Space resistance

Fig. 8-25 Element representing "space resistance" in radiation-net-AiFi2 work method.

A problem which may be easily solved with the network method is that of two flat surfaces exchanging heat with one other but connected by a third surface which does not exchange heat, i.e., one which is perfectly insulated. This third surface nevertheless influences the heat-transfer process because it absorbs and re-radiates energy to the other two surfaces which exchange heat. The network for this system is shown in Fig. 8-28. Notice that node is not connected to a radiation surface resistance because surface 3 does not exchange energy. Notice also that the values for the space resistances have been written... 

If the emissivities of all surfaces are equal, a rather simple relation may be derived for the heat transfer when the surfaces may be considered as infinite parallel planes. Let the number of shields be n. Considering the radiation network for the system, all the surface resistances would be the same since the emissivities are equal. There would be two of these resistances for each shield and one for each heat-transfer surface. There would be n + I space resistances, and these would all be unity since the radiation shape factors are unity for the infinite parallel planes. The total resistance in the network would thus be... 

The netwoikmelhod was first introduced by A. K. Oppenheim in the 1950s and found widespread acceptance because of its simplicity and emphasis on the physics of the problem. The application of Ihe method i.s straightforward draw a surface resistance associated with each surface of an enclosure and connect them with space resistances. Then solve the radiation problem by treating it as an electrical network problem where llie radiation heal transfer replaces the current and radiosity replaces Ihe potential. 

The radiation network of this two-surface enclosure consists of two surface resistances and one space resistance, as shown in Fig. 13-24. hi an electrical network, the electric current flowing through these resistances connected in series would be determined by dividing the potential difference between points A and B by the total resistance between the same two points. The net rate of radiation transfer is determined in the same manner and is expressed as... 

We now consider an enclosure consisting of three opaque, diffuse, and gray surfaces, as shown in Fig. 13-26. Surfaces 1, 2, and 3 have surface areas Aj, and A3 cmissivities C, e, and 3 and uniform temperatures T, T , and T 3. respective . The radiation network of this geometry is constructed by following the standard procedure draw a surface resistance associated with each of the three surfaces and connect these surface resistances with space resistances, as shown in the figtire. Relations for the surface and space resistances are given by Fqs. 13-26 and 13-31. The three endpoint potentials and... 

Now consider a radiation shield placed between these two plates, as shown in Fig. 13-30. Let the emissivities of the shield facing plates 1 and 2 be 3 j and E, 2, respectively. Note that the emissivity of different surfaces of the shield may be different. The radiation network of this geometry is constructed, as usual, by drawing a surface resistance associated with each surface and connecting these surface resistances with space resistances, as shown in the figure. The resistances are connected in series, and thus the rate of radiation heat transfer is... 

C What arc the radiation surface and space resistances How are they expressed For what kind of surfaces is the radiation surface resistance zero ... 

Figure 8. SEM photographs of 0.24 fjL m line-and-space resist patterns on a Si substrate treated with (a) TMSP or (b) HMDS (treatment time 30 sec., substrate temperature 100 C).

TTie necessary basic criteria for a wholly space resistant, space tailored composite are ... 

The resistivity values obtained represent the average resistivity of the soil to a depth equal to the pin spacing. Resistance measurements are typically performed to a depth equal to that of the buried system (pipeline) being evaluated. Typical probe spacing is in increments of 0.5 to 1 m. 

The smallest current amplitude required to cause excitation is known as the rheobase current (/rh). T is the membrane time constant of the axon if the axon is stimulated intracellularly. For extracellular stimulation, T is a time constant which takes into account the extracellular space resistance. The relationship between current amplitude and pulse width can also be derived theoretically using the cable equation by assuming that total charge on the cable for excitation is constant [Jack et al., 1983]. 

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