Thermal resistances in series

The reciprocals in Eq. (8.14) may be interpreted as resistances to heat transfer, and so it appears that thermal resistances in series are additive. 

R Thermal resistance, equals x/kA, 1/UA, l/hA Ri, Ro, R l, R for thermal resistance of sections 1, 2, 3, and n of a composite body Rj for sum of individual resistances of several resistances in series or parallel R -, and for dirt or scale resistance on inner and outer surface respectively Ratio of total outside surface of finned tube to area of tube having same root diameter (s-K)/J (h- F)/Btu... 

We can think of the air and liquid films as being resistances in series. In this respect, they are similar to thermal resistances. If we designate the acetone by subscript A (i.e., the diffusing species) and the air by subscript B (i.e., the inert or insoluble species), we can write an expression for the concentration of each species in terms of their individual molar densities ... 

Conduction with Resistances in Series A steady-state temperature profile in a planar composite wall, with three constant thermal conductivities and no source terms, is shown in Fig. 5-3a. The corresponding thermal circuit is given in Fig. 5-3b. The rate of heat transfer through each of the layers is the same. The total resistance is the sum of the individual resistances shown in Fig. 5-3b ... 

Example 1 Conduction with Resistances in Series and Parallel Figure 5-4 shows the thermal circuit for a furnace wall. The outside surface has a known temperature T2 = 625 K. The temperature of the surroundings... 

The subscripts 1 and 2 in the relations above indicate the first and the second layers, respectively. We could also obtain this result by following the approach already used for the single-layer case by noting that the rate of steady heat transfer (2 through a multilayer medium is constant, and thus it must be the same through each layer. Note from the thermal resistance network that the resistances are in series, and thus the total thermal resistance is simply the arithmetic sum of the individual thermal resistances in the path of heat transfer. 

Now consider steady one-dimensional heat transfer through a cylindrical or spherical layer that is exposed to convection on boili sides to fluids at temperatures and T 2 with heat transfer coefftcients /t, and h, respectively, as shown in Fig. 3-25. The thermal resistance network in this case consists of one conduction and two convection resistances in series, just like the one for the plane wall, and the rate of heat transfer under steady conditions can be expressed as... 

Analysis The thermal resistance network for this problem involves four resistances in series and is given in Fig. 3-29. Taking L = 1 m, the areas of the surfaces exposed to convection are determined to be... 

Analysis The thermal resistance network for this problem involves four resistances in series and is given in Fig. 7-40. The inner radius of the pipe is r-j = 0.8 cm and the outer radius of the pipe and thus the inner radius of the insulation is rj = 1.0 cm. Letting ra represent the outer radius of the insulation, the areas of the surfaces exposed to convection for an L = 1-m-long section of the pipe become... 

The course of this process can be subdivided into several steps, in which a series of resistances have to be overcome. The fraction of these individual resistances in the total resistance can be very different. First, as a result of flow (convective transport) and molecular motion (diffusion transport), the vapour reaches the phase interface. In the next step the vapour condenses at the phase interface, and finally the enthalpy of condensation released at the interface is transported to the cooled wall by conduction and convection. Accordingly, three resistances in series have to be overcome the thermal resistance in the vapour phase, the thermal resistance during the conversion of the vapour into the liquid phase, and finally the resistance to heat transport in the liquid phase. 

What about the current rating This is largely determined by the amount of heat dissipation the inductor can tolerate. But its thermal resistance (in degC/W) is not determined by the winding configuration, rather by the exposed area of the inductor, and other physical characteristics. Therefore, whether in series or in parallel configuration, we have to maintain the same total I2R loss. For example, suppose we call the current rating in parallel as Ip ,... 

COMI QpND RESISTANCES IN SERIES. Consider a flat wall constructed of a series pflayers, as shown in Fig. 10.2. Let the thicknesses of the layers be B,i, B, and Bq and e average conductivities of the materials of which the layers are made be /c, kj, and respectively. Also, let the area of the compound wail, at right angles to the plane of the illustration, be A. Let A7, ATb, and ATc be the temperature drops across layers A, B, and C, respectively. Assume, further, that the layers are in excellent thermal contact, so that no temperature difference exists across the interfaces between the layers. Then, if AT is the total temperature drop across the entire wall,... 

The rate of flow of heat through several resistances in series clearly is analogous to the current flowing through several electric resistances in series. In an electric circuit the potential drop over any one of several resistances is to the total potential drop in the circuit as the individual resistances are to the total resistance. In the same way the potential drops in a thermal circuit, which are the temperature differences, are to the total temperature drop as the individual thermal resistances are to the total thermal resistance. This can be expressed mathematically as... 

Here AT , is the true mean temperature difference dependent on the exchanger flow arrangement and degree of fluid mixing within each fluid stream. The inverse of the overall thermal conductance UA is referred to as the overall thermal resistance R , which consists of component resistances in series as shown in Fig. 17.22 as follows. 

Membranes with ordered structures such as zeolites or nanotubes have considerable potential as gas separation membranes [46-48], In addition to having thermal and chemical stability, the porosity of these structures is ordered, and therefore there is usually more control over the separation properties. The pores within these structures are such that gas transport can not be completely explained by the transition state theory. This is because, in nanotubes for example, there is only one transition, from outside of the tube to inside of the tube. Two alternative models are outlined here, the parallel transport model and the resistance in series transport model, which are illustrated in Figure 5.5, and they are explained in detail by the work of Gilron and Softer [27]. 

Figure 17.71 Thermal resistances in the DSC system. Source Reprinted from McNaughton JL, Mortimer CT, Differential scanning calorimetry, IRS Physical Chemistry Series, 2,10,1975.

If the dissipating device is close to the thermal boxmdaries as shown in Figure 3.7, then the model needs to be adjusted so that there are two resistances in series. The first resistance, 0] is the trapezoidal section as shown... 

The conclusion drawn from this result is that resistances in series are no longer additive. This is true whenever any of the resistances is not first order. In electrical or thermal systems, resistances are almost always first order. However, in chemical systems, resistances will not be first order when there are non-first-order chemical reactions. This occurs frequently. 

Manual rheostats can be used in series with the motor armature for the current-limiting func tion. If the rheostat has ample thermal capacity, it can also Be usedto vaiy speed. If this system is used, interlocks should be included to prevent closing of the contactor unless maximum resistance is in the circuit. 

Cooler Absorbers When the absorption of a gas is accompanied by the evolution of heat, an important function of the absorption equipment is the removal of the heat generated. This may be accomplished by using a number of towers in series, the liquid from each tower being circulated through an external cooler. There are different types of cooler-absorbers in which processes of this type can be carried out in a single unit. The materials of which these cooler-absorbers are constructed should be of high thermal conductivity and resistant to corrosion by the substances used in the process. As an example, in the manufacture of hydrochloric acid of the... 

It has been noted earlier that thermal resistances may be added together for the case of heat transfer through a complete section formed from different media in series. 

---