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

Publisher Summary This chapter focuses on the advances in free convection The average treatise on heat transfer dismisses free convection in a single chapter It is, nevertheless, potentially as large a subject as forced convection and has developed rapidly within the last decade The present review acknowledges this situation by confining its attention to one aspect only, that of free convection on a vertical surface The peculiarity that distinguishes free convection from forced, as far as analytical work is concerned, is that the equations of momentum and energy are coupled; they cannot be treated separately The motion is directly caused by the transfer of heat and has no independent existence Therefore, the principle of superposition cannot be used to develop solutions for complicated situations from solutions for simple, idealized cases The flow is assumed to be steady; the surface temperature is uniform and the physical properties of the fluid (apart from density) are unaffected by temperature For sufficiently large values of D/L , the cylinder can be regarded as effectively the same as the flat plate Attention has thus far been restricted to situations where the surface temperature is uniform, except that a brief reference has been made to the very similar problem where the surface heat flux is uniform In all the theoretical work so far considered, it has been assumed that the physical properties, other than density, do not vary with temperature Nonsteady conditions have also been discussed Theoretical work on laminar free convection is based on the assumption that motion is confined to a thin layer; it should, therefore, become increasingly reliable as the Grash of number increases

Advances in Free Convection

Variable viscosity effects in several natural convection flows

This review discusses recent work dealing with natural convection flow in a differentially heated cavity. The emphasis is placed primarily on work dealing with the non-Boussinesq regime, transitional flow, and turbulent flow. Direction for future work in areas where additional effort is required is also provided.

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The differentially heated cavity

The effects of the temperature dependence of properties on laminar natural convection transport from an isothermal vertical surface in water are calculated. Bounding temperature conditions in the range 0–100° C are considered in the laminar boundary-layer equations. Results are compared with those obtained assuming constant properties. Large effects on flow and transport arise. These predictions are in good agreement with the limited experimental data available. For bounding temperatures greater than 20° C, heat transfer is correctly predicted by a constant-property solution to within 5% when the film temperature is used to evaluate properties. Detailed transport parameters are tabulated and plotted over the whole temperature range.

The effect of variable properties on laminar natural convection boundary-layer flow over a vertical isothermal surface in water

The laminar free convection problem of a flat plate which is hung vertically in the air is solved, taking into account the variation of properties of air which depends on temperature. Previously the author solved the same problem by perturbation theory using e=(T0-T1)/T1 as a small parameter, where T0 and T1 are the absolute temperatures of the surface and the surrounding air, respectively. In this report the rigorous solution for a larger value of e(=2.0 and 4.0) by successive approach method is presented. The heat-transfer coefficient can be expressed as follows : α=αe=0(1-0.055e)

Tomoshige Hara

Papers

Heat Transfer by Laminar Free Convection about a Vertical Flat Plate with Large Temperature Difference