The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.
[1] Anderson H.I., Hansen O.R. and Holmedal B. (1994): Diffusion of a chemically reactive species from a stretching sheet. - Int. J. of Heat Mass Transfer, vol.37, No.4, pp.659-664.
[2] Xu H. and Liao S.J. (2009): Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. - Comput. Math. Appl., vol.57, pp.1425-1431.
[3] Mukhopadhyay S. (2013): Casson fluid flow and heat transfer over a nonlinearly stretching surface. - Chin. Phys. B 22, No.7, 074701.
[4] Prasad K.V., Santhi., S.R. and Datti P.S. (2012): Non-Newtonian power-law fluid flow and heat transfer over a non-linearly stretching surface. - Appl. Math., vol.3, No.5, pp.425-435.
[5] Wu J. and Thompson M.C. (1996): Non-Newtonian shear-thinning flows past a flat plate. - J. Non-Newton. Fluid Mech., vol.66, pp.127-144.
[6] Vieru D., Fetecau C. and Fetecau C. (2008): Flow of a viscoelastic fluid with fractional Maxwell model between two side walls perpendicular to a plate. - Appl. Math. Comput., vol.200, pp.459-464.
[7] Fetecau C., Jamil M., Fetecau C. and Siddique I. (2009): A note on the second problem of Stokes for Maxwell fluids. - Int. J. of Non-Linear Mech., vol.44, pp.1085-1090.
[8] Fetecau C., Athar M. and Fetecau C. (2009): Unsteady flow of generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate. - Comput. Math. Appl., vol.57, pp.596-603.
[9] Hayat T., Fetecau C. and Sajid M. (2008): On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame. - Phys. Lett. A 372, pp.1639-1644.
[10] Bataller R.C. (2007): Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet. - Comput. Math. Appl., vol.53, pp.305-316.
[11] Abel M.S. and Nandeppanavar Mahantesh M. (2009): Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with nonuniform heat source/sink. - Commun Nonlinear Sci Numer Simul., vol.14, pp.2120-2131.
[12] Mukhopadhyay S. (2012): Heat transfer analysis for unsteady flow of a Maxwell fluid over a stretching surface in the presence of a heat source/sink. - Chinese Phy. Lett., vol.29, No.5, pp.054703.
[13] Andersson H.I., Hansen O.R. and Holmedal B. (1994): Diffusion of a chemically reactive species from a stretching sheet. - Int. J. of Heat Mass Transfer, vol.37, pp.659-664.
[14] Cortell R. (2007): Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. - Chem. Engng. Processing: Process Intensification, vol.46, pp.982-989.
[15] Hayat T., Awais M., Qasim M. and Hendi A.A. (2011): Effects of mass transfer on the stagnation point flow of an upper-convected Maxwell (UCM) fluid. - Int. J. of Heat and Mass Transfer, vol.54, pp.3777-3782.
[16] Mukhopadhyay S. and Bhattacharyya K. (2012): Unsteady flow of a Maxwell fluid over a stretching surface in presence of chemical reaction. - J. of the Egyptian Math. Society, vol.20, pp.229-234.
[17] Choi SUS. (1995): Enhancing thermal conductivity of fluids with nanoparticles. - ASME, USA, pp.99-105.
[18] Buongiorno J. (2006): Convective transport in nanofluids. - J. of Heat Transf., vol.128, pp.240-250.
[19] Khan W.A. and Pop I. (2010): Boundary-layer flow of a nanofluid past a stretching sheet. - Int. J. Heat Mass Transf., vol.53, pp.2477-2483.
[20] Turkyilmazoglu M. (2012): Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids. - Chem. Eng. Sci., vol.84, pp.182-187.
[21] Hayat T., Muhammad T., Alsaedi A. and Alhuthali M.S. (2015): Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. - J. Magn. Magn. Mater., vol.385, pp.222-229.
[22] Ashraf M.B., Hayat T. and Alsaedi A. (2015): Three-dimensional flow of Eyring-Powell nanofluid by convectively heated exponentially stretching sheet. - Eur. Phys. J. Plus, vol.5, pp.130-142.
[23] Zhang C., Zheng L., Zhang X. and Chen G. (2015): MHD flow and radiation heat transfer of nanofluids in porous media with variable surface heat flux and chemical reaction. - Appl. Math. Model., vol.39, pp.165-181.
[24] Hayat T., Muhammad T., Shehzad S.A. and Alsaedi A. (2015): Similarity solution to three dimensional boundary layer flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink. - AIP Adv., vol.5, 017107.
[25] Liao Sj. (2003): Beyond perturbation: introduction to homotopy analysis method. - Boca Raton: Chapman & Hall/CRC Press.
[26] Liao Sj. (1992): The proposed homotopy analysis technique for the solution of non-linear problems. - Ph. D. Thesis; Shanghai Jiao Tong University.
[27] Mustafa M., Junaid Ahmad Khan, Hayat T. and Alsaedi A. (2015): Simulations for Maxwell fluid flow past a convectively heated exponentially stretching sheet with nanoparticles. - AIP Adv., vol.5, 037133.
[28] Hayat T., Taseer Muhammad, Shehzad S.A. Chen G.Q. and Ibrahim A. Abbas (2015): Interaction of magnetic field in flow of Maxwell nanofluid with convective effect. - Journal of Magnetism and Magnetic Materials, vol.389, pp.48-55.
[29] Brewster M.Q. (1972): Thermal Radiative Transfer Properties. - John Wiley and Sons.
[30] Liao Sj. (2012): Homotopy analysis method in nonlinear differential equations. - Beijing and Heidelberg: Higher Education Press and Springer.
[31] Mustafa M., Ahmad Khan J., Hayat T. and Alsaedi A. (2015): Sakiadis flow of Maxwell fluid considering magnetic field and convective boundary conditions. - AIP Adv., vol.5, 027106.
[32] Ramesh G.K. and Gireesha B.J. (2014): Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. - Ain Shams Engineering Journal, vol.5, pp.991-998.
[33] Chamka A.J., Rashad A.M. and Ram Reddy Ch. (2014): Murthy, PVSN, Effect of suction/injuction on free convection along a vertical plate in a nanofluid saturated non-Darcy porous medium with internal heat generation. - Indian J. Pure Appl. Math., vol.45, No.3, pp.321-341.
[34] Shehzad S.A., Hayat T. and Alsaedi A. (2015): Influence of convective heat and mass conditions in MHD flow of nanofluid. - Bulletin of the Polish Academy of Sciences Technical Sciences, vol.63, DOI: 10.1515/bpasts- 2015-0053.
[35] Swati Mukhopadhyay, Krishnendu Bhattacharyya and Layek G.C. (2014): Mass Transfer over an Exponentially Stretching Porous Sheet Embedded in a Stratified Medium. - Chem. Eng. Comm., vol.201, pp.272-286.
[36] Magyari E. and Keller B. (1999): Heat and mass transfer in the boundary layer on an exponentially stretching continuous surface. - J. Phys. D. Appl. Phys., vol.32, pp.577-585.