Slip flow in the hydrodynamic entrance region of a tube and a parallel plate channel

1965 ◽  
Vol 15 (1) ◽  
pp. 411-428 ◽  
Author(s):  
Alan Quarmby
Keyword(s):  
Parallel Plate ◽  
Slip Flow ◽  
Entrance Region ◽  
Plate Channel

Transient Analysis on the Onset of Thermal Instability in the Thermal Entrance Region of a Horizontal Parallel Plate Channel

1991 ◽  
Vol 113 (2) ◽  
pp. 363-370 ◽  
Author(s):  
F. S. Lee ◽  
G. J. Hwang
Keyword(s):  
Peclet Number ◽  
Parallel Plate ◽  
Transient Analysis ◽  
Thermal Instability ◽  
Entrance Region ◽  
Wave Number ◽  
Péclet Number ◽  
Thermal Entrance Region ◽  
Plate Channel ◽  
Thermal Entrance

A transient analysis on the onset of thermal instability in the thermal entrance region of a horizontal parallel plate channel, where the lower plate is heated isothermally, is presented. A novel time-dependent approach based on a three-dimensional linear stability theory is developed to determine the neutral stability position, where a disturbance neither grows nor decays with time. The range of parameters Pe=30, 40, 60, 80, and 100, and Pr=0.2, 0.7, 1.0, and 7.0 are covered in the study. One finds that increasing Prandtl number has a destabilizing effect on the flow for a fixed Peclet number along the streamwise direction. On the other hand, increasing Peclet number or Reynolds number tends to stabilize the flow. As the onset of thermal instability moves upstream, the critical Rayleigh number and the critical wave number are increased. The result shows a good agreement with the previous experimental investigations.

Convective Instability in the Thermal Entrance Region of a Horizontal Parallel-Plate Channel Heated from Below

1973 ◽  
Vol 95 (1) ◽  
pp. 72-77 ◽  
Author(s):  
G. J. Hwang ◽  
K. C. Cheng
Keyword(s):  
Prandtl Number ◽  
Parallel Plate ◽  
Entrance Region ◽  
Longitudinal Vortex ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Thermal Entrance Region ◽  
Plate Channel ◽  
Thermal Entrance ◽  
Perturbation Equations

An investigation is carried out to determine the conditions marking the onset of longitudinal vortex rolls due to buoyant forces in the thermal entrance region of a horizontal parallel-plate channel where the lower plate is heated isothermally and the upper plate is cooled isothermally. Axial heat conduction is included in an analytical solution for the Graetz problem with fully developed laminar velocity profile. Linear-stability theory based on Boussinesq approximation is employed in the derivation of perturbation equations. An iterative procedure using high-order finite-difference approximation is applied to solve the perturbation equations and a comparison is made against the conventional second-order approximation. It is found that for Pr ≥ 0.7 the flow is more stable in the thermal entrance region than in the fully developed region, but the situation is just opposite for small Prandtl number, say Pr ≤ 0.2. Graphical results for the critical Rayleigh numbers and the corresponding disturbance wavenumbers are presented for the case of Pe → ∞ with Prandtl number as a parameter and the case of air (Pr = 0.7) with Peclet number as a parameter in the range of dimensionless axial distance from the entrance between x = 0.001 and 4 × 10−1.

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