Mass flux convective

Lagranglan codes are characterized by moving the mesh with the material motion, u = y, in (9.1)-(9.4), [24]. The convection terms drop out of (9.1)-(9.4) simplifying all the equations. The convection terms are the first terms on the right-hand side of the conservation equations that give rise to fluxes between the elements. Equations (9.1)-(9.2) are satisfied automatically, since the computational mesh moves with the material and, hence, no volume or mass flux occurs across element boundaries. Momentum and energy still flow through the mesh and, therefore, (9.3)-(9.4) must be solved. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

The heat transfer coefficient of boiling flow through a horizontal rectangular channel with low aspect ratio (0.02-0.1) was studied by Lee and Lee (2001b). The mass flux in these experiments ranged from 50 to 200 kg/m s, maximum heat flux was 15 kW/m, and the quality ranged from 0.15 to 0.75, which corresponds to annular flow. The experimental data showed that under conditions of the given experiment, forced convection plays a dominant role. 

Heat transfer characteristics for saturated boiling were considered by Yen et al. (2003). From this study of convective boiling of HCFC123 andFC72 in micro-tubes with inner diameter 190, 300 and 510 pm one can see that in the saturated boiling regime, the heat transfer coefficient monotonically decreased with increasing vapor quality, but independent of mass flux. 

The gas-phase mass flux of species k at the surface is a combination of diffusive and convective processes. 

Operation conditions—pressure, inlet cooling, mass flux, power input, forced or natural convection... 

The contribution of transport under the influence of the electric field (migration), which, if appreciable, should be subtracted from the total mass flux. The use of excess inert (supporting) electrolyte is recommended to suppress migration effects. However, it should be remembered that this changes the composition of the electrolyte solution at the electrode surface. This is particularly critical in the interpretation of free-convection results, where the interfacial concentration of the inert as well as the reacting ions determines the driving force for fluid motion. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

Example 6.2 Estimate the mass flux evaporated for methanol in dry air at 25 °C and 1 atm. Assume natural convection conditions apply at the liquid-vapor surface with h = 8 W/m2 K. 

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. 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

Figures 3(a) and 3(b) show the computed fraction profiles of component A and B in the liquid film corresponding to, respectively, run 1 and run 6 from Table 1. Figure 3(a) shows that low fractions of A and B produce straight profiles, whereas high fractions of A and B result in curved profiles [see Fig. 3(b)]. The latter is due to the fact that the mass fluxes consist of a diffusive part as well as a convective (i.e. drift) part. This is also the reason why the fraction of B possesses a gradient, although the flux of component B equals zero.

In eq 51, the first term represents a convection term, and the second comes from a mass flux of water that can be broken down as flow due to capillary phenomena and flow due to interfacial drag between the phases. The velocity of the mixture is basically determined from Darcy s law using the properties of the mixture. The appearance of the mixture velocity is a big difference between this approach and the others, and it could be a reason the permeability is higher for simulations based on the multiphase mixture model. 

Figure 22 displays the time-integrated mean of mass flux as function of standard volume flux of primary air for all the three wood fuels, respectively. As indicated by Figure 22, the time-integrated mean of mass flux of conversion gas exhibits a hyperbolic relationship with the volume flux of primary air. In the low range of volume fluxes the conversion gas rate increases up to a maximum. After the maximum point is passed, the mass flux of conversion gas decreases due to convective cooling of the conversion reaction. 

The mass fluxes are expressed by the products of the convection-diffusion constants, k, ky and and the differences between the concentrations of the substances in the bulk of the solution far from the membrane (cx, Cy and CAgYj > of which the last equals zero) and the concentrations immediately next to the membrane cx(0), Cy(0) and CAgY,(0)-... 

Consider now increasing the heat flux after the condition described above is established. The temperature drop through the liquid layer will increase, thus increasing the wall temperature. Eventually the liquid superheat at the wall will be so large that nucleation will occur. When it does, it augments the forced convection effect. Now the heat transfer coefficient is higher than for cases where the heat flux is the same, but where the higher mass flux suppresses the nucleation. 

Determine the profiles of the diffusive mass flux by ordinary diffusion (i.e., jk,-)-Plot the profiles for the major species, as well as the net mass flux by ordinary diffusion. How do the magnitudes and the directions of the species diffusive mass fluxes compare with the net convective mass flux Discuss the results in the context of the solution profiles. 

Heterogeneous reactions at a gas-surface interface affect the mass and energy balance at the interface, and thus have an important influence on the boundary conditions in a chemically reacting flow simulation. The convective and diffusive mass fluxes of gas-phase species at the surface are balanced by the production (or destruction) rates of gas-phase species by surface reactions. This relationship is... 

Opposite to the downward transport of 03s, upward transport of 03t from the troposphere into the stratosphere takes place. This maximizes in summer when deep convective mixing is strongest, concurrent with the maximum photochemical activity. After transport, 03t is chemically destroyed in the stratosphere. We note that reversible cross-tropopause transports of 03s and 03t are not included in the budgets, so Figure 3a and Table 2 represent net mass fluxes. 

Let us consider the symmetrical burning of a spherical droplet with the radius rp in surroundings without convection. Assume that there is an infinitely thin flame zone from the surface of the droplet to the radial distance rn [137], which is much larger than the radius of the droplet, rp. The heat released from the burning is conducted back to the surface to evaporate liquid fuel for combustion. Because the reaction is extremely fast, there exists no oxidant in the range of rp< r < m while no fuel vapor is available at r > rn. At a quasi steady state the mass flux through the spherical surface with the radius r (>rp), Mfv, can be obtained with Fick s law as... 

The simulator used was a DISMOL, described previously by Batistella and Maciel (2). All explanations of the equations used, the solution methods, and the routine of solution are described in Batistella and Maciel (5). DISMOL is a simulator that permits changes in feed composition, feed temperaturethe evaporation rate, as well as feed flow rate. The effective rate of surface evaporation is obtained from the kinetic theory of gases. The liquid film thickness is obtained by mass balance and geometry of the evaporator. The temperature in the liquid obeys the Fourier-Kirchhoff equation. The solution of the velocity profile requires knowledge of the viscosity and the liquid film thickness over the evaporator. The solution for the temperature and the concentration profiles requires knowledge of the velocity profiles, which determine the convective heat and mass fluxes. 

The vector quantity px represents both the convective mass flux and the concentration of linear momentum. Its vector product x x px with a position vector x from some axis of rotation represents the concentration of angular momentum about that axis. If g= — V is an external body or action-at-a-distance force per unit mass, where is a potential energy field, then the vector pg represents the volumetric rate of generation or production of linear momentum. The vector x x pg is the volmetric production rate of angular momentum. 

Figure 4 Normalised mass G(a), energy H(a), average enthalpy increase K(a) and transition mass flux g(a) of a droplet for the cases of (a) enthalpy improved 3EM and (b) for standard 3EM. Ambient temperature dFiame = 900°C, initial temperature 910 = 270°C, transition temperature STrans = 420 °C, initial droplet diameter di,0= 400mm, Nusselt number 18 and amplification factor of the heat conduction coefficient due to internal forced convection IWkmoiec = 2.72 (Beer [5]), residence time t=30 ms.

---