Abstract
Analytical results are presented for a steady three-dimensional free convection flow in the stagnation point region over a general curved isothermal surface placed in a nanofluid. The momentum equations in x- and y-directions, energy balance equation, and nanoparticle concentration equation are reduced to a set of four fully coupled nonlinear differential equations under appropriate similarity transformations. The well known technique optimal homotopy analysis method (OHAM) is used to obtain the exact solution explicitly, whose convergence is then checked in detail. Besides, the effects of the physical parameters, such as the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the buoyancy ratio on the profiles of velocities, temperature, and concentration, are studied and discussed. Furthermore the local skin friction coefficients in x- and y-directions, the local Nusselt number, and the local Sherwood number are examined for various values of the physical parameters.
Highlights
The stagnation point is defined as the point on the surface of objects in the flow field where the fluid is brought at rest by the object
The problem of flow and heat transfer at a general three-dimensional stagnation-point region has important applications in many manufacturing processes in petrochemical industries, the aerodynamic of plastic sheet, solar central receivers exposed to wind currents, and so forth
The boundary layer flows near a three-dimensional stagnation point of attachment on an isothermal surface have been examined several times in the past
Summary
The stagnation point is defined as the point on the surface of objects in the flow field where the fluid is brought at rest by the object. Poots [3] formulated the boundary-layer equations for the free convection flow at three-dimensional lower stagnation point on a general curved isothermal surface. Slaouti et al [11] described the momentum and the thermal boundary layer characteristics for unsteady free convection flow in the stagnation-point region of a heated three-dimensional body. Admon et al [15] presented flow and heat transfer analysis for the unsteady free convection flow near the stagnation point of a three-dimensional body. Bachok et al [23] studied the effects of nanoparticle volume fraction parameter and the ratio of gradients of velocities on the flow and heat transfer for the steady threedimensional stagnation-point flow in a nanofluid. In this paper the three-dimensional laminar free convection stagnation-point flow of a nanofluid on a general curved isothermal surface is considered. Besides The effects of the physical parameters such as Le, Nb, Nt, and Nr on profiles of velocities, temperature, and concentration as well as the important quantities such as the local skin friction coefficients, the local Nusselt number, and the local Sherwood number are explored in detail
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