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and viscous flows .− In: Comput Fluid Dyn. Berlin Heidelberg: Springer-Verlag. [4] Hayat T. and Waqas M. (2014): Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions .− Scientia Iranica. Transaction B, Mechanical Engineering, vol.21, pp.682-692. [5] Rana P. and Bhargava R. (2011): Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study. − . [6] Sheikholeslami M. (2016): CVFEM for magnetic nanofluid convective heat transfer in a porous

References [1] Sakiadis B.C. (1961): Boundary-layer equations for two-dimensional and axisymmetric flow . – A.I.Ch.E. Journal, vol.7, No.1, pp.26-28. [2] Sakiadis B.C. (1961): The boundary layer on a continuous flat surface . – Vol.7, No.2, pp.221-225. [3] Goldsmith P. and May F.G. (1966): Diffusiophoresis and thermophoresis in water vapour systems, Aerosol science . – Academic Press, pp.163-194. [4] Uddin Md. J., Khan W.A. and Ismail A.I. Md. (2012): Scaling group transformation for MHD boundary layer slip flow of a nanofluid over a convectively heated

-18. [21] Falana A., Ojewale O.A., Adeboje T.B. (2016): Effect of Brownian motion and thermophoresis on a nonlinearly stretching permeable sheet in a nanofluid. – Advances in Nanoparticles, vol.5, pp.123-134. [22] Nield D.A. and Kuznetsov A.V. (2014): Thermal instability in a porous medium layer Saturated by a nanofluid: A revised model. – Int. J. Heat Mass Transfer, vol.68, pp.211-214. [23] Rosseland S. (1936): Theoretical Astrophysics. – Oxford: Clarendon Press. [24] Anjali Devi S.P. and Mekala S. (2015): Thermal radiation effects on hydromagnetic flow of


The study of radiative heat transfer in a nanofluid with the influence of magnetic field over a stretching surface is investigated numerically. Physical mechanisms responsible for magnetic parameter, radiation parameter between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. The parameters for Prandtl number Pr, Eckert number Ec, Lewis number Le, stretching parameter b/a and constant parameter m are examined. The governing partial differential equations were converted into nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with previously published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature and concentration distributions as well as skin-friction coefficient, Nusselt number and Sherwood number are discussed at the sheet for various values of physical parameters.


The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.

of various researchers. A benchmark study of convective transport in nanofluid was organized by Buongiorno [ 1 ]. A new model was developed in his study, which consists of the effects of two important mechanisms, namely, Brownian diffusion and thermophoresis. There are several studies in which the phenomena related to the onset of nanofluid convection in porous media have been examined under different aspects. Using Buongiorno’s model, Nield and Kuznetsov [ 2 ] analytically studied the onset of convection in a layer of porous medium saturated by a nanofluid. The


In this paper, we study the effects of variable gravity on thermal instability in a horizontal layer of a nanofluid in an anisotropic porous medium. Darcy model been used for the porous medium. Also, it incorporates the effect of Brownian motion along with thermophoresis. The normal mode technique is used to find the confinement between two free boundaries. The expression of the Rayleigh number has been derived, and the effects of variable gravity and anisotropic parameters on the Rayleigh number have been presented graphically


The stretching sheets with variable thickness may occur in engineering applications more frequently than a flat sheet. Due to its various applications, in the present analysis we considered a three dimensional unsteady MHD nanofluid flow over a stretching sheet with a variable wall thickness in a porous medium. The effects of radiation, viscous dissipation and slip boundary conditions are considered. Buongiorno’s model is incorporated to study the combined effects of thermophoresis and Brownian motion. The dimensionless governing equations are solved by using MATLAB bvp4c package. The impact of various important flow parameters is presented and analysed through graphs and tables. It is interesting to note that all the three boundary layer thicknesses are diminished by slip parameters. Further, the unsteady parameter decreases the hydromagnetic boundary layer thickness.


In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

.B. (2009): Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction . – Heat Mass Transf., vol.45, pp.703–712. [13] Nanda R.S. and Sharma V.P. (1962): Free convection laminar boundary layers in oscillatory flow . – J. Fluid Mech., vol.15, pp.419–428. [14] Sinha P.C. and Singh P. (1970): Transient free convection flow due to the arbitrary motion of a vertical plate . – Proc. Camb. Phil. Soc., vol.67, pp.677–688. [15] Butcher J.C. (1964): Implicit Runge-Kutta method . – Math