Experiments on the Onset of Longitudinal Vortices in Laminar Forced Convection Between Horizontal Plates

1971 ◽  
Vol 93 (4) ◽  
pp. 335-341 ◽  
Author(s):  
M. Akiyama ◽  
G. J. Hwang ◽  
K. C. Cheng
Keyword(s):  
Rayleigh Number ◽  
Temperature Gradient ◽  
Forced Convection ◽  
Critical Rayleigh Number ◽  
Profile Measurement ◽  
Axial Temperature Gradient ◽  
Longitudinal Vortices ◽  
Axial Temperature ◽  
Laminar Forced Convection ◽  
Limiting Case

An experimental investigation is carried out to determine the onset of longitudinal columnar vortices due to buoyant forces for fully developed laminar forced convection between two infinite horizontal plates, each wall subjected to identical uniform axial temperature gradient but maintained at temperatures T1 and T2 (T1 > T2, T1 < T2, and T1 = T2) at lower and upper surfaces, respectively. The limiting case with vanishing axial temperature gradient and heating from below (T1 > T2) is known to have a critical Rayleigh number of 1708 and is used to check the accuracy of the testing apparatus. The onset of secondary flow is determined by a direct flow-visualization technique using cigarette smoke, and confirmed by a transverse temperature-profile measurement using a single thermocouple traverse. Experimental results for the critical Rayleigh number are compared with theory and the agreement is found to be good.

Controlling the axial temperature gradient in inductively heated Czochralski systems

2003 ◽  
Vol 38 (1) ◽  
pp. 42-46 ◽  
Author(s):  
S. Ganschow ◽  
P. Reiche ◽  
M. Ziem ◽  
R. Uecker
Keyword(s):  
Temperature Gradient ◽  
Axial Temperature Gradient ◽  
Axial Temperature

An Experimental Investigation of Heat Transfer and Buoyancy Induced Transition from Laminar Forced Convection to Turbulent Free Convection over a Horizontal Isothermally Heated Plate

1978 ◽  
Vol 100 (3) ◽  
pp. 429-434 ◽  
Author(s):  
H. Imura ◽  
R. R. Gilpin ◽  
K. C. Cheng
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Forced Convection ◽  
Leading Edge ◽  
Finite Amplitude ◽  
Heated Plate ◽  
Transfer Rates ◽  
Longitudinal Vortices ◽  
Turbulent Flow Regime ◽  
Laminar Forced Convection

The flow over a horizontal isothermally heated plate at Reynolds numbers below that at which hydrodynamic instabilities exist, is characterized by a region of laminar forced convection near the leading edge, followed by the onset of longitudinal vortices and their growth to a finite amplitude and finally a transition to a turbulent flow regime. Results are presented for the temperature profiles, the thermal boundary layer thickness, and the local Nusselt number. They are used to identify the various flow regimes. It was found that the transition from laminar forced convection to turbulent convection was characterized by the parameter Grx/Rex1.5 falling in the range 100 to 300. For values of this parameter greater than 300 the heat transfer rates were independent of Reynolds number and typical of those for turbulent free convection from a horizontal surface.

Amplification of energy flux of nonlinear acoustic waves in a gas-filled tube under an axial temperature gradient

2002 ◽  
Vol 456 ◽  
pp. 377-409 ◽  
Author(s):  
N. SUGIMOTO ◽  
K. TSUJIMOTO
Keyword(s):  
Boundary Layer ◽  
Temperature Gradient ◽  
Energy Flux ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Main Flow ◽  
Nonlinear Wave Equations ◽  
Axial Temperature Gradient ◽  
Axial Temperature ◽  
Nonlinear Acoustic

