Boundary layer forced convective

A. M. Jacobi, A Scale Analysis Approach to the Correlation of Continuous Moving Sheet (Backward Boundary Layer) Forced Convective Heat Transfer, J. Heat Transfer, 115, pp. 1058-1061,... 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

Above this size, the flow of air over the condenser surface will be by forced convection, i.e. fans. The high thermal resistance of the boundary layer on the air side of the heat exchanger leads to the use, in all but the very smallest condensers, of an extended surface. This takes the form of plate fins mechanically bonded onto the refrigerant tubes in most commercial patterns. The ratio of outside to inside surface will be between 5 1 and 10 1. 

J6. Jiji, L. M Incipient boiling and the bubble boundary layer formation over a heated plate for forced convection flow in a pressurized rectangular channel, Ph.D. Thesis, Univ. of Michigan, Ann Arbor, 1962. 

Jiji, L. M.,andJ. A. Clark, 1964, Bubble Boundary Layer and Temperature Profiles for Forced Convection Boiling in Channel Flow, Trans. ASME, J. Heat Transfer 56 50 58. (4)... 

Stefanovic, M., N. Afgan, V. Pislar, and L. Jovanovic, 1970, Experimental Investigation of the Superheated Boundary Layer in Forced Convection Boiling, Proc. 4th Int. Heat Transfer Conf, Versailles, Paper B 4.12. (3)... 

Fig. 4. Migration contribution to the limiting current in acidified CuS04 solutions, expressed as the ratio of limiting current (iL) to limiting diffusion current (i ) r = h,so4/(( h,so, + cCuS(>4). "Sulfate refers to complete dissociation of HS04 ions. "bisulfate" to undissociated HS04 ions. Forced convection" refers to steady-state laminar boundary layers, as at a rotating disk or flat plate free convection refers to laminar free convection at a vertical electrode penetration to unsteady-state diffusion in a stagnant solution. [F rom Selman (S8).]...

Unsteady-state effects and transition times are also significant in forced convection. Whenever the mass-transfer boundary layer is large anywhere on the working electrode surface, the commonly employed experimental time range of a few minutes may not be adequate to reach the steady-state limiting current. 

In free-convection mass transfer at electrodes, as well as in forced convection, the concentration (diffusion) boundary layer (5d extends only over a very small part of the hydrodynamic boundary layer <5h. In laminar free convection, the ratio of the thicknesses is... 

Weder s experiments were carried out with opposing body forces, and large current oscillations were found as long as the negative thermal densification was smaller than the diffusional densification. [Note that the Grashof numbers in Eq. (41) are based on absolute magnitudes of the density differences.] Local mass-transfer rates oscillated by 50%, and total currents by 4%. When the thermal densification dominated, the stagnation point moved to the other side of the cylinder, while the boundary layer, which separates in purely diffusional free convection, remained attached. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

There are two types of convection in an air boundary layer (1) forced convection created by air movement across the water body and (2) free convection created by a difference in density between the air in contact with the water surface and the ambient air. If the water body is warmer than the surrounding air, free convection will occur. The combination of these two processes is illustrated in Figure 8.15. 

It is difficult to solve the system of Eqs. (39)—(41) for these boundary conditions. However, certain simplifying assumptions can be made, if the Prandtl number approaches large values. In this case, the thermal boundary layer becomes very thin and, therefore, only the fluid layer near the plate contributes significantly to the heat transfer resistance. The velocity components in Eq. (41) can then be approximated by the first term of their Taylor series expansions in terms of y. In addition, because the nonlinear inertial terms are negligible near the wall, one can further assume that the combined forced and free convection velocity is approximately equal to the sum of the velocities that would exist when these effects act independently. Therefore, for assisting flows at large Prandtl numbers (theoretically for Pr -> oo), Eq. (41) can be rewritten in the form ... 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

Knaff and Schlunder [9] studied the evaporation of naphthalene and caffeine from a cylindrical surface (a sintered metallic rod impregnated with the solute) to high-pressure carbon dioxide flowing over an annular space around the rod. They studied the diffusion flux within the bar and in the boundary layer. The mass-transfer coefficient owing to forced convection from cylinder to the gas flowing in the annular duct was correlated, using the standard correlation due to Stephan [7]. For caffeine, it does not require a free-convection correction, as the Reynolds dependence is that expected by a transfer by forced convection. This is... 

These relationships have been used by Spalding in the dimensionless presentation both of theoretical values obtained in his approximate solution of the boundary layer equations (58) and of the experimental data (51, 55, 60). Emmons (3), who has solved the problem of forced convection past a burning liquid plane surface in a more rigorous fashion, shows graphically the rather close correspondence between values obtained from his exact solution and that of Spalding, and between the calculated values for flat plates and the experimental values for spheres. 

Air movement indoors is much slower than outdoors, but it is usually enough to ensure that concentrations are fairly uniform in a room. Convection from heating appliances gives air speeds typically in the range 0.05-0.5 m s-1 (Daws, 1967). However, to undergo deposition, vapour molecules or particles must be transported across the boundary layer, typically a few millimetres thick, of almost stagnant air over surfaces. This may be achieved by sedimentation, molecular or Brownian diffusion, or under the action of electrostatic or thermophoretic forces. 

Because the surface-particle interaction forces are important only near to the surface of the collector, it is natural to divide the domain into two regions. The inner region, called the interaction-force boundary layer, has a thickness determined by the range over which interaction forces are important (less than about 10-5 cm). Because of the proximity of the surface, convection is negligible. Outside the... 

In the previous section it was shown that, when double-layer repulsions are sufficiently strong, the resistance of the interaction-force boundary layer can be taken into account by imposing on the convective-diffusion equation a virtual, first-order,... 

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