In the present work, an analysis has been carried out to study a problem of natural convection past a vertical porous plate, in a porous medium saturated by a nanofluid with the streamwise distance x. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The Darcy model is employed for the porous medium. Non-similar solution has been obtained. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb and a thermophoresis number Nt. The variation of the reduced Nusselt number with Nr, Nb and Nt is expressed by correlation formulas. The dependency of the Nusselt umber on these four parameters and the effect of suction and injection are investigated graphicly. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.

In the present work, an analysis has been carried out to study a problem of natural convection past a vertical porous plate, in a porous medium saturated by a nanofluid with the streamwise distance x. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The Darcy model is employed for the porous medium. Non-similar solution has been obtained. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb and a thermophoresis number Nt. The variation of the reduced Nusselt number with Nr, Nb and Nt is expressed by correlation formulas. The dependency of the Nusselt umber on these four parameters and the effect of suction and injection are investigated graphicly. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.

In the present work, an analysis has been carried out to study a problem of natural convection past a vertical porous plate, in a porous medium saturated by a nanofluid with the streamwise distance x. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The Darcy model is employed for the porous medium. Non-similar solution has been obtained. This solution depends on a Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb and a thermophoresis number Nt. The variation of the reduced Nusselt number with Nr, Nb and Nt is expressed by correlation formulas. The dependency of the Nusselt umber on these four parameters and the effect of suction and injection are investigated graphicly. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR , and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR , and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of Al2 O3 as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range (0, 0.2)with prandtl number Pr=6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles, stretching plate parameter and power law index. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when skin friction parameter increased. On the other hand, we concluded that the increase in stretching plate parameter and power law index made heat transfer rate increases and skin fraction decreases.

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of Al2 O3 as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range (0, 0.2)with prandtl number Pr=6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles, stretching plate parameter and power law index. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when skin friction parameter increased. On the other hand, we concluded that the increase in stretching plate parameter and power law index made heat transfer rate increases and skin fraction decreases.

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of Al2 O3 as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range (0, 0.2)with prandtl number Pr=6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles, stretching plate parameter and power law index. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when skin friction parameter increased. On the other hand, we concluded that the increase in stretching plate parameter and power law index made heat transfer rate increases and skin fraction decreases.

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of Al2 O3 as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range (0, 0.2)with prandtl number Pr=6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles, stretching plate parameter and power law index. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when skin friction parameter increased. On the other hand, we concluded that the increase in stretching plate parameter and power law index made heat transfer rate increases and skin fraction decreases.

This work aims to study the problem of unsteady mixed convection flow near the stagnation point of a heated vertical surface embedded in a nanofluid-saturated porous medium. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The presence of a solid matrix, which exerts first and second resistance parameters, is considered in this study. The selfsimilar solutions for the system of equations governing the problem are obtained. The resulting system of ordinary differential equations that govern the flow are solved numerically using fourth-fifth order Runge-Kutta with shooting method. Numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction, skin friction, Nusselt number and Sherwood number are produced for different values of the influence parameters.