Convection boundary layer

Turbulent free convection attracted early attention in limiting-current studies, because the laminar, free convection boundary layer at a vertical plate becomes turbulent at a height characterized approximately by the Rayleigh number... 

The stagnant layer analysis offers a pedagogical framework for presenting the essence of diffusive burning. For the most part the one-dimensional stagnant layer approximated a two-dimensional boundary layer in which 6 = <5(x), with x the flow direction. For a convective boundary layer, the heat transfer coefficient, hc, is defined as... 

Venkatram (1980) has summarized the aspects of dispersion in the convective boundary layer ... 

Lamb, R. G., and Duran, D. R. (1977). Eddy diffusivities derived from a numerical model of the convective boundary layer. Nuov. Cimento [1] 1C, 1-17. 

Venkatram, A. (1980). The relationship between the convective boundary layer and dispersion from tall stacks. Atmos. Environ. 14, 763-767. 

Schumann, U. 1989. Large eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmospheric Environment 23(8) 1713-26. 

An important feature of sohds reaction is that there are essential mass transport steps of reactants and products either in convective boundary layers or within the reacting sohds. These can cause sohds reaction processes to be mass transfer limited where the surface reaction rate coefficient does not appear in the reaction rate expression. 

Trial A.F. and Spera F.J. (1988) Natural convection boundary layer flows in isothermal ternary systems role of diffusive coupling. Int. J. Heat Transfer 31, 941-955. 

Problem . Derive an expression for the maximum velocity in the flee convection boundary layer on a vertical flat plate. At what position in the boundary layer does this maximum velocity occur ... 

Laminar and turbulent free convective boundary layers on a vertical surface. 

Since the basic assumption of boundary layer theory is that (8/L) is small, it follows from this that V is also small. Thus, in a free convective boundary layer, as in the forced convective boundary layer, the lateral velocity component, v, is very much smaller than the longitudinal component, u, which is, of course, what is physically to be expected. 

Dimensionless velocity profiles in natural convective boundary layer on a vertical plate for various values of Prandtl number. 

NUMERICAL SOLUTION OF THE NATURAL CONVECTIVE BOUNDARY LAYER EQUATIONS... 

The other limiting solution is that in which the flow essentially consists of boundary layers on each wall of the duct, these boundary layers being so thin compared to W that there is no interaction between the flows in the two boundary layers, i.e., the boundary layer on each wall of the duct behaves as a boundary layer on a vertical plate in a large environment. Now, for free convective boundary layer flow over a vertical plate of height l, it was shown earlier in this chapter that ... 

Eqs. (8.120) and (8.121) represent the limiting boundary layer solution for natural convective flow through a vertical plane duct. For the particular case of Pr = 0.7, the similarity solution for natural convective boundary layer flow on a vertical plate... 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

In using these equations, the forms of the velocity and temperature profiles in the boundary layer are assumed. Now, in turbulent forced convective boundary layer flows it has been found that the velocity profile is well described by ... 

Equation (8.166) cannot be directly applied to natural convective boundary layer flows because in such flows the velocity is zero at the outer edge of the boundary layer. However, Eq. (8.166) should give a good description of the velocity distribution near the wall. It is therefore assumed that in a turbulent natural convective boundary layer ... 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

Solution. The following integrals arise in the approximate solution for turbulent natural convective boundary layer flow over a flat plate discussed above ... 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

A 0.3-m vertical plate is maintained at a surface temperature of 65°C imd is exposed to stagnant air at a temperature of 15°C and standard ambient pressure. Compare the natural convective heat transfer rate from this plate w ith that which would result from forcing air over the plate at a velocity equal to the maximum velocity that occurs in the natural convective boundary layer. 

Plot the free-convection boundary-layer thickness along a 0.3-m high vertical plate which is maintained at a uniform surface temperature of 50CC and exposed to stagnant air at ambient pressure and a temperature of 10°C. Assume the flow remains laminar. 

It will be seen from the results given by the similarity solution that the velocities are very low in natural convective boundary layers in fluids with high Prandtl numbers. In such circumstances, the inertia terms (i.e., the convective terms) in the momentum equation are negligible and the boundary layer momentum equation for a vertical surface effectively is ... 

A 30-cm high vertical plate has" a surface temperature that varies linearly from 15°C at the lower edge to 45°C at the upper edge. This plate is exposed to air at 1S°C and ambient pressure. Use the computer program for natural convective boundary layer flow to determine how the local heat transfer rate varies with distance up die plate from the lower edge. 

Pera, L. and Gebhart, B., "Natural Convection Boundary Layer Flow Over Horizontal and Slightly Inclined Surfaces , Int. J. Heat Mass Transfer. Vol. 16, p. 1131. 1973. 

Oosthuizen. P.H.. A Note on the Transition Point in a Free Convective Boundary Layer on an Isothermal Vertical Plane Surface . JS.A. Inst. Mech. Engs., Vol. 13, No. 10, pp. 265-268, 1964. 

Eckert, E.R.G. and Soehnghen. E., "Interferometric Studies on the Stability and Transition to Turbulence of a Free-Convection Boundary Layer , Proc. of the General Discussion on Heat Transfer, pp. 321-323. ASME-1ME. London. 1951. 

Eckert, E.R.G. and Jackson. T.W.. "Analysis of Turbulent Free Convection Boundary Layer on a Flat Plate , NACA Rept. 1015, 1951. 

Brewster, R.A. and Gebhart, B., Instability and Disturbance Amplification in a Mixed-convection Boundary Layer , J. Fluid Mechanics, Vol. 229, pp. 115-133. 1991. 

Natural convective boundary layer-type solutions have beer obtained for a number of other geometrical configurations. A number of studies of mixed convective flows in porous media are also available, e.g., [23] to [35]. 

---