A transformation of the boundary layer equations for free convection past a vertical flat plate with arbitrary blowing and wall temperature variations

1980 ◽  
Vol 23 (9) ◽  
pp. 1286-1288 ◽  
Author(s):  
M. Vedhanayagam ◽  
R.A. Altenkirch ◽  
R. Eichhorn
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Flat Plate ◽  
Wall Temperature ◽  
Temperature Variations ◽  
Boundary Layer Equations ◽  
Vertical Flat Plate

Unsteady laminar flow of gas near an infinite flat plate

1950 ◽  
Vol 46 (4) ◽  
pp. 603-613 ◽  
Author(s):  
C. R. Illingworth
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Flat Plate ◽  
Constant Temperature ◽  
Vortex Sheet ◽  
Absolute Temperature ◽  
Convection Current ◽  
Uniform Motion ◽  
Boundary Layer Equations ◽  
Set Up

AbstractBoundary-layer equations for the unsteady flow near an effectively infinite flat plate set into motion in its own plane are subjected to von Mises's transformation. Solutions are obtained for the flows in which gravity is neglected, the Prandtl number σ is arbitrary, and the plate has a constant temperature and a velocity that is either uniform or, with dissipation neglected, non-uniform. Explicit solutions are obtained for the case in which the viscosity μr varies directly as the absolute temperature Tr. Solutions are also obtained for the diffusion of a plane vortex sheet in a gas, and for the boundary layer near a uniformly accelerated plate of constant temperature when gravity is not neglected. For the non-uniform motion of a heat-insulated plate, dissipation not being negligible, a solution is obtained when σ is 1 and μr ∝ Tr. The relative importance of free convection due to gravity and forced convection due to viscosity is discussed, and a solution is obtained, with μr ∝ Tr, for the free convection current set up near a plate that is at rest in a gas at a temperature different from that of the plate, dissipation being neglected.

Free Convective Heat Transfer Over a Nonisothermal Body of Arbitrary Shape Embedded in a Fluid-Saturated Porous Medium

1987 ◽  
Vol 109 (1) ◽  
pp. 125-130 ◽  
Author(s):  
A. Nakayama ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Wall Temperature ◽  
Arbitrary Shape ◽  
Saturated Porous Medium ◽  
Axisymmetric Body ◽  
Two Dimensional ◽  
Vertical Flat Plate

The problem of free convective heat transfer from a nonisothermal two-dimensional or axisymmetric body of arbitrary geometric configuration in a fliud-saturated porous medium was analyzed on the basis of boundary layer approximations. Upon introducing a similarity variable (which also accounts for a possible wall temperature effect on the boundary layer length scale), the governing equations for a nonisothermal body of arbitrary shape can be reduced to an ordinary differential equation which has been previously solved by Cheng and Minkowycz for a vertical flat plate with its wall temperature varying in an exponential manner. Thus, it is found that any two-dimensional or axisymmetric body possesses a corresponding class of surface wall temperature distributions which permit similarity solutions. Furthermore, a more straightforward and yet sufficiently accurate approximate method based on the Ka´rma´n-Pohlhausen integral relation is suggested for a general solution procedure for a Darcian fluid flow over a nonisothermal body of arbitrary shape. For illustrative purposes, computations were carried out on a vertical flat plate, horizontal ellipses, and ellipsoids with different minor-to-major axis ratios.

Velocity Measurements in Two Natural Convection Air Flows Using a Laser Velocimeter

1979 ◽  
Vol 101 (2) ◽  
pp. 256-260 ◽  
Author(s):  
R. D. Flack ◽  
C. L. Witt
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Free Convection ◽  
Flat Plate ◽  
Air Flow ◽  
Two Dimensional ◽  
Velocity Measurements ◽  
Side Walls ◽  
Triangular Enclosure ◽  
Vertical Flat Plate

Velocities in two laminar free convection air flow fields were measured using a laser velocimeter. Velocities were first measured in the boundary layer around a heated vertical flat plate and results compare within two percent of theoretical and previous experimental (streak photography) data. Second, velocities were measured throughout a two-dimensional triangular enclosure, which consisted of two isothermal side walls (one heated and one cooled), an insulated bottom, and glass end plates. Enclosure data are compared to simple inclined isothermal plate data and are also presented so that the flow patterns can be observed.

Mixed Convection on a Vertical Flat Plate With Transition and Separation

1990 ◽  
Vol 112 (1) ◽  
pp. 144-150 ◽  
Author(s):  
T. Cebeci ◽  
D. Broniewski ◽  
C. Joubert ◽  
O. Kural
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stability Theory ◽  
Separation Bubble ◽  
Boundary Layer Separation ◽  
Laminar Flows ◽  
Linear Stability Theory ◽  
Boundary Layer Equations ◽  
Heating And Cooling ◽  
Vertical Flat Plate

A numerical method has been developed and used to calculate the flow properties of laminar, transitional, and turbulent boundary layers on a vertical flat plate with heat transfer. The governing boundary-layer equations include a buoyancy-force term and are solved by a two-point finite-difference method due to Keller and results obtained for heating and cooling and, in the case of the laminar flows, for an isothermal surface corresponding to that of Merkin. Cooled plates with unheated sections can give rise to boundary-layer separation and reattachment and, on occasions, transition can occur within the separation bubble. Flows of this type have been examined with the inviscid-viscous interaction procedure developed by Cebeci and Stewartson and the location of transition obtained by the en method based on the linear stability theory for air with Pr = 1. Results are given in dimensionless form as a function of Reynolds number, Richardson number, and Prandtl number and quantify those parameters that give rise to separation. Consequences of the use of interaction and stability theory are examined in detail.

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