Abstract and Applied Analysis

Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

Arshad Khan, Ilyas Khan, Farhad Ali, Asma Khalid, and Sharidan Shafie

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Abstract

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

Article information

Source
Abstr. Appl. Anal., Volume 2015, Special Issue (2014), Article ID 975201, 16 pages.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1442420397

Digital Object Identifier
doi:10.1155/2015/975201

Mathematical Reviews number (MathSciNet)
MR3395992

Zentralblatt MATH identifier
06929094

Citation

Khan, Arshad; Khan, Ilyas; Ali, Farhad; Khalid, Asma; Shafie, Sharidan. Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature. Abstr. Appl. Anal. 2015, Special Issue (2014), Article ID 975201, 16 pages. doi:10.1155/2015/975201. https://projecteuclid.org/euclid.aaa/1442420397


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References

  • J. Singh, “Flow of elasto-viscous fluid past an accelerated porous plate,” Astrophysics and Space Science, vol. 106, no. 1, pp. 41–45, 1984.
  • M. Narahari, “Effects of thermal radiation and free convection currents on the unsteady Couette flow between two vertical parallel plates with constant heat flux at one boundary,” WSEAS Transactions on Heat and Mass Transfer, vol. 5, no. 1, pp. 21–30, 2010.
  • M. Narahari and M. Y. Nayan, “Free convection flow past an impulsively started infinite vertical plate with Newtonian heating in the presence of thermal radiation and mass diffusion,” Turkish Journal of Engineering and Environmental Sciences, vol. 35, no. 3, pp. 187–198, 2011.
  • M. Narahari and A. Ishak, “Radiation effects on free convection flow near a moving vertical plate with newtonian heating,” Journal of Applied Sciences, vol. 11, no. 7, pp. 1096–1104, 2011.
  • R. C. Chaudhary and P. Jain, “Unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating,” Romanian Journal of Physics, vol. 51, p. 911, 2006.
  • U. N. Das, R. Deka, and V. M. Soundalgekar, “Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction,” Forschung im Ingenieurwesen, vol. 60, no. 10, pp. 284–287, 1994.
  • V. M. Soundalgekar, N. S. Birajdar, and V. K. Darwhekar, “Mass-transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux,” Astrophysics and Space Science, vol. 100, no. 1-2, pp. 159–164, 1984.
  • R. Muthucumaraswamy, P. Ganesan, and V. M. Soundalgekar, “On flow and heat transfer of a viscous incompressible fluid past an impulsively started vertical isothermal plate,” International Journal of Thermal Sciences, vol. 40, no. 3, pp. 297–302, 2001.
  • R. Muthucumaraswamy, P. Ganesan, and V. M. Soundalgekar, “Heat and mass transfer effects on flow past an impulsively started vertical plate,” Acta Mechanica, vol. 146, no. 1-2, pp. 1–8, 2001.
  • S. S. Das, S. R. Biswal, U. K. Tripathy, and P. Das, “Mass transfer effects on unsteady hydromagnetic convective flow past a vertical porous plate in a porous medium with heat source,” Journal of Applied Fluid Mechanics, vol. 4, no. 4, pp. 91–100, 2011.
  • C. J. Toki and J. N. Tokis, “Exact solutions for the unsteady free convection flows on a porous plate with time-dependent heating,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 87, no. 1, pp. 4–13, 2007.
  • N. Senapati, R. K. Dhal, and T. K. Das, “Effects of chemical reaction on free convection MHD flow through porous medium bounded by vertical surface with slip flow region,” American Journal of Computational and Applied Mathematics, vol. 2, pp. 124–135, 2012.
  • I. Khan, K. Fakhar, and S. Shafie, “Magnetohydrodynamic free convection flow past an oscillating plate embedded in a porous medium,” Journal of the Physical Society of Japan, vol. 80, no. 10, Article ID 104401, 2011.
