Interfacial convection heat transfer

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

After the formal derivations, the energy equation for each phase ((T)f and (T) ) can be written in a more compact form by defining the following coefficients. Note that both the hydrodynamic dispersion, that is, the influence of the presence of the matrix on the flow (noslip condition on the solid surface), as well as the interfacial heat transfer need to be included. The total thermal diffusivity tensors Dff, D , D/s, and Dv/ and the interfacial convective heat transfer coefficient hsf are introduced. The total thermal diffusivity tensors include both the effective thermal diffusivity tensor (stagnant) as well as the hydrodynamic dispersion tensor. A total convective velocity v is defined such that the two-medium energy equations become... 

Equations (13-115) to (13-117) contain terms, for rates of heat transfer from the vapor phase to the hquid phase. These rates are estimated from convective and bulk-flow contributions, where the former are based on interfacial area, average-temperature driving forces, and convective heat-transfer coefficients, which are determined from the Chilton-Colburn analogy for the vapor phase and from the penetration theoiy for the liquid phase. 

The interfacial boundary condition may be written in terms of the convective heat transfer of sensible heat, latent heat transfer due to evaporation, and, if the surface temperature is high enough, radiant heat transfer. Mathematically, the surface boundary condition is... 

At the catalytic solid surfaces the interfacial heat transfer due to phase change vanishes, instead the convective contributions in (3.175) are incorporated into the convective heat transfer coefficients. 

From the simulated results of foregoing sections, the interfacial effect is influenced by many factors, such as Marangoni convection, Rayleigh convection, heat transfer, interface deformation, physical properties of the process, and others. Each factor may be positive or negative the overall effect depends on their coupling result. For the flowing system, it is also in connection with the behaviors of fluid dynamics. 

Conductive and micro-convective heat transfer in the liquid/vapour interfacial region leading to surface evaporation as the only normal boil-off mechanism in LNG. 

As noted, two principles of heat transfer are involved evaporation and convection. The rate of heat transfer by both convection and evaporation increases with an increase in air-to-water interfacial surface, relative velocity, contact time and temperature differential. Packing and fill in a tower serve to increase the interfacial surface area the tower chimney or fans create the relative air-to-water velocity and contact time is a function of tower size. These three factors all may be influenced by the tower design. 

In this paper, we now report measurements of heat transfer coefficients for three systems at a variety of compositions near their lower consolute points. The first two, n-pentane--CO2 and n-decane--C02 are supercritical. The third is a liquid--liquid mixture, triethylamine (TEA)--H20, at atmospheric pressure. It seems to be quite analogous and exhibits similar behavior. All measurements were made using an electrically heated, horizontal copper cylinder in free convection. An attempt to interpret the results is given based on a scale analysis. This leads us to the conclusion that no attempt at modeling the observed condensation behavior will be possible without taking into account the possibility of interfacial tension-driven flows. However, other factors, which have so far eluded definition, appear to be involved. 

Whilst heat transfer in convection can be described by physical quantities such as viscosity, density, thermal conductivity, thermal expansion coefficients and by geometric quantities, in boiling processes additional important variables are those linked with the phase change. These include the enthalpy of vaporization, the boiling point, the density of the vapour and the interfacial tension. In addition to these, the microstructure and the material of the heating surface also play a role. Due to the multiplicity of variables, it is much more difficult to find equations for the calculation of heat transfer coefficients than in other heat transfer problems. An explicit theory is still a long way off because the physical phenomena are too complex and have not been sufficiently researched. 

Similar constitutive equations are used to approximate the integrals representing the interfacial heat transfer rates by convection and conduction through the stagnant films in the vicinity of a catalytic solid surface. Hence, the film model can be used to approximate the interfacial heat transport (3.167) by ... 

To be consistent with the mass transfer model, the interfacial heat transfer flux through each of the films consists of both conductive (3.167) and convective (3.175) contributions. The heat transfer terms are approximated by... 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

It was previously indicated that the analysis of the previous sections of this chapter could apply equally well to heat transfer problems or to the single-solute mass transfer problem with 0 interpreted as the dimensionless concentration, 9 = (c — Coo)/(co — Coo), with c representing the mass fraction of solute and the Schmidt number substituted for the Prandtl number. The key assumption in this assertion is that the interfacial velocity generated that is due to the transfer of solute to or from the body surface is small enough to play a neghgible role in both the fluid motion and as a convective contribution to the mass transfer rate. In this section, we consider how the problem changes if this assumption is not satisfied.4... 

At high enough qualities and mass fluxes, however, it would be expected that the nucleate boiling would be suppressed and the heat transfer would be by forced convection, analogous to that for the evaporation for pure fluids. Shock [282] considered heat and mass transfer in annular flow evaporation of ethanol water mixtures in a vertical tube. He obtained numerical solutions of the turbulent transport equations and carried out calculations with mass transfer resistance calculated in both phases and with mass transfer resistance omitted in one or both phases. The results for interfacial concentration as a function of distance are illustrated in Fig. 15.112. These results show that the liquid phase mass transfer resistance is likely to be small and that the main resistance is in the vapor phase. A similar conclusion was reached in recent work by Zhang et al. [283] these latter authors show that mass transfer effects would not have a large effect on forced convective evaporation, particularly if account is taken of the enhancement of the gas mass transfer coefficient as a result of interfacial waves. 

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

Thus, the interfacial mass and heat transfer fluxes are composed of a laminar, steady state diffusion term in the stagnant film and a convection term from the complete turbulent bulk phase (Taylor and Krishna, 1993),... 

Modelling the three-phase distillation based on nonequilibrium contains some specific features compared to the normal two-phase distillation or the equilibrium model. In the equilibrium model of three-phase distillation only two of the three equilibrium equations are independent. In the nonequilibrium model every phase is balanced separately. Therefore all three equilibrium equations are used in the model for the interfaces. A further characteristic is, although a three-phase problem is existing, that only the mass transfer between two phases has to be calculated at every interfacial area. Additionally, the convective and conductive part of the heat transfer have to be taken into consideration, as the own investigations presented. Often the conductive part is neglected due to the small difference of the temperatures of the phase interface and the bulk phase. For the modelling of the three-phase distillation this simplification is inadmissible. 

Heat transfer at the interfacial surfaces is complex and involves radiation, convection, and at the covered bed/covered wall interface, conduction as well. Although a heat transfer coefficient can be allocated to each transport path shown in Figure 8.8 (Gorog et al., 1983) this should not obscure the difficulty associated with realistic determination of values for these coefficients. As mentioned earlier, the one-dimensional model is required only to produce a framework from which to operate... 

All modules use the 2-fluid model to describe steam-water flows and four non-condensable gases may be transported. The thermal and mechanical non-equilibrium are described. All kinds of two-phase flow patterns are modelled co-current and counter-current flows are modelled with prediction of the counter-current flow limitation. Heat transfer with wall structures and with fuel rods are calculated taking into account all heat transfer processes ( natural and forced convection with liquid, with gas, sub-cooled and saturated nucleate boiling, critical heat flux, film boiling, film condensation). The interfacial heat and mass transfers describe not only the vaporization due to superheated steam and the direct condensation due to sub-cooled liquid, but also the steam condensation or liquid flashing due to meta-stable subcooled steam or superheated liquid. 

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