Heat flux density balances equations

The equations of heat flux density balances between the disk and the rod are ... 

Figure 10 presents the interface shape of the rivulet for wall superheat as 0.5 K and Re = 2.5. Here also presented the data on pressure in liquid and heat flux density in rivulet cross-section. The intensive liquid evaporation in near contact line region causes the interface deformation. As a result the transversal pressure gradient creates the capillarity induced liquid cross flow in direction to contact line. Finally the balance of evaporated liquid and been bring by capillarity is established. This balance defines the interface shape and apparent contact angle value.For the inertia flow model, the solution is obtained from a non-stationary system of equations, i.e., it is time-dependable. In this case the disturbances in flow interface can create the wave flow patterns. The solutions of unsteady state liquid spreading on heat transfer surface without and with evaporation are presented on Fig. 11. When the evaporation is not included (for zero wall superheat) the wave pattern appears on the interface. When the evaporation includes, the apparent contact angle increase immediately and deform the interface. It causes the wave suppression due to increasing of the film curvature.

The condensed phase density p, specific heat C, thermal conductivity A c, and radiation absorption coefficient Ka are assumed to be constant. The species-A equation includes only advective transport and depletion of species-A (generation of species-B) by chemical reaction. The species-B balance equation is redundant in this binary system since the total mass equation, m = constant, has been included the mass fraction of B is 1-T. The energy equation includes advective transport, thermal diffusion, chemical reaction, and in-depth absorption of radiation. Species diffusion d Y/cbfl term) and mass/energy transport by turbulence or multi-phase advection (bubbling) which might potentially be important in a sufficiently thick liquid layer are neglected. The radiant flux term qr... 

This is the first output quantity according to Figure 28.3. The mass flux densities, Hj, can be obtained from Faraday s law combined with the component mass balance [Eqs. (28.68) and (28.69)]. The heat source density, q, is obtained from an enthalpy balance around the electrode pore, similar to Eq. (28.70). Corresponding equations were given by Wolf and Wilemski [2, 3], although not aU of them are formulated as part of the electrode model. 

The output quantities required from this model are obtained in a similar approach as in the film model the current density from the electrode is proportional to the potential gradient at the bottom of the agglomerate, the mass fluxes are obtained from mass balances in the macropores, and the heat flux is obtained from an enthalpy balance over the complete pore, ffowever, in the pubUcations listed in Table 28.3, these equations are not mentioned expHcitly. 

To investigate the thermo-mechanical interactions, the laws of thermodynamics are applied. The first law of thermodynamics can be considered as a balance equation with the internal energy density m and the heat fluxes q and r due to close-range and long-range effects, respectively. Considering the direct energy production density f one can obtain... 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that if an inconsistent diffusive flux closure like the Wilke equation is adopted (i.e., the sum of the diffusive mass fluxes is not necessarily equal to zero) instead, the sum of the species mass balances does not exactly coincide with the mixture continuity equation. 

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