Triple convective-diffusion boundary layer along a vertical flat plate in a porous medium saturated by a water-based nanofluid Z.H. Khan a, d , J.R. Culham b , W.A. Khan b, * , I. Pop c a School of Mathematical Sciences, Peking University, Beijing 100871, PR China b Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada c Department of Mathematics, Babes ¸-Bolyai University, 400084 Cluj-Napoca, Romania d Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa, Pakistan article info Article history: Received 17 July 2014 Received in revised form 28 November 2014 Accepted 7 December 2014 Available online Keywords: Triple diffusion Free convection Porous media Convective boundary condition Buongiorno model Nanofluids abstract In this article, we investigate steady triple convective-diffusive boundary layer free convection flow past a vertical flat plate embedded in a porous medium filled by a water-based nanofluid and two salts. The plate is assumed to be convectively cooled by a surrounding fluid. It is assumed that there is no nano- particle flux at the surface and the effect of thermophoresis is taken in to account in the boundary condition. The effects of Brownian motion and thermophoresis parameters are also introduced through a Buongiorno model in the governing equations. The self-similar solutions are obtained numerically using an implicit finite difference method. The effects of the buoyancy ratio, regular Lewis numbers and modified Dufour parameters of both salts and nanofluid parameters on the flow and heat transfer are investigated. It is found that the heat transfer rate increases as we include nanoparticles and salts. Furthermore, it is also shown that the Brownian motion has negligible effects on reduced Nusselt number. © 2014 Elsevier Masson SAS. All rights reserved. 1. Introduction In medical sciences and engineering, the use of nanofluids in enhancing convective heat transfer is increasing day by day. Nanofluids are the liquid suspension containing nano-sized parti- cles of various materials, such as oxide ceramics, nitride ceramics, carbide ceramics, metals, semiconductors, carbon nanotubes and nanocomposites. Convective flow in porous media saturated with nanofluids have been extensively studied by many investigators owing to its several applications in engineering such as post acci- dental heat removal in nuclear reactors, solar collectors, and heat exchangers. Steady free convection about a vertical flat plate embedded in a saturated porous medium without any nanofluid has been investigated by a large number of researchers [1e 15] among others. They considered different thermal boundary con- ditions and obtained analytical and numerical solutions. They investigated the effects of suction/injection, internal heat genera- tion, radiation on the dimensionless velocity, temperature, local skin friction and the local rate of heat transfer with uniform and variable thermophysical properties. Natural convective boundary layer flow in a porous medium saturated with a nanofluid over a vertical plate under different thermal boundary conditions has been considered by a number of researchers. For example, Kuznetsov and Nield [16] studied analytically the natural convective boundary-layer flow of a nano- fluid past a vertical plate. Later on, Kuznetsov and Nield [17] studied the double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. They employed a Buongiorno model and included regular diffusion and cross-diffusion terms in the energy equation. A similarity solution was presented. Numerical calculations were performed in order to obtain correlation for- mulas giving the reduced Nusselt number as a function of the various relevant parameters. Khan and Aziz [18e20] used the nanofluid mathematical model proposed by Buongiorno to study double-diffusive natural con- vection from a vertical plate under different thermal boundary conditions. A porous medium saturated with a binary base fluid containing nanoparticles was considered, the porous medium be- ing described by the Darcy model. They investigated the effects of various parameters on the flow, heat and mass transfer character- istics. Also, correlations for the Nusselt and Sherwood numbers * Corresponding author. E-mail addresses: wkhan_2000@yahoo.com, wkhan1956@hotmail.com (W.A. Khan). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts http://dx.doi.org/10.1016/j.ijthermalsci.2014.12.002 1290-0729/© 2014 Elsevier Masson SAS. All rights reserved. International Journal of Thermal Sciences 90 (2015) 53e61