External thermal resistances

The solution for the isoflux boundary condition and with external thermal resistance was recently reexamined by Song et al. [156] and Lee et al. [157]. These researchers nondimen-sionalized the constriction resistance based on the centroid and area-average temperatures using the square root of the contact area as recommended by Chow and Yovanovich [15] and Yovanovich [132,137,144-146,150], and compared the analytical results against the numerical results reported by Nelson and Sayers [158] over the full range of the independent parameters Bi, e, and x. Nelson and Sayers [158] also chose the square root of the contact area to report their numerical results. The analytical and numerical results were reported to be in excellent agreement. 

External thermal resistance 0e>ct. primarily convective, from the case/package surface to the coolant fluid (gas or Hquid)... 

External thermal resistance A term used to represent thermal resistance from a convenient point on the outside surface of an electronic package to an ambient reference point. 

The temperature gradient is not to be confused with thermal lag, which is another physical property that should also be minimized in DSC experiments. Thermal lag is the difference between the average sample temperature and the sensor temperature and is caused by so-called thermal resistance, which characterizes the ability of the material to hinder the flow of heat. Thermal lag is smaller in DSC than in DTA because of smaller sample size (milligrams in DSCs), but more types of thermal resistance develop in DSC than in DTA. These effects are caused by introduction of the sample and reference pans into the DSC sample and reference holders. Thus, in DTA thermal resistance develops between the sample holder (in some instruments called the sample pod) and the sample (analogously, between the reference holder and the reference material), and within the sample and the reference materials. On the other hand, in DSC thermal resistance will develop between the sample holder and the bottom of the sample pan and the bottom of the sample pan and the sample (these are called external thermal resistances), and within the sample itself (this is called internal thermal resistance). These thermal resistances should be taken into account since they determine the thermal lag. Let us suppose that the cell is symmetric with regard to the sample and reference pods or holders, the instrumental thermal resistances are identical for the sample and reference holders, the contact between the pans and the pods are intimate, no crosstalk exists between the sample and reference sensors (i.e.. 

From a methodological perspective, DSC of films is more important than DSC of fibers. For good thermal contact, it is often desirable to run films in DSC, since in the DSC pans a film will have the maximum contact with the bottom of the pan, thus minimizing the external thermal resistance. 

Similar to fibers, films are often oriented. The simplest case of orientation is called uniaxial orientation, when the macromolecular segments are oriented in one preferred orientation. But a film may also be oriented in two directions (called biaxial orientation) having no fiber analog. Isotropic, unoriented film would correspond to the as-spun fiber (both having no preferred molecular orientation). Thus, DSC experiments carried out on unoriented films give results similar to those obtained from experiments performed on chips, powders, or as-spun fibers, but with minimum external thermal resistance. 

Larger and larger areas of copper do not help, especially with thinner copper. A point of diminishing returns is reached for a square copper area of size lin. x lin. Some improvement continues up to about 3in. (on either side), especially for 2-oz boards and better. But beyond that, external heatsinks are required. A reasonable practical value attainable for the thermal resistance (from the case of the power device to the ambient) is about 30°C/W. That means a 30°C rise for every Watt of dissipation inside the IC. 

Boersma5) showed that quantitative calorimetric data could be obtained from a modified DTA instrument in which the sample and reference are in separate containers connected by a controlled thermal resistance, and with external thermocouples. In such an instrument the sample-reference temperature difference can be related to the heat flow, and this is the basis of heat flux DSC. The DuPont 910 DSC is based on a further development of this principle, and it is illustrated by Fig. 2. 

Thus, an apparently slower mass uptake is observed as compared with the isothermal uptake or the case when heat transfer is controlled by the external film resistance. Consequently, ignoring the internal thermal resistance may lead to erroneously low mass transfer coefficient. 