  • A. Khan, I. Khan, F. Ali, S. Ulhaq, and S. Shafie, “Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature,” PLoS ONE, vol. 9, no. 3, Article ID e90280, 2014.
  • A. Hussanan, Z. Ismail, I. Khan, A. G. Hussein, and S. Shafie, “Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating,” The European Physical Journal Plus, vol. 129, article 46, 2014.
  • R. N. Barik, G. C. Dash, and M. Kar, “Free convection heat and mass transfer MHD flow in a vertical porous channel in the presence of chemical reaction,” Journal of Fluids, vol. 2013, Article ID 297493, 14 pages, 2013.
  • P. Chandran, N. C. Sacheti, and A. K. Singh, “Natural convection near a vertical plate with ramped wall temperature,” Heat and Mass Transfer, vol. 41, no. 5, pp. 459–464, 2005.
  • M. Narahari, O. A. Beg, and S. K. Ghosh, “Mathematical modelling of mass transfer and free convection current effects on unsteady viscous flow with ramped wall temperature,” World Journal of Mechanics, vol. 1, pp. 176–184, 2011.
  • V. Rajesh, “Chemical reaction and radiation effects on the transient MHD free convection flow of dissipative fluid past an Infinite vertical porous plate with ramped wall temperature,” Chemical Industry & Chemical Engineering Quarterly, vol. 17, no. 2, pp. 189–198, 2011.
  • R. R. Patra, S. Das, R. N. Jana, and S. K. Ghosh, “Transient approach to radiative heat transfer free convection flow with ramped wall temperature,” Journal of Applied Fluid Mechanics, vol. 5, no. 2, pp. 9–13, 2012.
  • G. S. Seth, G. K. Mahatoo, and S. Sarkar, “Effects of Hall current and rotation on MHD natural convection flow past an impulsively moving vertical plate with ramped temperature in the presence of thermal diffusion with heat absorption,” International Journal of Energy & Technology, vol. 5, pp. 1–12, 2013.
  • Samiulhaq, I. Khan, F. Ali, and S. Shafie, “MHD free convection flow in a porous medium with thermal diffusion and ramped wall temperature,” Journal of the Physical Society of Japan, vol. 81, no. 4, Article ID 044401, 2012.
  • N. Ghara, S. Das, S. L. Maji, and R. N. Jana, “Effect of radiation on MHD free convection flow past an impulsively moving vertical plate with ramped wall temperature,” American Journal of Scientific and Industrial Research, vol. 3, no. 6, pp. 376–386, 2012.
  • S. Das, C. Mandal, and R. N. Jana, “Effects of radiation on unsteady Couette flow between two vertical parallel plates with ramped wall temperature,” International Journal of Computer Applications, vol. 39, pp. 34–42, 2012.
  • C. L. M. H. Navier, “Sur les lois dee mouvement des fluids,” Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. 6, pp. 389–440, 1827.
  • C. Fetecau, C. Fetecau, and M. Rana, “General solutions for the unsteady flow of second-grade fluids over an infinite plate that applies arbitrary shear to the fluid,” Zeitschrift für Naturforschung–-Section A: Journal of Physical Sciences, vol. 66, no. 12, pp. 753–759, 2011.
  • T. Hayat, I. Khan, R. Ellahi, and C. Fetecau, “Some MHD flows of a second grade fluid through the porous medium,” Journal of Porous Media, vol. 11, no. 4, pp. 389–400, 2008.
  • E. Magyari and A. Pantokratoras, “Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows,” International Communications in Heat and Mass Transfer, vol. 38, no. 5, pp. 554–556, 2011.
  • A. David Maxim Gururaj and S. P. Anjali Devi, “MHD boundary layer flow with forced convection past a nonlinearly stretching surface with variable temperature and nonlinear radiation effects,” International Journal of Development Research, vol. 4, pp. 75–80, 2014.
  • C. Fetecau, M. Rana, and C. Fetecau, “Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid,” Zeitschrift für Naturforschung–-Section A: Journal of Physical Sciences, vol. 68, no. 1-2, pp. 130–138, 2013. \endinput