Analytical and Numerical Investigation of Second Grade Magnetohydrodynamics Flow over a Permeable Stretching Sheet

[1]           K. Vajravelu, T. Roper, Flow and heat transfer in a second grade fluid over a stretching sheet, International Journal of Non-Linear Mechanics, Vol. 34, No. 6, pp. 1031-1036, 1999/11/01, 1999.

[2]           M. Massoudi, Boundary layer flow of a second grade fluid with variable heat flux at the wall, Appl. Math. Comput., Vol. 143, No. 2-3, pp. 201-212, 2003.

[3]           K. Vajravelu, D. Rollins, Hydromagnetic flow of a second grade fluid over a stretching sheet, Applied Mathematics and Computation, Vol. 148, No. 3, pp. 783-791, 1/30/, 2004.

[4]           R. Cortell, Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field, International Journal of Heat and Mass Transfer, Vol. 49, No. 11–12, pp. 1851-1856, 6//, 2006.

[5]           M. Sajid, T. Hayat, S. Asghar, On the analytic solution of the steady flow of a fourth grade fluid, Physics Letters A, Vol. 355, No. 1, pp. 18-26, 6/19/, 2006.

[6]           V. Marinca, N. Herişanu, C. Bota, B. Marinca, An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate, Applied Mathematics Letters, Vol. 22, No. 2, pp. 245-251, 2//, 2009.

[7]           M. Sajid, R. Mahmood, T. Hayat, Finite element solution for flow of a third grade fluid past a horizontal porous plate with partial slip, Computers & Mathematics with Applications, Vol. 56, No. 5, pp. 1236-1244, 9//, 2008.

[8]           S. Aïboud, S. Saouli, Second Law Analysis of Viscoelastic Fluid over a Stretching Sheet Subject to a Transverse Magnetic Field with Heat and Mass Transfer, Entropy, Vol. 12, No. 8, pp. 1867, 2010.

[9]           B. Sahoo, Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet, Computers & Mathematics with Applications, Vol. 61, No. 5, pp. 1442-1456, 3//, 2011.

[10]         B. I. Olajuwon, Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion, International Communications in Heat and Mass Transfer, Vol. 38, No. 3, pp. 377-382, 3//, 2011.

[11]         S. Islam, Z. Bano, I. Siddique, A. M. Siddiqui, The optimal solution for the flow of a fourth-grade fluid with partial slip, Computers & Mathematics with Applications, Vol. 61, No. 6, pp. 1507-1516, 3//, 2011.

[12]         B. Sahoo, S. Poncet, Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition, International Journal of Heat and Mass Transfer, Vol. 54, No. 23–24, pp. 5010-5019, 11//, 2011.

[13]         A. Aziz, T. Aziz, MHD flow of a third grade fluid in a porous half space with plate suction or injection: An analytical approach, Applied Mathematics and Computation, Vol. 218, No. 21, pp. 10443-10453, 7/1/, 2012.

[14]         M. Hosseini, Z. Sheikholeslami, D. D. Ganji, Non-Newtonian fluid flow in an axisymmetric channel with porous wall, Propulsion and Power Research, Vol. 2, No. 4, pp. 254-262, 12//, 2013.

[15]         T. Gul, S. Islam, R. A. Shah, I. Khan, S. Shafie, M. A. Khan, Analysis of thin film flow over a vertical oscillating belt with a second grade fluid, Engineering Science and Technology, an International Journal, Vol. 18, No. 2, pp. 207-217, 6//, 2015.

[16]         T. E. Akinbobola, S. S. Okoya, The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink, Journal of the Nigerian Mathematical Society, Vol. 34, No. 3, pp. 331-342, 12//, 2015.

[17]         M. Mustafa, Viscoelastic Flow and Heat Transfer over a Non-Linearly Stretching Sheet: OHAM Solution, Journal of Applied Fluid Mechanics, Vol. 9, No. 3, pp. 1321-1328, 2016.

[18]         S. M. Ebrahimi, M. Javanmard, M. H. Taheri, M. Barimani, Heat transfer of fourth-grade fluid flow in the plane duct under an externally applied magnetic field with convection on walls, International Journal of Mechanical Sciences, Vol. 128–129, pp. 564-571, 8//, 2017.

[19]         P. G. Moakher, M. Abbasi, M. Khaki, Fully developed flow of fourth grade fluid through the channel with slip condition in the presence of a magnetic field, Journal of Applied Fluid Mechanics, Vol. 9, No. 7, pp. 2239-2245, 2016.

[20]         R. S. Rivlin, J. L. Ericksen, Stress-Deformation Relations for Isotropic Materials,  in: G. I. Barenblatt, D. D. Joseph, Collected Papers of R.S. Rivlin: Volume I and II, Eds., pp. 911-1013, New York, NY: Springer New York, 1997.

[21]         J. E. Dunn, R. L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Archive for Rational Mechanics and Analysis, Vol. 56, No. 3, pp. 191-252, 1974.

[22]         S. A. R. Sahebi, H. Pourziaei, A. R. Feizi, M. H. Taheri, Y. Rostamiyan, D. D. Ganji, Numerical analysis of natural convection for non-Newtonian fluid conveying nanoparticles between two vertical parallel plates, The European Physical Journal Plus, Vol. 130, No. 12, pp. 238, 2015.

[23]         P. G. Moakhar, M. Abbasi, M. Khaki, Fully Developed Flow of Fourth Grade Fluid through the Channel with Slip Condition in the Presence of a Magnetic Field, Journal of Applied Fluid Mechanics, Vol. 9, No. 5, pp. 2239-2245, 2016.

[24]         S. M. Ebrahimi, M. Abbasi, M. Khaki, Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 40, No. 4, pp. 315-324, 2016.