Vortex sheet method for solving unsteady thermal boundary layer equations

2000 ◽  
Author(s):  
Zhiyun Lu
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Vortex Sheet ◽  
Boundary Layer Equations

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.

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

The thermal boundary layer in the flow between converging plane walls

1963 ◽  
Vol 59 (1) ◽  
pp. 225-229 ◽  
Author(s):  
N. Riley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Analytical Solutions ◽  
Thermal Boundary Layer ◽  
Parallel Plane ◽  
Boundary Layer Equations ◽  
Converging Flow

AbstractThe thermal boundary layer in the converging flow between non-parallel plane walls is studied. Analytical solutions of the boundary-layer equations are derived and the heat transfer across the wall is obtained from these solutions.

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