Interface heat balance

The heat balance at the burning surface, i. e., at the interface between the soHd phase and zone I, is represented by... 

The velocity at any point uy(6) is determined by the rate of melting at the interface (Fig. 6.67), which is obtained from the Stefan condition or heat balance between conduction and the rate of melting at that interface,... 

The coordinate xs has its origin at the external surface when melting started, and it is stationary. In addition to the boundary conditions just given, we can write a heat balance for the interface (this is occasionally referred to as the Stefan condition). 

We cannot, however, calculate the melting rate of this geometrical configuration from Eq. 5.8-9 because we do not yet know the value of S. This value is determined by the rate of heat conducted into the solid-melt interface. If we make use of one more of the simplifying assumptions just given, namely, that viscous dissipation is negligible, the following simple heat balance can be made on the interface (see Eq. 5.7-14)... 

The two slabs of materials, steel mold and rubber, were assumed to be in perfect contact at the interface. He desired to employ the same modulus and the same incremental time At for both materials, so the thickness of the slices had to be different for the mold and the rubber. The heat balance at the interface led to the conclusion that the ratio of the thicknesses of the slices had to be taken as equal to the square root of the thermal diffusivities amo, j and... 

In the chemical engineering community the interfacial heat balance concept proposed by Colburn and Drew [23] to treat the latent heat of vaporization term may be more familiar. A consistent expression for the net latent heat of vaporization of the multicomponent mixture terms of the pure vapor s enthalpies can be derived from the Colburn and Drew theory [23, 162, 9] (sect 4.1.8). In their two-film model approach the heat balance includes (1) the heat flux at the interface due to condensation Rqj -, (2) sensible heat loss by the gas film, and (3) sensible heat loss by the liquid film. The interfacial heat jump balance (3.173) is then approximated by ... 

Budget methods. Vertical exchange rates and turbulent diffusivities Kz can be calculated from the heat balance or the mass balance of tracers for which transformation rates are known. Assuming horizontal homogeneity, the temporal change of tracer mass below a given depth z must be the sum of the net vertical mass flux through the cross-section at z and all sources and sinks of tracer mass below z. In the case of conservative tracers sources and sinks below z must be mass fluxes across the sediment-water interface. In the case of H, radioactive decay is an additional sink. In the case of He, tritium decay represents a source. If the increase of mass due to all sources and sinks, Sm, is known, the net mass flux can be calculated ... 

As a solution to momentum transport (Navier-Stokes equation) is usually not available for bioreactor velocity field, we are left with mass and heat balances. A local balance describing mixing, flow and interface transfer, including reaction is known as the dispersed model (3) ... 

From a heat balance at the vapor-liquid interface, it is found that the net mass-transfer energy must equal the difference between the heat transferred from the gas to the interface and the heat transferred from the interface through the liquid. This difference is represented by the previously developed natural convection heat-transfer relation for the gas-phase portion of the balance (7) and by a moving boundary steady-state conduction heat-transfer relation for the liquid-phase portion of the balance. This leads to the expression... 

Designing apparel for recreational snow sports is centred on keeping the participants thermal comfort within acceptable levels thus clothing has to act as a buffer between the varying temperatures of the environment and the micro climate at the skin textile interface. This balance is, of course, further complicated by the variation in heat output generated by flucmations in activity. 

Let the temperature below the solvent-air interface be T and that above the interface be Carrying out the one-dimensional heat balances for the two segments of the rod, we obtain... 

Note that at any time t the concentration at the pore mouth of the micropore is in equilibrium with the gas phase pressure P, and the instant temperature of the agglomerate, T. Since this temperature is time variant and is governed by the heat balance equation (10.3-2), the adsorbed concentration at the solid-fluid interface (z = L) is also time variant. 

From a heat balance of the interface, the melting rate can be determined. The heat used to melt the polymer at the interface is determined by the heat flux into the interface minus the heat flux out of the interface ... 

The heat flux from the interface into the solid bed qo , is determined from the temperature profile in the solid bed. This is given by Eq. 7.99. The melting rate can be determined from a heat balance at the interface. This can be written as ... 

The maximum reaction rate that occurs at the top end of the tubes will be limited by heat transfer. The heat transfer from the liquid surface to the tube wall can be described by a coefficient that is simply VS (X = thermal conductivity of liquid). In order to limit the liquid phase temperature (at the gas/liquid interface), the following heat balance has to fulfilled ... 

The same conclusion can be attained via the PFR evaluation. The respective data from the ProCell unit (gray cycles) are located in Fig. 4.16 significantly lower than Sherwood numbers evaluated with the CSTR assumption, because back-mixing reduces the efficiency of interface heat and mass transfer and, thus, leads to lower values of transfer coefficients, if taken into account in such coeffidents instead of being considered in the balance equation of the model. For the reference case of the conventional fluidized bed, so-called apparent Sherwood numbers (Shapp) must be used in combination with the PFR model (Groenewold and Tsotsas, 1999). 

Take heat balance at the interface and consider the deformation we yield... 

In high-pressure processes, often droplets and bubbles are important owing to their high surface area for heat and mass transport. Whereas plane fluid surfaces without external forces are pressure equilibrated, curved interfaces are balanced by the size keeping surface forces and the forces that are acting by the inner pressure in a spherical geometry like a bubble or a droplet with diameter D in equilibrium. 

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