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The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in a fluid-saturated porous medium is investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the Darcy-Brinkman, , mixed convection, λ, and slip, γ , parameters, are analysed and discussed in detail for the cases of assisting and opposing flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ = 0 (slip absent) and = 1 the lower solution branch is unstable while the upper solution branch is stable.

It has been more than two decades since the discovery of nanofluids-mixtures of common liquids and solid nanoparticles less than 100 nm in size. As a type of colloidal suspension, nanofluids are typically employed as heat transfer fluids due to their favorable thermal and fluid properties. There have been numerous numerical studies of nanofluids in recent years (more than 1000 in both 2016 and 2017, based on Scopus statistics). Due to the small size and large numbers of nanoparticles that interact with the surrounding fluid in nanofluid flows, it has been a major challenge to capture both the macro-scale and the nano-scale effects of these systems without incurring extraordinarily high computational costs.To help understand the state of the art in modeling nanofluids and to discuss the challenges that remain in this field, the present article reviews the latest developments in modeling of nanofluid flows and heat transfer with an emphasis on 3D simulations. In part I, a brief overview of nanofluids (fabrication, applications, and their achievable thermo-physical properties) will be presented first.Next, various forces that exist in particulate flows such as drag, lift (Magnus and Saffman), Brownian, thermophoretic, van der Waals, and electrostatic double layer forces and their significance in nanofluid flows are discussed. Afterwards, the main models used to calculate the thermophysical properties of nanofluids are reviewed. This will be followed with the description of the main physical models presented for nanofluid flows and heat transfer, from single-phase to Eulerian and Lagrangian two-phase models. In part II, various computational fluid dynamics (CFD) techniques will be presented. Next, the latest studies on 3D simulation of nanofluid flow in various regimes and configurations are reviewed. The present review is expected to be helpful for researchers working on numerical simulation of nanofluids and also for scholars who work on experimental aspects of nanofluids to understand the underlying physical phenomena occurring during their experiments.

a b s t r a c tThe steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream is investigated. The plate is assumed to move in the same or opposite directions to the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using the Kellerbox method. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle volume fraction profiles for some values of the governing parameters, namely, the plate velocity parameter, Prandtl number, Lewis number, the Brownian motion parameter and the thermophoresis parameter. The results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.