surface with heat generation,” Thammasat International Journal of Science and Technology, 11, pp. 1–8 (2006).Google Scholar
20. Ravikumar, V., Raju, M.C. and Raju, G.S.S., “Combined effects of heat absorption and MHD on convective Rivlin-Ericksen flow past a semi-infinite vertical porous plate with variable temperature and suction,” Ain Shams Engineering Journal, 5, pp. 867–875 (2014).Google Scholar
21. Seth, G. S., Sarkar, S. and Nandkeolyar, R., “Unsteady hydromagnetic natural convection flow past an impulsively moving vertical plate with Newtonian heating in a rotating system,” Journal of Applied Fluid Mechanics, 8, pp. 623–633 (2015).Google Scholar
22. Chamkha, A. J., “Thermal radiation and buoyancy effects on hydromagnetic flow over an accelerating permeable surface with heat source or sink,” International Journal of Engineering. Science, 38, pp. 1699–1712 (2000).Google Scholar
23. Seddeek, M. A., “Thermal radiation and buoyancy effects on MHD free convective heat generating flow over an accelerating permeable surface with temperature-dependent viscosity,” Canadian Journal of Physics, 79, pp. 725–732 (2001).CrossRefGoogle Scholar
24. Saha, G., Sultana, T. and Saha, S., “Effect of thermal radiation and heat generation on MHD flow past a uniformly heated vertical plate,” Desalination and Water Treatment, 16, pp. 57–65 (2010).Google Scholar
25. Reddy, P. B. A., Reddy, N. B. and Suneetha, S., “Radiation effects on MHD flow past an exponentially accelerated isothermal vertical plate with uniform mass diffusion in the presence of heat source,” Journal of Applied Fluid Mechanics, 5, pp. 119–126. (2012).Google Scholar
26. Vieru, D., Fetecau, C., Fetecau, C. and Nigar, N., “Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid,” Zeitschrift für Naturforschung A, 69a, pp. 714–724 (2014).Google Scholar
27. Uddin, Z., Kumar, M. and Harmand, S., “Influence of thermal radiation and heat generation/absorption on MHD heat transfer flow of a micropolar fluid past a wedge considering hall and ion slip currents,” Thermal Science, 18, pp. 489–502 (2014).Google Scholar
28. Anjalidevi, S. P. and Kandasamy, R., “Effects of chemical reaction, heat and mass transfer on laminar flow along a semi-infinite horizontal plate,” Heat and Mass Transfer, 35, pp. 465–467 (1999).Google Scholar
29. Postelnicu, A., “Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects,” Heat and Mass Transfer, 43, pp. 595–602 (2007).Google Scholar
30. Patil, P.M. and Kulkarni, P.S., “Effects of chemical reaction on free convective flow of a polar fluid through a porous medium in the presence of internal heat generation,” International Journal of Thermal Science, 47, pp. 1043–1054 (2008).CrossRefGoogle Scholar
31. Ibrahim, F.S., Elaiw, A.M. and Bakr, A.A., “Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi-infinite vertical permeable moving plate with heat source and suction,” Communication in Nonlinear Science and Numerical Simulation, 13, pp. 1056–1066. (2008).CrossRefGoogle Scholar
32. Pal, D. and Talukdar, B., “Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating,” Communication in Nonlinear Science and Numerical Simulation, 15, pp. 2878–2893 (2010).Google Scholar
33. Ali, F., Khan, I., Shafie, S. and Musthapa, N., “Heat and Mass Transfer with Free Convection MHD Flow Past a Vertical Plate Embedded in a Porous Medium,” Mathematical Problems in Engineering, DOI: 10.1155/2013/346281 (2013).Google Scholar
34. Khan, M. S., Karim, I., Islam, M. S. and Wahiduzzaman, M., “MHD boundary layer radiative, heat generating and chemical reacting flow past a wedge moving in a nanofluid,” Nano Convergence, 1, 20 (2014).Google Scholar
35. Seth, G. S., Kumbhakar, B. and Sarkar, S., “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, pp. 87–94 (2014).Google Scholar
36. Tripathy, R.S., Dash, G.C., Mishra, S.R. and Baag, S., “Chemical reaction effect on MHD free convective surface over a moving vertical plate through porous medium,” Alexandria Engineering Journal, 54, pp. 673–679 (2015).Google Scholar
37. Gorla, M. G., Chand, K. and Singh, A., “Effects of rotation and heat source on MHD free convective flow on vertically upwards heated plate with gravity modulation in slip flow region,” Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 85, pp. 427–437 (2015).Google Scholar
38. Chandran, P., Sacheti, N.C. and Singh, A.K., “Natural convection near a vertical plate with ramped wall temperature,” Heat and Mass Transfer, 41, pp. 459–464. (2005).Google Scholar
39. Nandkeolyar, R. and Das, M., “Unsteady MHD free convection flow of a heat absorbing dusty fluid past a flat plate with ramped wall temperature,” Afrika Matematika, 25, pp. 779–798 (2014).Google Scholar
40. Mohamad, A.Q., Khan, I., Ismail, Z. and Shafie, S., “The unsteady free convection flow of second grade fluid in rotating frame with ramped wall temperature,” AIP conference proceedings, 1605, pp. 398–403 (2014).Google Scholar
41. Samiulhaq, , Ahmad, S., Vieru, D., Khan, I. and Shafie, S., “Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature,” PLOS ONE, 9, e88766 (2014).CrossRefGoogle Scholar
42. Rajesh, V. and Chamkha, A. J., “Effects of ramped wall temperature on unsteady two-dimensional flow past a vertical plate with thermal radiation and chemical reaction,” Communications in Numerical Analysis, 2014, pp. 1–17 (2014).Google Scholar
43. Kundu, P.K., Das, K. and Acharya, N., “Flow features of a conducting fluid near an accelerated vertical plate in porous medium with ramped wall temperature,” Journal of Mechanics, 30, pp. 277–288 (2014).Google Scholar
44. Das, M., Mahatha, B.K., Nandkeolyar, R., Mandal, B.K. and Saurabh, K., “Unsteady hydromagnetic flow of a heat absorbing dusty fluid past a permeable vertical Plate with ramped temperature,” Journal of Applied Fluid Mechanics, 7, pp. 485–492 (2014).Google Scholar
45. Khalid, A., Khan, I. and Shafie, S., “Exact solutions for free convection flow of nanofluids with ramped wall temperature,” European Physical Journal Plus, 130, 57 (2015).Google Scholar
46. Seth, G.S. and Sarkar, S., “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, pp. 66–79 (2015).Google Scholar
47. Seth, G. S., Kumbhakar, B. and Sarkar, S., “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,” International Journal of Engineering, Science and Technology, 7, pp. 94–108 (2015).Google Scholar
48. Cebeci, T., Convective heat transfer, Horizons Publishing Inc., Long Beach (2002).Google Scholar