Turbulent boundary layer natural convection

The phenomenon of free convection results in nature, primarily from the fact that when the fluid is heated, the density (usually) decreases the warmer fluid portions move upward. This process is dramatically evident in rural areas on sunny days with low to no-wind when the soil surface is significantly hotter than the air above. The air at the soil surface becomes heated and rises vertically, producing velocity updrafts that carry the chemical vapor and the fine aerosol particles, laden with adsorbed chemical fractions, upward into the atmospheric boundary layer. When accompanied by lateral surface winds, the combined processes produce a very turbulent boundary layer and numerically large MTCs. This section will outline the major aspects of the theory of natural convection using elementary free convection concepts. Details are presented in Chapter 10 of Transport Phenomena (Bird et al., 2002). 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

Let us just consider the piloted ignition case. Then, at Tpy a sufficient fuel mass flux is released at the surface. Under typical fire conditions, the fuel vapor will diffuse by turbulent natural convection to meet incoming air within the boundary layer. This will take some increment of time to reach the pilot, whereby the surface temperature has continued to rise. 

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. 

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. 

Henkes, R.A.W.M. and Hoogendoom. C.J., Comparison of Turbullence Models for the Natural Convection Boundary Layer Along a Heated Vertical Plate , Int. J. Heat Mass Transfer, Vol. 32, pp. 157-169, 1989. 

Metzner and Friend [Ind. Eng. Chem., 51, 879 (1959)] present relationships for turbulent heat transfer with nonnewtonian fluids. Relationships for heat transfer by natural convection and through laminar boundary layers are available in Skellands book (op. cit.). 

There are two types of convection, free and forced (Holman, 2009 Incropera et al., 2007 Kreith and Bohn, 2007). Free (natural) convection occurs when the heat transferred from a leaf causes the air outside the unstirred layer to warm, expand, and thus to decrease in density this more buoyant warmer air then moves upward and thereby moves heat away from the leaf. Forced convection, caused by wind, can also remove the heated air outside the boundary layer. As the wind speed increases, more and more heat is dissipated by forced convection relative to free convection. However, even at a very low wind speed of 0.10 m s-1, forced convection dominates free convection as a means of heat loss from most leaves (0.10 m s-1 = 0.36 km hour-1 = 0.22 mile hour-1). We can therefore generally assume that heat is conducted across the boundary layer adjacent to a leaf and then is removed by forced convection in the surrounding turbulent air. In this section, we examine some general characteristics of wind, paying particular attention to the air boundary layers adjacent to plant parts, and introduce certain dimensionless numbers that can help indicate whether forced or free convection should dominate. We conclude with an estimate of the heat conduction/convection for a leaf. 

The simulations were performed assuming that the flow is laminar. Additionally, the contact angle is assumed to be known. The initial velocity is assumed to be zero everywhere in the domain. The initial fluid temperature profile is taken to be linear in the natural convection thermal boundary layer and the thermal boundary layer thickness, 5j, is evaluated using the correlation for the turbulent natural convection on a horizontal plate as, Jj. =1. 4(vfiCil ... 

The details of the flow in the mixed convection regime have been clarified by Gilpin et al. [113]. After an initial development of the laminar forced convection boundary layer, rolls with axes aligned with the flow appear at the location marked Onset in Fig. 46. These persist until the end of the transition regime, marked Breakup, after which the motion appears as fully detached turbulent natural convection flow. 

G. C. Vliet and C. K. Liu, An Experimental Study of Turbulent Natural Convection Boundary Layers, J. Heat Transfer (91) 517-531,1969. 

An important heat-transfer system occurring in process engineering is that in which heat is being transferred from a hot vertical plate to a gas or liquid adjacent to it by natural convection. The fluid is not moving by forced convection but only by natural or free convection. In Fig. 4.7-1 the vertical flat plate is heated and the free-convection boundary layer is formed. The velocity profile differs from that in a forced-convection system in that the velocity at the wall is zero and also is zero at the other edge of the boundary layer since the free-stream velocity is zero for natural convection. The boundary layer initially is laminar as shown, but at some distance from the leading edge it starts to become turbulent. The wall temperature is T K and the bulk temperature T. ... 

The fluid dynamic structure within the boundary layers adjacent to natural solid surfaces such as soil, sediment, snow, and ice, is complex. Typically, the flows fields have both laminar and turbulent regions. The flows magnitudes and directions respond according to the angle of incidence to the surface and the overall shape of the object as well as thermal-induced fluid density differences (i.e., stratification) and so on. All these factors operate into shaping the mass transfer boundary layer which controls the chemical flux. Ironically, the traditional approach to handling such complex flow situations has been to use a simple flux equation. The so-called convective mass flux equation is... 

The dishes were 5, 7, and 10 cm in diameter (Thibodeaux et al., 1980). Using heat transfer data for a cold plate facing upward. Equation 2.34 in Table 2.3 can be applied to assess natural convection as well. In the above cases, the correlations relate chemical dissolution at the sediment-water interface, which forms a boundary layer with fluid density slightly greater than that of pure water. This particular mass transfer process is very slow since a high-density fluid accumulates on the bottom surface and forms a stable layer, which resist the generation of BL turbulence. The resulting estimated MTCs should be the lowest for the water-side bed sediment surfaces, and appropriate for waterbodies in the absence of bottom of currents. 

Generally speaking, the conventional numerical analysis with a k-e turbulence model and accurate treatment of thermophysical properties can successfully explain the unusual heat transfer phenomena of supercritical water. Heat transfer deterioration occurs due to two mechanisms depending on the flow rate. When the flow rate is large, viscosity increases locally near the wall by heating. This makes the viscous sublayer thicker and the Prandtl number smaller. Both effects reduce the heat transfer. When the flow rate is small, buoyancy force accelerates the flow velocity near the wall. This makes the flow velocity distribution flat and generation of turbulence energy is reduced. This type of heat transfer deterioration appears at the boundary between forced and natural convection. As the heat flux increases above the deterioration heat flux, a violent oscillation of wall temperature is observed. It is explained by the unstable characteristics of the steep boundary layer of temperature. 

From measurements of the local heat transfer from heated vertical surfaces to cryogens in the natural convection regime, it appears that the laminar boundary layer flow undergoes a transition to turbulence when the modified Grashof number (Gr ) is of the order of 10. This agrees with experiments performed with water. For a heat flux of 100 W/m, the wall boundary layer can be expected to be turbulent above a liquid height of 0.3 m in LNG, with an increase in heat transfer coefficient for wall/liquid heat transfer [ 1 ]. 

---