Table of Contents
Journal of Computational Engineering
Volume 2016 (2016), Article ID 9160956, 14 pages
http://dx.doi.org/10.1155/2016/9160956
Research Article

Influence of Cross-Diffusion on Slip Flow and Heat Transfer of Chemically Reacting UCM Fluid between Porous Parallel Plates with Hall and Ion Slip Currents

Department of Applied Mathematics, Defence Institute of Advanced Technology (Deemed University), Pune 411025, India

Received 9 March 2016; Revised 10 May 2016; Accepted 15 May 2016

Academic Editor: Clement Kleinstreuer

Copyright © 2016 Odelu Ojjela et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. S. Berman, “Laminar flow in channels with porous walls,” Journal of Applied Physics, vol. 24, pp. 1232–1235, 1953. View at Google Scholar · View at MathSciNet
  2. F. M. White Jr., B. F. Barfield, and M. J. Goglia, “Laminar flow in a uniformly porous channel,” Journal of Applied Mechanics, vol. 25, no. 4, pp. 613–617, 1958. View at Google Scholar
  3. G. Walker and T. Davies, “Mass transfer in laminar flow between parallel permeable plates,” AIChE Journal, vol. 20, no. 5, pp. 881–889, 1974. View at Publisher · View at Google Scholar · View at Scopus
  4. E. A. Hamza, “Suction and injection effects on a similar flow between parallel plates,” Journal of Physics D: Applied Physics, vol. 32, no. 6, pp. 656–663, 1999. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Srinivasacharya, J. V. Ramana Murthy, and D. Venugopalam, “Unsteady stokes flow of micropolar fluid between two parallel porous plates,” International Journal of Engineering Science, vol. 39, no. 14, pp. 1557–1563, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Sheikholeslami, M. Hatami, and D. D. Ganji, “Micropolar fluid flow and heat transfer in a permeable channel using analytical method,” Journal of Molecular Liquids, vol. 194, pp. 30–36, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. Y.-L. Chen and K.-Q. Zhu, “Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions,” Journal of Non-Newtonian Fluid Mechanics, vol. 153, no. 1, pp. 1–11, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. K. D. Singh and R. Pathak, “Effect of slip conditions and Hall current on an oscillatory convective MHD flow in a rotating vertical porous channel with thermal radiation,” International Journal of Applied Mathematics and Mechanics, vol. 9, pp. 60–77, 2013. View at Google Scholar
  9. A. N. Bhat and M. L. Mittal, “Heat transfer in a MHD channel with uniform wall heat flux—effects of Hall and ion slip currents,” International Journal of Heat and Mass Transfer, vol. 23, no. 7, pp. 919–926, 1980. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Srinivasacharya and K. Kaladhar, “Mixed convection flow of couple stress fluid between parallel vertical plates with Hall and Ion-slip effects,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2447–2462, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. K. Singh and R. S. R. Gorla, “Free convection heat and mass transfer with Hall current, Joule heating and thermal diffusion,” Heat and Mass Transfer, vol. 45, no. 11, pp. 1341–1349, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Raptis, C. Massalas, and G. Tzivanidis, “Hydromagnetic free convection flow through a porous medium between two parallel plates,” Physics Letters A, vol. 90, no. 6, pp. 288–289, 1982. View at Publisher · View at Google Scholar · View at Scopus
  13. O. Abdulaziz and I. Hashim, “Fully developed free convection heat and mass transfer of a micropolar fluid between porous vertical plates,” Numerical Heat Transfer; Part A: Applications, vol. 55, no. 3, pp. 270–288, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. O. D. Makinde and A. Aziz, “MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1813–1820, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Yao, T. Fang, and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 752–760, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. C. RamReddy, T. Pradeepa, and D. Srinivasacharya, “Similarity solution for free convection flow of a micropolar fluid under convective boundary condition via Lie scaling group transformations,” Advances in High Energy Physics, vol. 2015, Article ID 650813, 16 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. A. Postelnicu, “Heat and mass transfer by natural convection at a stagnation point in a porous medium considering Soret and Dufour effects,” Heat and Mass Transfer, vol. 46, no. 8-9, pp. 831–840, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Hayat, T. Muhammad, S. A. Shehzad, and A. Alsaedi, “Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 25, no. 4, pp. 762–781, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. A. J. Chamkha and A. M. Rashad, “Unsteady heat and mass transfer by MHD mixed convection flow from a rotating vertical cone with chemical reaction and Soret and Dufour effects,” The Canadian Journal of Chemical Engineering, vol. 92, no. 4, pp. 758–767, 2014. View at Publisher · View at Google Scholar · View at Scopus
