Electrical analog

The procedure of Mason and Evans has the electrical analog shown in Figure 2.2, where voltages correspond to pressure gradients and currents to fluxes. As the argument stands there is no real justification for this procedure indeed, it seems improbable that the two mechanisms for diffusive momentum transfer will combine additively, without any interactive modification of their separate values. It is equally difficult to see why the effect of viscous velocity gradients can be accounted for simply by adding... 

Figure 2.2. Electrical analog of the procedure of Mason and Evans.

Models are the handiwork of theoreticians and may be mechanical or electrical analogs, pictorial representations, or purely mathematical constructs. 

Radiation heat transfer in a hollow can be represented by electrical analogy as... 

Countercurrent electrophoresis can be nsed to split a mixtnre of mobile species into two fractions by the electrical analog of elntria-tion. In such countercurrent electrophoresis, sometimes termed an ion still, a flow of the suspending flnid is maintained parallel to the direction of the voltage gradient. Species which do not migrate fast enough in the applied electric field will be physically swept out of the apparatus. An apparatus based mainly on this principle bnt nsing also natural convection currents has been developed (Bier, Electrophoresis, vol. II, Academic, New York, 1967). 

The mechanical problem treated above has its electrical analogy in the circuit shown in Fig. 3. It is composed of three elements, an inductance , a capacitance C and a resistance R. If there are no other elements in the closed... 

By making use of these analogies, electrical analog models can be constructed that can be used to determine the pressure and flow distribution in a porous medium from measurements of voltage and current distribution in a conducting medium, for example. The process becomes more complex, however, when the local permeability varies with position within the medium, which is often the case. 

Kurana and Kumar (K20) have written the general equations taking the variation of flow into consideration for the two step mechanism of bubble formation. The fluctuations of pressure and the corresponding variations in flow are treated by an electrical analog. 

To express the flow rate as a function of time, an electrical analog shown in Fig. 27 has been used. 

If a film is heterogeneous, there may be parallel paths of sohd transformations (Figure 9-15). A transformation process can be short circuited by the presence of a parallel process, and this can greatly accelerate solid-state transformations. These can also be simplified by considering them as series and parallel processes, and, as long as they are linear (first order in concentrations), the electrical analogs can be used (Figure 9-15). 

For resistors in parallel, the current (flux) branches between paths while the voltage (concentration at each end) is constant. The electrical analogy of resistors in series and parallel allows one to solve these problems quite simply. 

A more general treatment that applies readily to homogeneous and heterogeneous equilibria alike was developed by von Stein (Ref 11a). It was originally formulated to facilitate computations by desk computer of isobaric multicomponent flame product compns, but has been adapted at PicArsn to the calcn by electrical analog computer of isochoric expln products... 

Various other physical processes lead in their mathematical description to equations of the same form as Flq (2). especially in its steady-state form, Such processes include the conduction of electricity in a conductor, or the shape of a thin membrane stretched over a curved boundary. This situation has led to the development of analogies (electric analogy, soap film analogy) to heal conduction processes, which are useful because they often offer the advantages of simpler experimentation. 

In the analysis of thermal performance, an electrical analogy is often... 

This model leads to A = 0.67 at the gel point, using the zero-frequency values for s and u. Use of the values for s and u calculated by treating the gelation phenomena as a three-dimensional percolation model of a supra-conductor/resistor network (electrical analogy), gives A = 0.72 0.02. 

Strictly, vg should be defined relative to the reference height at which the airborne concentration is measured. When this is not specified, it is understood to be about 1 m above ground. On the electrical analogy, the velocity of deposition is sometimes called the conductance, and its reciprocal the resistance. 

The difference %i Xo in concentration of a vapour or aerosol in the free stream and at a surface is the driving force for deposition. Since the ratio Q/(x 1 — Xo) has the dimensions of a velocity, it is called the velocity of deposition, denoted vg. Alternatively, on the electrical analogy, vg is the conductance and its reciprocal, r is the resistance to mass transfer. If the boundary layer of an airflow over a surface has two or more parts, for example above and below the top of the roughness elements, the resistances of these layers are additive, since... 

In the electrical analogy, these are resistances in series. In other instances, it may be the conductances which are additive, as for example where water is transpired from the leaves of plants acting in parallel with evaporation from the ground. 

It is assumed that e i ec and es ec. With these conditions, the equivalent thermal resistance is approximatively equal to the thermal resistance of the activated carbon. Therefore, the equivalent thermal conductivity along the radial direction is considered as equal to the activated carbon conductivity (Xr Xj. Along the axial direction, the thermal conductivity, Xy, is assumed to be the same as the aluminum conductivity. This condition is deduced from the electrical analog used to represent the heat flow inside the DLC by the parallel thermal resistances as follows ... 

The dimensions of this constant are clearly [Lz T l] = rate of flow, q/t = 0. Gardner regards this constant as equivalent to the capillary conductivity on the basis of heat and electrical analogies. This result is remarkable considering the assumptions involved. Eq (15-30) indicates that Xfl, the capillary conductivity, may be determined directly from measurement of the volume moisture-content V, the actual volume of flow per unit cross section Vv, and the gradient moisture-content dV/dx at the point x. These quantities are all experimentally observable. 

Two types of electrical analogy model for the interpretation of impedance data can be used based on combinations of resistances and capacitances, or based on transmission lines. These possibilities are now described. 

Figure 28 Randles circuit that serves as an electrical analog of the corroding interface.

The electrical analogy may be used to solve more complex problems involving both series and parallel thermal resistances. A typical problem and its analogous electric circuit are shown in Fig. 2-2. The one-dimensional heat-flow equation for this type of problem may be written... 

Flfl. 2-1 One-dimensional heat transfer through a composite wall and electrical analog. 

Fig. 2-4 One-dimensional heat flow through multiple cylindrical sections and electrical analog.

The accuracy of this method is dependent entirely on the skill of the person sketching the curvilinear squares. Even a crude sketch, however, can frequently help to give fairly good estimates of the temperatures that will occur in a body and these estimates may then be refined with numerical techniques discussed in Sec. 3-5. An electrical analogy may be employed to sketch the curvilinear squares, as discussed in Sec. 3-9. 

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