Infinite flux

This method is valid for systems without thermal relaxation. Therefore, all data concerning the photostationary state were extrapolated to infinite flux. 

If we introduce the extent of trans cis conversion at infinite flux, then ... 

This equation is also valid when at the infinite flux photostationary state ... 

Recall that A was introduced in Equation 3A.5 and that it is measured at the same wavelength as the irradiation. The infinite flux extrapolated value A is the intercept of the curve corresponding to Equation 3A.6. Introducing Equation 3A.12 for A and A" into Equation 3A.10, we have ... 

The models above may be useful for predicting mass fluxes in MD however, each of these models has its limitations. The Knudsen and Poiseuille model require knowledge of r, 8, and e, which in general can be estimated by applying the models to experimental gas fluxes through the given membrane. The molecular diffusion model is inadequate at low-partial pressures of air, as it predicts infinite flux since, in totally deaerated membrane 7 tends to zero. 

The influence of single and multiple layers of different thermal conductivities and thicknesses is of great interest. The solutions given below can be used to determine the effect of oxide layers and coatings on the spreading resistance. Solutions are available for semi-infinite flux tubes and finite systems such as circular disks. 

Transient Spreading Resistance Within Semi-Infinite Flux Tlibes and Channels... 

In this equation, 8 and denote the relative change of absorbance observed at wavelengths A and A", respectively, when a solution of truns-isomers is photoequilibrated with an infinite-flux light at the respective wavelength. Furthermore, the ratio p p = of at two different excitation wave-... 

Maxwell obtained equation (4.7) for a single component gas by a momentum transfer argument, which we will now extend essentially unchanged to the case of a multicomponent mixture to obtain a corresponding boundary condition. The flux of gas molecules of species r incident on unit area of a wall bounding a semi-infinite, gas filled region is given by at low pressures, where n is the number of molecules of type r per... 

One nice feature of the finite element method is the use of natural boundaiy conditions. It may be possible to solve the problem on a domain that is shorter than needed to reach some limiting condition (such as at an outflow boundaiy). The externally applied flux is still apphed at the shorter domain, and the solution inside the truncated domain is still vahd. Examples are given in Refs. 67 and 107. The effect of this is to allow solutions in domains that are smaller, thus saving computation time and permitting the solution in semi-infinite domains. 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

For axial dispersion in a semi-infinite bed with a linear isotherm, the complete solution has been obtained for a constant flux inlet boundary condition [Lapidiis and Amundson,y. Phy.s. Chem., 56, 984 (1952) Brenner, Chem. Eng. Set., 17, 229 (1962) Coates and Smith, Soc. Petrol. Engrs. J., 4, 73 (1964)]. For large N, the leading term is... 

Infinite-cis experiments. In this type of experiment, the net flux of glucose from a limitingly high concentration on the cis face of the membrane is measured as a function of the concentration on the trans face. Both entry and exit infinite-m (ic) experiments can be performed, yielding two Am values, A i and K, respectively. Maximal fluxes are obtained when the concentration on the trans side of the membrane is zero. Since this is the zero-trans situation, = Fq and F o =... 

Analysis of data obtained from the RDC usually involves plotting the reciprocal of the measured flux, against and extrapolating to infinite rotation speed... 

The data analysis procedure for the case of constant heat flux is based on the theory describing the response of an infinite line source model (Ingersoll and Plass, 1948 Mogeson, 1983). Although this model is a simplification of the actual experiment, it can successfully be used to derive the geothermal properties (e.g. Kavenaugh, 1984 Austin,. 1998 Gehlin, 1998). 

Figure 125 shows the cooling of the semi-infinite PCM layer. Because the heat capacity cp is negligible, the temperature change from the location of the phase front at distance s to the surface is linear. The heat flux at the surface as a function of the location of the phase front is then... 

Thus the time during which the transport process attains the steady state depends strongly on the radius of the sphere r0. The steady state is connected with the dimensions of the surface to which diffusion transport takes place and does, in fact, not depend much on its shape. Diffusion to a semispherical surface located on an impermeable planar surface occurs in the same way as to a spherical surface in infinite space. The properties of diffusion to a disk-shaped surface located in an impermeable plane are not very different. The material flux is inversely proportional to the radius of the surface and the time during which stationary concentration distribution is attained decreases with the square of the disk radius. This is especially important for application of microelectrodes (see page 292). 

Note that, unlike the steady-state case, the flux in the semi-infinite membrane decreases with increasing time and distance. The flux at the interface is... 

The interfacial heat transfer coefficient can be evaluated by using the correlations described by Sideman (S5), and then the dimensionless parameter Ni can be calculated. If the Peclet numbers are assumed to be infinite, Eqs. (30) can be applied to the design of adiabatic cocurrent systems. For nonadiabatic systems, the wall heat flux must also be evaluated. The wall heat flux is described by Eqs. (32) and the wall heat-transfer coefficient can be estimated by Eq. (33) with... 

It should be noted that the derivative is negative, so that at certain conditions the denominator of Eq. (15-51) can be zero, resulting in an infinite pressure gradient. This condition corresponds to the speed of sound, i.e., choked flow. For a nonflashing liquid and an ideal gas mixture, the corresponding maximum (choked) mass flux G follows directly from the definition of the speed of sound ... 

When heat is liberated or absorbed in the calorimeter vessel, a thermal flux is established in the heat conductor and heat flows until the thermal equilibrium of the calorimetric system is restored. The heat capacity of the surrounding medium (heat sink) is supposed to be infinitely large and its temperature is not modified by the amount of heat flowing in or out. The quantity of heat flowing along the heat conductor is evaluated, as a function of time, from the intensity of a physical modification produced in the conductor by the heat flux. Usually, the temperature difference 0 between the ends of the conductor is measured. Since heat is transferred by conduction along the heat conductor, calorimeters of this type are often also named conduction calorimeters (20a). 

As explained above, one long side of the compartment wall was split into a large number of thin strips and the heat flux to the center of each strip calculated. For a constant heat flux, assuming the wall material to be semi—infinite, the wall surface temperature... 

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