This paper considers nonlinear acoustic waves propagating unidirectionally in a gas-filled tube under an axial temperature gradient, and examines whether the energy flux of the waves can be amplified by thermoacoustic effects. An array of Helmholtz resonators is connected to the tube axially to avoid shock formation which would otherwise give rise to nonlinear damping of the energy flux. The amplification is expected to be caused by action of the boundary layer doing reverse work, in the presence of the temperature gradient, on the acoustic main flow outside the boundary layer. By the linear theory, the velocity at the edge of the boundary layer is given in terms of the fractional derivatives of the axial velocity of the gas in the acoustic main flow. It is clearly seen how the temperature gradient controls the velocity at the edge. The velocity is almost in phase with the heat flux into the boundary layer from the wall. With effects of both the boundary layer and the array of resonators taken into account, nonlinear wave equations for unidirectional propagation in the tube are derived. Assuming a constant temperature gradient along the tube, the evolution of compression pulses is solved numerically by imposing the initial profiles of both an acoustic solitary wave and of a square pulse. It is revealed that when a positive gradient is imposed, the excess pressure decreases while the particle velocity increases and that the total energy flux can indeed be amplified if the gradient is suitable.

Effect of a stabilizing gradient of solute on thermal convection

1968 ◽  
Vol 34 (2) ◽  
pp. 315-336 ◽  
Author(s):  
George Veronis
Keyword(s):  
Rayleigh Number ◽  
Temperature Gradient ◽  
Prandtl Number ◽  
Critical Rayleigh Number ◽  
Effective Diffusion ◽  
Stratified Fluid ◽  
Finite Amplitude ◽  
Oscillatory Motion ◽  
Linear Stability Theory ◽  
Onset Of Convection

A stabilizing gradient of solute inhibits the onset of convection in a fluid which is subjected to an adverse temperature gradient. Furthermore, the onset of instability may occur as an oscillatory motion because of the stabilizing effect of the solute. These results are obtained from linear stability theory which is reviewed briefly in the following paper before finite-amplitude results for two-dimensional flows are considered. It is found that a finite-amplitude instability may occur first for fluids with a Prandtl number somewhat smaller than unity. When the Prandtl number is equal to unity or greater, instability first sets in as an oscillatory motion which subsequently becomes unstable to disturbances which lead to steady, convecting cellular motions with larger heat flux. A solute Rayleigh number, Rs, is defined with the stabilizing solute gradient replacing the destabilizing temperature gradient in the thermal Rayleigh number. When Rs is large compared with the critical Rayleigh number of ordinary Bénard convection, the value of the Rayleigh number at which instability to finite-amplitude steady modes can set in approaches the value of Rs. Hence, asymptotically this type of instability is established when the fluid is marginally stratified. Also, as Rs → ∞ an effective diffusion coefficient, Kρ, is defined as the ratio of the vertical density flux to the density gradient evaluated at the boundary and it is found that κρ = √(κκs) where κ, κs are the diffusion coefficients for temperature and solute respectively. A study is made of the oscillatory behaviour of the fluid when the oscillations have finite amplitudes; the periods of the oscillations are found to increase with amplitude. The horizontally averaged density gradients change sign with height in the oscillating flows. Stably stratified fluid exists near the boundaries and unstably stratified fluid occupies the mid-regions for most of the oscillatory cycle. Thus the step-like behaviour of the density field which has been observed experimentally for time-dependent flows is encountered here numerically.

scholarly journals Stability of a Buoyant Oldroyd-B Flow Saturating a Vertical Porous Layer with Open Boundaries

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 375
Author(s):  
Stefano Lazzari ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Critical Rayleigh Number ◽  
Stationary Flow ◽  
Vertical Axis ◽  
Seepage Flow ◽  
Neutral Stability ◽  
Linear Viscoelastic ◽  
Infinite Height ◽  
Limiting Case

The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with permeable and isothermal boundaries is investigated. Seepage flow is modelled through an extended version of Darcy’s law which accounts for the Oldroyd-B rheology. The basic stationary flow is parallel to the vertical axis and describes a single-cell pattern where the cell has an infinite height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. This analysis is performed numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are evaluated for different retardation time and relaxation time characteristics of the fluid. The study highlights the extent to which the viscoelasticity has a destabilising effect on the buoyant flow. For the limiting case of a Newtonian fluid, the known results available in the literature are recovered, namely a critical value of the Darcy–Rayleigh number equal to 197.081 and a corresponding critical wavenumber of 1.05950.

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