Boundary layer wall flux

Seldom is the temperature difference across the wall thickness of an item of equipment known. Siace large temperature gradients may occur ia the boundary layers adjacent to the metal surfaces, the temperature difference across the wall should not be estimated from the temperatures of the fluids on each side of the wall, but from the heat flux usiag equation 27... 

Fig. 1. General dialysis is a process by which dissolved solutes move through a membrane in response to a difference in concentration and in the absence of differences in pressure, temperature, and electrical potential. The rate of mass transport or solute flux, ( ), is directly proportional to the difference in concentration at the membrane surfaces (eq. 1). Boundary layer effects, the difference between local and wall concentrations, are important in most...

Further neglecting the first term allows integration from y = 0 at the wall (membrane surface) into the boundary layer. At the wall, the net flux is represented by convection into the permeate... 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

Although the correlations given by Eq. (6.48) are useful for practical evaluation of heat transfer to a wall, one must not lose sight of the fact that the temperature gradient at the wall actually determines the heat flux there. In transpiration cooling problems, it is not so much that the injection of the transpiring fluid increases the boundary layer thickness, thereby decreasing the... 

As time goes by, the interface looks more and more like a wall boundary. Eventually, the concentration gradient across the boundary layer becomes zero (CB/A CB) and the flux takes the form of Eq. 19-26 with the extra factor KA/B expressing the partition equilibrium across the interface (see Eq. 19-29). 

Figure 19.11 Wall boundary with boundary layer Relative variation of concentration difference across boundary layer and relative boundary flux as a function of relative time r = t / fcrit (Eq. 19-45).

Consider a steady, laminar boundary layer flow of incompressible, transparent fluid along a flat plate, with a constant applied heat flux qw Btu/(hr ft2) at the wall surface. The properties of the fluid are assumed constant. The main considerations are conduction to the fluid, and radiation from the plate to the environment at Te. Surface of the plate is opaque and gray, and the uniform emissivity is 8. The fluid which is at a temperature of T,, flows at a uniform velocity of Uo. Flow velocities are sufficiently small so that viscous dissipation may be neglected. 

Air flows over a wide t-m long flat plate which has a uniform surface temperature of 80°C, the temperature of the air ahead of the plate being 20°C. The air velocity is such that the Reynolds number bas J on the length of the plate is 5 x 106. Derive an expression for the local wall heat flux variation along the plate. Use the Reynolds analogy and assume the boundary layer transition occurs at a Reynolds number of 10 ... 

Tbe numerical procedure for solving the laminar boundary layer equations for forced convection that was described in Chapter 3 is easily extended to deal with combined convection. The details of the procedure are basically the same as those for forced convection and the details will not be repeated here [16]. A computer program, LAMBMIX, based on the procedure is available in the way discussed in the Preface. This program can actually allow the wall temperature or wall heat dux to vary with X but as available, the program is set for the case of a uniform wall temperature or a uniform wall heat flux. 

Consider the system shown in Fig. 5-7. The temperature of the wall is T ., the temperature of the fluid outside the thermal boundary layer is T, and the thickness of the thermal boundary layer is designated as 8,. At the wall, the velocity is zero, and the heat transfer into the fluid takes place by conduction. Thus the local heat flux per unit area, q", is... 

We shall employ a simplified analysis of the ablation problem utilizing the coordinate system and nomenclature shown in Fig. 12-18. The solid wall is exposed to a constant heat flux of (q/A)0 at the surface. This heat flux may result from combined convection- and radiation-energy transfer from the highspeed boundary layer. As a result of the high-heat flux the solid body melts, and a portion of the surface is removed at the ablation velocity V . We assume that a steady-state situation is attained so that the surface ablates at a constant... 

Boundary layers appear in flow situations near the walls or other non-deform-able structures that exist in the flow field [3.8]. Their formation and development, stability and local thickness are of great interest to engineers and researchers because all the gradients of property concentration are concentrated here. Consequently, we can write a very simple expression for the flux of the property. 

In this section the heat and mass transport coefficients for turbulent boundary layers are examined. In this case the model derivation is based on the governing Reynolds averaged equations. In these equations statistical covariances appear which involve fluctuating velocities, temperatures and concentrations. The nature of these terms is not known a priori and their effects must by estimated by semi-empirical turbulence modeling. The resulting parameterizations allow us to express the unknown turbulent fluctuations in terms of the mean flow field variables. It is emphasized that the Reynolds equations are not actually solved, merely semi-empirical relations are derived for the wall fluxes through the inner boundary layer. 

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