Hydrodynamic and hydromagnetic stability

Physical vapor growth of centimeter-sized crystals of α-hexathiophene

Steady-state two-dimensional results obtained from numerical solutions to the transient Navier-Stokes equations are given for laminar convective motion of a gas in an enclosed vertical slot with large horizontal temperature differences. We present results for air using the ideal-gas law and Sutherland-law transport properties, although the results are also valid for hydrogen. Wide ranges of aspect-ratio, Rayleigh-number and temperature-difference parameters are examined. The results are compared in detail with the exact solution in the conduction and fully developed merged boundary-layer limits for arbitrary temperature difference, and to the well-established Boussinesq limit for small temperature difference. It is found that the static pressure, and temperature and velocity distributions are very sensitive to property variations, even though the average heat flux is not. In addition we observe a net vertical heat flux to be the same as that obtained from the Boussinesq equations. We concentrate on the boundary-layer regime, but we present a rather complete picture of different flow regimes in Rayleigh-number, aspect-ratio and temperaturedifference parameter space. We observe that, with increasing temperature difference, lower critical Rayleigh numbers for stationary and oscillatory instabilities are obtained. In addition we observe that in some cases the physical nature of the instability changes with increasing temperature difference.

Natural convection in an enclosed vertical air layer with large horizontal temperature differences

The aim of this paper is to carry out a review of radiative heat transfer in dispersed media. Firstly, the solution of the governing equations for radiative transfer in such media as well as the theoretical basis for the modelling of their radiative properties are briefly recalled and discussed. Thereafter, emphasis is placed on practical applications dealing with several types of particulate media which play an important role in a number of industrial processes. Radiative property predictive models as well as studies dealing with property experimental determination are examined and discussed.

Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization

A model which takes into account the main phenomena occurring during the laser-cladding process is proposed. For a given laser power, beam radius, powder jet geometry, and clad height, this model evaluates two other processing parameters, namely, the laser-beam velocity and the powder feed rate. It considers the interactions between the powder particles, the laser beam, and the molten pool. The laser power reaching the surface of the workpiece is estimated and, assuming this power is used to remelt the substrate with the clad having been predeposited, the melt-pool shape is computed using a three-dimensional (3-D) analytical model, which produces mmediate results, even on personal computers. The predictions obtained with this numerical model are in good agreement with experimental results. Processing engineers may therefore use this model to choose the correct processing parameters and to establish cladding maps.

A Simple but Realistic Model for Laser Cladding

In this article we present numerical solutions to multicellular natural convection in a vertical enclosure The calculated streamlines faithfully represent what has been seen in the laboratory by smoke traces in air and particle traces in oils The calculated isotherms for air correspond to reported interferometric patterns Solutions exhibiting travelling waves for water were calculated near conditions where they should occur according to linear stability theory Heat-transfer results for air are given and their dependence on the aspect ratio of the enclosure exhibited

Multicellular natural convection in a vertical slot

On the stability of the conduction regime of natural convection in a vertical slot

The stability of natural convection in a vertical annular enclosure has been studied by the linear theory. It was found that for all Prandtl numbers the instability sets in as a wave travelling upward. For low Prandtl numbers, the larger the curvature the more stable the flow; the reverse is true for high Prandtl numbers. The theoretical predictions of the mode of instability were verified for air. A multicellular flow pattern was observed to drift upward with the predicted wave speed. The measured wavelength of the cells is in good agreement with the linear analysis.

Stability of the conduction regime of natural convection in a tall vertical annulus

Si le nombre de Prandtl est suffisamment faible il apparait des cellules transversales comme resultat de l'instabilite hydrodynamique. On considere le cas de frontieres inferieure et superieure, conductrice et isolante

Natural convection in a shallow cavity

The stability of laminar natural convection in a shallow cavity has been studied theoretically. The flow is driven by a horizontal temperature gradient between isothermal vertical sidewalls of the cavity, the top and bottom of which are insulated. It was found that for a Prandtl number (Pr) less than 0.033, shear instability causes stationary transverse cells to be formed in the flow. For larger values of Prandtl number the instability sets in as oscillating longitudinal rolls in the range 0.033<Pr<0.2; and as stationary longitudinal rolls for larger values of Pr. The importance of three‐dimensional disturbances was investigated for Pr=0.02 and they were found to be less critical than two‐dimensional ones. Finite amplitude motions of the stationary transverse cells were simulated by solving the nonlinear equations numerically with the use of pseudospectral methods. This simulation supports the calculations of the onset of the instability by linear theory, and explains why the Nusselt number decreases when secondary flows are present.

Seppo A. Korpela

Papers

Multicellular natural convection in a vertical slot

On the stability of the conduction regime of natural convection in a vertical slot

Stability of the conduction regime of natural convection in a tall vertical annulus

Natural convection in a shallow cavity

Stability and finite amplitude natural convection in a shallow cavity with insulated top and bottom and heated from a side