Development of Wall and Free Plumes Above a Heated Vertical Plate

1978 ◽  
Vol 100 (2) ◽  
pp. 184-190 ◽  
Author(s):  
E. M. Sparrow ◽  
S. V. Patankar ◽  
R. M. Abdel-Wahed
Keyword(s):  
Boundary Layer ◽  
Vertical Plate ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Heated Plate ◽  
Adiabatic Wall ◽  
Similarity Type ◽  
Vertical Extension ◽  
Prandtl Numbers ◽  
Wall Plume

An analysis has been made to determine the successive stages of development as the natural convection boundary layer on a steadily heated vertical plate evolves into a plume. Both the wall plume and the free plume are investigated. The wall plume develops along an adiabatic wall which is the vertical extension of the heated plate. The free plume is created as the boundary layer streams away from the upper edge of the plate. Since the plate is heated on only one of its faces, the free plume is initially unsymmetric. The development of these plumes does not admit similarity-type boundary layer solutions, and numerical techniques were, therefore, employed, with results being obtained for Prandtl numbers of 0.7, 2, 5, and 10. It was found that at sufficient downstream distances both plumes attain their respective fully developed behaviors (i.e., similar profiles at successive streamwise stations). For the wall plume, the development for all Prandtl numbers is completed at a position that is about five plate lengths above the leading edge of the heated plate. The development length for the free plume for Pr = 0.7 is about the same as that for the wall plume, but about 30 plate lengths are required for the development of the free plume when Pr = 10. The fully developed free plume is symmetric.

scholarly journals The laminar free-convection boundary layer on a vertical heated plate in the neighbourhood of a discontinuity in plate temperature

1970 ◽  
Vol 11 (2) ◽  
pp. 149-168 ◽  
Author(s):  
R. K. Smith
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Heated Plate ◽  
Plate Temperature ◽  
Expansion Procedure ◽  
Isothermal Case ◽  
Free Convection Boundary Layer

If velocity and temperature profiles are known at a particular distance along a vertical heated plate, the equations of motion determine the velocity and temperature at points downstream, for a given varition of plate temperature. The problem of continuing the boundary layer solution for given initial conditions was investigated by Goldstein [2], for the isothermal case of the laminar, incompressible flow past plate, with a given streamwise varitain of pressure gradient outside the boundary layer. He showed that the solution is not always free from singularities and developed an expansion procedure to calculate the flow downstream when these occurred. Typical singularities occur, for instance, near the leading edge of the plate where the no-slip condition is imposed on the plate surface and near the trailing edge, where this condition is relaxed to one of zero stress along the axis of symmetry of the wake.

Experimental Investigation of Turbulence Transition of Natural Convection Boundary Layer Along a Vertical Plate in Water With Sub-Millimeter-Bubble Injection

2011 ◽  
Author(s):  
Atsuhide Kitagawa ◽  
Hiroki Endo ◽  
Yoshimichi Hagiwara
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Natural Convection ◽  
Velocity Fluctuation ◽  
Vertical Plate ◽  
Liquid Velocity ◽  
Convection Boundary Layer ◽  
Layer Width ◽  
Turbulence Transition ◽  
Convection Boundary

This paper presents an experimental investigation of the turbulence transition of the natural convection boundary layer along a vertical plate in water with sub-millimeter-bubble injection. In this study, we focus on the relationship between the bubble injection position L and the turbulence transition of the boundary layer. Temperature and velocity measurements show that sub-millimeter-bubble injection for L = 1.6 mm suppresses the turbulence transition of the natural convection boundary layer, while that for L = 3.6 mm enhances the turbulence transition of the boundary layer. For L = 1.6 mm, the appearance region of the bubble-induced liquid velocity fluctuation at the upstream unheated section is restricted near the wall, though the peak value of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation induced by bubbles at the upstream unheated section distributes widely over the laminar boundary layer width. Therefore, we expect that the turbulence transition of the natural convection boundary layer for the case with bubble injection depends on the magnitude and appearance region of the bubble-induced liquid velocity fluctuation at the upstream unheated section.

scholarly journals Separation Points of Magneto-hydrodynamic Boundary Layer Flow Along a Vertical Plate with Exponentially Decreasing Free Stream Velocity

1970 ◽  
Vol 5 (1) ◽  
pp. 11-18 ◽  
Author(s):  
MA Alim ◽  
MM Rahman ◽  
MM Karim
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Vertical Plate ◽  
Free Stream ◽  
Stream Velocity ◽  
Convection Boundary Layer ◽  
Boundary Layer Equations ◽  
Box Scheme ◽  
Convection Boundary ◽  
Layer Flow

The points of separation of magneto-hydrodynamic mixed convection boundary layer flow along a vertical plate have been investigated. The free stream velocity is considered decreasing exponentially in the stream wise direction. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to local non-similar boundary layer equations, which are solved numerically by implicit finite difference method known as Keller box scheme. Here we have focused our attention to find the effects of suction, magnetic field and other relevant physical parameters on the position of boundary layer separation. The numerical results are expressed in terms of local shear stress showing the effects of suction, buoyancy, Prandlt number and magnetic field on the shear stress as well as on the points of separation. Keywords: Separation points, magneto-hydrodynamic, mixed convection, boundary layer, suction, finite difference method, Keller box scheme.   doi:10.3329/jname.v5i1.1868Journal of Naval Architecture and Marine Engineering Vol. 5, No. 1 (June, 2008) 11-18. 

Instability of a thermal boundary layer in a constant electric field

1971 ◽  
Vol 47 (2) ◽  
pp. 231-239 ◽  
Author(s):  
Robert J. Turnbull
Keyword(s):  
Boundary Layer ◽  
Electric Field ◽  
Threshold Voltage ◽  
Thermal Boundary Layer ◽  
Vertical Plate ◽  
Constant Electric Field ◽  
Heated Plate ◽  
Conducting Liquid ◽  
Theoretical Predictions

The thermal boundary layer near a heated vertical plate in a poorly conducting liquid is subject to a horizontal d.c. electric field. If the electric field is strong enough, the boundary layer becomes unstable. In this paper a theory is developed to predict the onset of this instability. Experiments measuring the threshold voltage for instability are compared with the theoretical predictions. Other experiments are reported which determine the effect of this instability on the heat transferred from the heated plate.

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