Three-Dimensional Stagnation Flow Research Articles

Discussion: “Three-Dimensional Stagnation Flow and Heat Transfer of a Viscous, Compressible Fluid on a Flat Plate” (Mozayyeni, H. R., and Rahimi, A. B., 2013, ASME J. Heat Transfer, 135(10), p. 101702)

The present comment concerns some doubtful results included in the discussed paper.

Similarity Solutions of Unsteady Three-Dimensional Stagnation Flow and Heat Transfer of a Viscous, Compressible Fluid on an Accelerated Flat Plate

The most general form of the problem of stagnation-point flow and heat transfer of a viscous, compressible fluid impinging on a flat plate is solved in this paper. The plate is moving with a constant or time-dependently variable velocity and acceleration toward the impinging flow or away from it. In this study, an external low Mach number flow impinges on the plate, along z-direction, with strain rate a and produces three-dimensional flow. The wall temperature is assumed to be maintained constant, which is different from that of the main stream. The density of the fluid is affected by the temperature difference existing between the plate and the incoming far-field flow. Suitably introduced similarity transformations are used to reduce the unsteady, three-dimensional, Navier–Stokes, and energy equations to a coupled system of nonlinear ordinary differential equations. The fourth-order Runge–Kutta method along with a shooting technique is applied to numerically solve the governing equations. The results are achieved over a wide range of parameters characterizing the problem. It is revealed that the significance of the aspect ratio of the velocity components in x and y directions, λ parameter, is much more noticeable for a plate moving away from impinging flow. Moreover, negligible heat transfer rate is reported between the plate and fluid viscous layer close to the plate when the plate moves away with a high velocity.

Three-dimensional stagnation flow of a nanofluid containing both nanoparticles and microorganisms on a moving surface with anisotropic slip

In this paper, we have extended Wang’s (2013) problem of the three-dimensional stagnation flow of a Newtonian fluid on a moving plate with anistropic slip to the case of a nanofluid in suspension of both the nanoparticles and microorganisms. The passively controlled nanofluid model is taken into account to describe this problem, which is believed to be physically more realistic than previously commonly used models. The problem is then reduced by a set of similarity transformations to seven coupled nonlinear ordinary equations with coupled boundary conditions. Numerical solutions are given by means of a very efficient finite difference method. The influences of various physical parameters on the distributions of the velocity, the temperature, the nanoparticle volumetric fraction, the density of motile microorganisms profiles, as well as the local skin friction coefficient, the local Nusselt number, the local wall mass flux and the local density of the motile microorganisms are presented and discussed.

Three-Dimensional Stagnation Flow and Heat Transfer of a Viscous, Compressible Fluid on a Flat Plate

The steady-state three-dimensional flow and heat transfer of a viscous, compressible fluid in the vicinity of stagnation point region on a flat plate with constant wall temperature is investigated by similarity solution approach, taking into account the variation of density of the fluid with respect to temperature. The free stream, along z-direction, impinges on the flat plate to produce a flow with different velocity components. An exact solution of the problem is obtained for the three dimensional case by the reduction of the Navier–Stokes and energy equations using appropriate similarity transformations introduced for the first time. The nonlinear ordinary differential equations are solved numerically using a finite difference scheme. Computations have been conducted for different values of the parameters characterizing the problem. The obtained results show that increasing the value of compressibility factor and wall temperature both cause the value of the velocity components and temperature gradients and pressure gradients in the vicinity of the plate to increase.

Three-Dimensional Stagnation Flow and Heat Transfer on a Flat Plate with Transpiration

DOI: 10.2514/1.41529 The existing solutions of Navier–Stokes and energy equations in the literature regarding the three-dimensional problemofstagnation-point flow,eitherona flatplateoronacylinderwithorwithouttranspiration,areonlyforthe case of axisymmetric formulation. In this study, the nonaxisymmetric three-dimensional steady viscous stagnationpoint flow and heat transfer in the vicinity of a flat plate are investigated when suction and blowing are also consideredinthemodel.Anexternal fluid,alongzdirection,withstrainrateaimpingesonthis flatplateandproduces a two-dimensional flow with different components of velocity on the plate. This external flow, as an example, can be generatedintheformofmultiplejetstreamsinarowinwhichthejetsareinequaldistancesfromeachotheralongthe x axis. A similarity solution of the Navier–Stokes equations and energy equation is presented in this problem. A reduction of these equations is obtained by use of appropriate similarity transformations. Velocity profiles and surface stress tensors and temperature profiles along with pressure profiles are presented for different values of velocity ratios and Prandtl number for sample cases of transpiration.

Unsteady axisymmetric stagnation point flow

The unsteady axisymmetric case of a three-dimensional stagnation flow is investigated. The incompressible potential flow far away from the stagnation point oscillates about a constant mean value. Using perturbation methods, an analytical solution of the problem is obtained for the extreme cases of low and high oscillation frequencies.

Heat transfer in unsteady laminar boundary layers at an incompressible three-dimensional stagnation flow

Heat transfer in unsteady laminar boundary layers at an incompressible three-dimensional stagnation flow

Heat transfer in a radiating, nonsteady, three-dimensional stagnation flow

A similar solution has been obtained to the problem of simultaneous radiation and convection for nonsteady stagnation point flow over a three-dimensional blunt body with both boundary layer suction and injection.