  20. O. Ojjela and N. Naresh Kumar, “Unsteady MHD mixed convective flow of chemically reacting and radiating couple stress fluid in a porous medium between parallel plates with Soret and Dufour effects,” Arabian Journal for Science and Engineering, vol. 41, no. 5, pp. 1941–1953, 2016. View at Publisher · View at Google Scholar
  21. J. G. Oldroyd, “On the formulation of rheological equations of state,” Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, vol. 200, pp. 523–591, 1950. View at Publisher · View at Google Scholar · View at MathSciNet
  22. M. Awais, T. Hayat, A. Alsaedi, and S. Asghar, “Time-dependent three-dimensional boundary layer flow of a Maxwell fluid,” Computers and Fluids, vol. 91, pp. 21–27, 2014. View at Publisher · View at Google Scholar · View at Scopus
  23. J. J. Choi, Z. Rusak, and J. A. Tichy, “Maxwell fluid suction flow in a channel,” Journal of Non-Newtonian Fluid Mechanics, vol. 85, no. 2-3, pp. 165–187, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. T. Hayat, N. Ali, and S. Asghar, “Hall effects on peristaltic flow of a Maxwell fluid in a porous medium,” Physics Letters A, vol. 363, no. 5-6, pp. 397–403, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. Z. Abbas, M. Sajid, and T. Hayat, “MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel,” Theoretical and Computational Fluid Dynamics, vol. 20, no. 4, pp. 229–238, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. S. Mukhopadhyay and R. S. Gorla, “Unsteady MHD boundary layer flow of an upper convected Maxwell fluid past a stretching sheet with first order constructive/destructive chemical reaction,” Journal of Naval Architecture and Marine Engineering, vol. 9, no. 2, pp. 123–133, 2012. View at Publisher · View at Google Scholar
  27. T. Hayat and Z. Abbas, “Channel flow of a Maxwell fluid with chemical reaction,” Zeitschrift für ange-wandte Mathematik und Physik, vol. 59, no. 1, pp. 124–144, 2008. View at Google Scholar
  28. A. Alizadeh-Pahlavan and K. Sadeghy, “On the use of homotopy analysis method for solving unsteady MHD flow of Maxwellian fluids above impulsively stretching sheets,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1355–1365, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. J. K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  30. C. K. Chen and S. H. Ho, “Solving partial differential equations by two-dimensional differential transform method,” Applied Mathematics and Computation, vol. 106, no. 2-3, pp. 171–179, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 547–567, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  32. S. Mosayebidorcheh, M. Vatani, D. D. Ganji, and T. Mosayebidorcheh, “Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability,” Alexandria Engineering Journal, vol. 53, no. 4, pp. 779–785, 2014. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Sheikholeslami, M. M. Rashidi, D. M. Al Saad, F. Firouzi, H. B. Rokni, and G. Domairry, “Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects,” Journal of King Saud University—Science, 2015. View at Publisher · View at Google Scholar · View at Scopus
  34. M. Sheikholeslami and D. D. Ganji, “Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM,” Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 651–663, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. M. Hatami and D. Jing, “Differential transformation method for newtonian and non-newtonian nanofluids flow analysis: compared to numerical solution,” Alexandria Engineering Journal, 2016. View at Publisher · View at Google Scholar
  36. S. H. Esmail and M. M. Taha, “Application of the differential transform method to the advection-diffusion equation in three-dimensions,” Progress in Physics, vol. 12, no. 3, pp. 205–210, 2016. View at Google Scholar
  37. N. M. Bujurke, V. S. Madalli, and B. G. Mulimani, “Long series analysis of laminar flow through parallel and uniformly porous walls of different permeability,” Computer Methods in Applied Mechanics and Engineering, vol. 160, no. 1-2, pp. 39–56, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  38. G. W. Sutton and A. Sherman, Engineering Magnetohydrodynamics, McGraw-Hill, New York, NY, USA, 1965.