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

The existing solutions of Navier–Stokes and energy equations in the literature regarding the three-dimensional problem of stagnation-point flow either on a flat plate or on a cylinder are only for the case of axisymmetric formulation. The only exception is the study of three-dimensional stagnation-point flow on a flat plate by Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near Stagnation Point,” Philos. Mag., 42, pp. 1433–1440), which is based on boundary layer theory approximation and zero pressure assumption in direction of normal to the surface. In our study the nonaxisymmetric three-dimensional steady viscous stagnation-point flow and heat transfer in the vicinity of a flat plate are investigated based on potential flow theory, which is the most general solution. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces a two-dimensional flow with different components of velocity on the plate. This situation may happen if the flow pattern on the plate is bounded from both sides in one of the directions, for example x-axis, because of any physical limitation. A similarity solution of the Navier–Stokes equations and energy equation is presented in this problem. A reduction in these equations is obtained by the use of appropriate similarity transformations. Velocity profiles and surface stress-tensors and temperature profiles along with pressure profile are presented for different values of velocity ratios, and Prandtl number.

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

Journal of Heat Transfer ◽

10.1115/1.4024386 ◽

2013 ◽

Vol 135 (10) ◽

Cited By ~ 3

Author(s):

H. R. Mozayyeni ◽

Asghar B. Rahimi

Keyword(s):

Heat Transfer ◽

Flat Plate ◽

Wall Temperature ◽

Compressible Fluid ◽

Three Dimensional ◽

Compressibility Factor ◽

Viscous Compressible Fluid ◽

Constant Wall Temperature ◽

Solution Approach ◽

Flow And Heat Transfer

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.

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

Journal of Heat Transfer ◽

10.1115/1.4032288 ◽

2016 ◽

Vol 138 (4) ◽

Author(s):

H. R. Mozayyeni ◽

Asghar B. Rahimi

Keyword(s):

Heat Transfer ◽

Flat Plate ◽

Compressible Fluid ◽

Three Dimensional ◽

Similarity Solutions ◽

Main Stream ◽

Viscous Compressible Fluid ◽

Flow And Heat Transfer ◽

Wide Range ◽

Impinging Flow

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.

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Numerical Simulation of Laminar Flow and Heat Transfer Over a Blunt Flat Plate in Square Channel

Journal of Heat Transfer ◽

10.1115/1.1420715 ◽

2001 ◽

Vol 124 (1) ◽

pp. 8-16 ◽

Cited By ~ 13

Author(s):

Hideki Yanaoka ◽

Hiroyuki Yoshikawa ◽

Terukazu Ota

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Flat Plate ◽

Stokes Equations ◽

Three Dimensional ◽

Flow Region ◽

Recirculation Region ◽

Square Channel ◽

Flow And Heat Transfer ◽

Side Walls

Three-dimensional simulations of laminar separated and reattached flow and heat transfer over a blunt flat plate in a square channel are presented. Numerical calculations of Navier-Stokes equations and energy equation are carried out using the finite difference method. Results of three-dimensional calculation are compared with two-dimensional ones and effects of the side walls are described. It is clarified from the present results that the reattachment length increases with an increase of Reynolds number and the flow in the recirculation region becomes three-dimensional. The reattachment line is curved by the side wall effects. Two-dimensionality of the flow is reduced as Reynolds number increases. The horseshoe-vortex formed near the side walls has great effects upon the heat transfer in the redeveloping flow region. The separated shear layer around the center of plate becomes unstable with a further increase of Reynolds number and the vortices are periodically shed from the reattachment flow region. Such vortices exhibit a hairpin-like structure and greatly influence the heat transfer.

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