Thermal-electric analogies

The thermal-electric analogy method is useful to represent the accepted structures, which distinguish the domains and the modes of their connection with themselves and the environment. It is also useful to formulate a suitable system of the balance equations for the bodies (domains). The increase in the number of its applications is related to the development of analog computer calculation methods. 

Zhu and Zhang [53] developed a novel experimental apparatus to evaluate the heat transmission of protective fabries subjected to an external heat flux. The fabric has a cold side (maintained at around 36 °C) and a side which is exposed to dry hot air, heated by a hot plate. Thermal conduetivity of the fabric is determined by thermal-electric analog principle. The thermal resistanee of the sample R2) is given by ... 

These thermal-electrical analogies provide a powerful tool one may construct analog computers to simulate heat flow problems. The electrical analog circuit to the detector arrangement of Fig. 5.11.1 is shown in Fig. 5.11.2. The conditions required to maximize the voltage, AT, for a given and a certain current, AIT,are now clear. The difficulties in making small and about are in the practical implementation, however. 

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

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 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... 

Note that the heat transfer area A is constant tor a plane wall, and the rate of heat transfer through a wall separating two mediums is equal to the temperature difference divided by the total thermal resistance between the mediums. Also note that (he thermal resistances are in series, and the equivalent thermal resistance is determined by simply adding the individual resistances, just like the electrical resistances connected in series. Thus, the electrical analogy still applies. We summarize this as the rate of steady heat transfer between two surfaces is equal to the temperature difference divided by the total thermal resistance behveen those Uvo surfaces. 

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. 

FIGURE 14-20 Analogy between thermal, electrical, and mass diffusion resistance concepts. 

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. 

Again, we can make use of electrical analogy, noting that thermal capacitance Q is analogous to electrical capacitance C(F). 

Conduction usually occurs in conjunction with convection, and if the temperatures are high, they also occur with radiation. In some practical situations where radiation cannot be readily estimated, convection heat transfer coefficients can be enhanced to include the effect of radiation. Combined conduction and convection led to the concept of thermal resistances, analogous to electrical resistances, which can be solved similarly. 

The operation of the Tzero (To) technology, as for the TA Instruments 910, 2910, and 2920 DSC modules, is also based on a thermal equivalent of Ohm s law. With the assumptions that the cell offers thermal resistance analogous to an electrical resistance and that the heat capacity of the platform pods needs to be accounted for, a heat balance equation can be constructed for each sensor pod ... 

Capacitance, thermal - This term is used to describe heat capacity in terms of an electrical analog, where loss of heat is analogous to loss of charge on a capacitor. Structures with high thermal capacitance change temperature more slowly than those with low thermal capacitanee. 

Based on the case of the semiinfinite solid, one may foretell the temperature history, temperature gradient, and heating rate of the stratified fluid portion beneath the liquid—vapor interface where numerous succeeding initial and boundary conditions are to be imposed in the manner of trial and error, where these conditions are to vary with time for any one given situation, or where a variation of thermal properties must be taken into account, the electrical-analog method may better be adapted to the problem with respect to time involved in solution attainment. 

Fig. 5.11.2 Electrical analog circuit of thermal detector shown in Fig. 5.11.1.

Alternatively, reactant and product gases can be distributed to and removed from individual cells through internal pipes in a design analogous to that of filter presses, (iare must be exercised to assure an even flow distribution between the entiv and exit cells. The seals in internally manifolded stacks are generally not subject to electrical, thermal, and mechanical stresses, but are more numerous than in externally manifolded stacks. 

Table A-1 Analogous Elements between tbe Thermal and Electrical Domains...

It is convenient to consider thermal systems as being analogous to electrical systems so that they contain both resistive and capacitive elements. 

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. 

The ferroelectricity usually disappears above a certain transition temperature (often called a Curie temperature) above which the crystal is said to be paraelectric this is because thermal motion has destroyed the ferroelectric order. Occasionally the crystal melts or decomposes before the paraelectric state is reached. There are thus some analogies to ferromagnetic and paramagnetic compounds though it should be noted that there is no iron in ferroelectric compounds. Some typical examples, together with their transition temperatures and spontaneous permanent electric polarization P, are given in the Table. 

A general method of estimating the temperature distribution in a body of any shape consists of replacing the heat flow problem by the analogous electrical situation and measuring the electrical potentials at various points. The heat capacity per unit volume C.,p is represented by an electrical capacitance, and the thermal conductivity k by an... 

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