Conduction electrical analogies

Conduction takes place at a solid, liquid, or vapor boundary through the collisions of molecules, without mass transfer taking place. The process of heat conduction is analogous to that of electrical conduction, and similar concepts and calculation methods apply. The thermal conductivity of matter is a physical property and is its ability to conduct heat. Thermal conduction is a function of both the temperature and the properties of the material. The system is often considered as being homogeneous, and the thermal conductivity is considered constant. Thermal conductivity, A, W m, is defined using Fourier s law. 

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. 

The conductance value C is the flow volume through a piping element. The equation (1.11) could be thought of as Ohm s law for vacuum technology , in which qpy corresponds to current, Ap the voltage and C the electrical conductance value. Analogous to Ohm s law in the science of electricity, the resistance to flow... 

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. 

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. 

Water thus causes the electrolytic dissociation of the hydrogen chlpride, which means the formation of a hydroxonium cation on one side and a chloride anion on the other side, so that the solution conducts electrical current. Ions of other acids are formed by analogical reaction with water. )... 

In practice we often encounter plane walls that consist of several layers of different materials. The tbermal resistance concept can still be used to detennine the rate of steady heat transfer through such composite walls. As you may have already guessed, this is done by simply notiifg that the conduction resistance of each wall i.s IJkA connected in series, and using the electrical analogy. That is, by dividing the temperature difference between two surfaces at known temperatures by the total thermal resistance between them. 

In terms of the electric analogy, the total (convective + conductive) resistance is... 

We have already encountered the application of electrical analogy to conduction. Now we proceed to the use of electrical analogy for radiation. This method is based on two circuit elements. For the first element, reconsider the opaque gray surface of Fig. 9.3. The radiant heat flux from this surface is... 

The most widely accepted view of diffusion in semicrystalline polymers stems from the extensive series of studies conducted by Michaels and coworkers (18-23). Using an electrical analog of a porous medium consisting of conducting channels, the flux of a penetrant through a semicrystalline polymer can be expressed as follows... 

Using another electrical analog approach, Klute (26,27) arrived at a similar expression in which the impedance factor was termed the "transmission function." In both cases, however, the properties of the conducting phase are considered not to be influenced by the crystalline phase. Although this was found to be true for sorption, Michaels et al asserted that the crystallites would reduce the mobility of the chains in the amorphous phase and, thus, further reduce penetrant diffusion rates. The "chain... 

FIGURE 1.1 One-dimensional heat conduction through a plane wall (a) and electric analog (b). 

Thermal energy is transported by two mechanisms in solids—electronic conduction and lattice or phonon conduction. An electrical analog for thermal conduction is shown in Fig. 2 [% The total thermal conductivity. A, is the sum of the electronic term and the lattice term. For pure metals and dilute alloys, thermal conduction is dominated by the electronic term, while for heavily alloyed metals, the phonon contribution is appreciable. 

---