The problem of mixed convection heat transfer of nanofluid in a lid driven square cavity containing several heated triangular cylinders is studied numerically using the finite volume discretization method. The upper and bottom walls are thermally insulated while the left and right walls are cooled at constant temperature, T_c. The present investigation considered the effects of pertinent parameters such as; size and number of the heated triangular cylinders on the flow and Nusselt number. The other parameters governing the problem are the Richardson number (0.1? Ri ? 100), the Prandtl number of the pure water (Pr = 6.2) and the volume fraction of nanoparticles (0 ? ? ? 0.05). Results show that increasing size and number of the heated triangular cylinders leads to increase the heat transfer rate. It is also found that by reducing Richardson number and increasing the volume fraction of nanoparticles, the average Nusselt number increases.

The aim of this paper, is to use a more realistic model which incorporates the effects of Brownian motion and thermophoresis for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform heat source in a confined medium filled of a Newtonian nanofluid layer and heated from below, this layer is assumed to have a low concentration of nanoparticles. The linear study which was achieved in this investigation shows that the thermal stability of Newtonian nanofluids depends of the state of the horizontal boundaries (rigid or free), the heat source strength ,the buoyancy forces, the Brownian motion, the thermophoresis and other thermo-physical properties of nanoparticles. The governing differential equations are transformed into a set of ordinary differential equations by using similarity transformations, these equations will be solved analytically by converting our boundary value problem to an initial value problem, after this step we will approach the searched solutions numerically with polynomials of high degree to obtain a fifth-order-accurate solution.

The aim of this paper, is to use the Buongiorno's mathematical model for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform vertical magnetic field in a confined Darcy-Brinkman porous medium filled of an electrically conducting nanofluid which will be considered as Newtonian and heated uniformly from below. The linear study which was achieved in this investigation shows that the thermal stability of nanofluids depends of the state of the horizontal boundaries (rigid or free), the magnetic Chandrasekhar number, the buoyancy forces, the Brownian motion, the thermophoresis and other thermo-physical properties of nanoparticles. The governing differential equations are transformed into a set of ordinary differential equations by using similarity transformations, these equations will be solved analytically by converting our boundary value problem to an initial value problem, after this step we will approach the searched solutions numerically by polynomials of high degree to obtain a fourth-order-accurate solution.