Burton has derived an equation for preferred air temperature indoors (T ), which is expressed as a function of body heat generated minus external mechanical work, heat lost by evaporation of water, and thermal resistances provided by air boundary layers on the outer surface and clothing layers (J5). His concept of the interrelationship of persons and their indoor environment by heat transfer at the skin is straightforward and useful (Figure 3). 

Silica in the form of thin films as well as oxide monoliths, fibers, and powders can be prepared from sol-gel method. In contrast with the fabrication of conventional inorganic glasses at much higher melting temperature, sol-gel processing is performed at low temperatures to produce oxide materials with desirable hardness, optical transparency, chemical durability, tailored porosity, and thermal resistance. The sol-gel method involves formation of a colloidal suspension (sol) and gelation to form a network in a continuous liquid phase (gel). One starts with an aqueous solution containing oxides or alkoxides, mutual solvent, and catalyst. Usually an external catalyst is added like mineral acids and ammonia as well as acetic acid, KOH, amines, KF, and HF for rapid and... 

The differential equations involve the effective diffusivity and thermal conductivity of the porous pellet. Data and theories for these quantities are given in Secs. 11-1 to 11-5, and in Secs. 11-6 to 11-11 the results are used to establish the rate for the whole pellet. The method of combining the effects of internal and external transport resistance to give the global rate in terms of bulk fluid properties is discussed in Chap. 12. 

There are many cases where the external mass transfer resistance can be neglected while the external heat resistance in not negligible. In gas-solid systems, external heat transfer resistances are usually much higher than external mass transfer resistances especially for light components. Also there are cases where the intraparticle resistances are appreciable while the intraparticle heat transfer resistance is negligible due to the high thermal conductivity of the metal or metal oxides forming the bulk of the catalyst pellet. 

Equation 9.4 neglects thermal resistance in the wall or in the external heat transfer media. See Appendix 8.2 but note that there is an extra resistance term. 

Heat Transfer on Convection Duct Walls. For this boundary condition, denoted as , the wall temperature is considered to be constant in the axial direction, and the duct has convection with the environment. An external heat transfer coefficient is incorporated to represent this case. The dimensionless Biot number, defined as Bi = heDhlkw, reflects the effect of the wall thermal resistance, induced by external convection. 

Carnavos [155] reported typical overall improvements that can be realized with a variety of commercially available enhanced horizontal condenser tubes. The heat flux for single 130-mm-long tubes, in most cases with outside diameters of 19 mm, is plotted in Fig. 11.22 against AT/m for 12 tubes qualitatively described in the accompanying table. The overall heat transfer performance gain of the enhanced tubes over the smooth tube is as high as 175 percent. Internal enhancement is a substantial contributor to the overall performance, since the more effective external enhancements produce a large decrease in the shell-side thermal resistance. 

The right hand term of the equation shows the Biot number to characterize the ratio of the thermal resistance of the liquid layer to the thermal resistance of the external environment. 

Further discussion of nuclear reactor control problems resulting from water leakage is beyond the scope of the present paper, and the discussion presented hereafter is on the effects of the chemical reaction between sodium and water. As a corollary of this discussion, the necessity for the use of a double-barrier heat exchanger in systems where nuclear control problems are absent has been examined. The desirability of eliminating the double-barrier design where feasible is obvious. The double-barrier results in a more complex design with associated fabrication and operational problems, requires additional heat transfer area due to the increased thermal resistance of the double barrier, and requires external equipment to handle the third-fluid system. All these factors increase the size and cost of the heat exchanger. 

The dilemma can be summarized as follows. Plug-flow mass and thermal energy balances in a packed catalytic tubular reactor are written in terms of gas-phase concentrations and temperature of the bulk fluid phase. However, the volumetrically averaged rate of reactant consumption within catalytic pellets is calculated via concentrations and temperature on the external surface of the pellets. When external transport resistances are negligible, design of these reactors is simplified by equating bulk gas-phase conditions to those on the external catalytic surface. In this chapter, we address the dilemma when bulk gas-phase conditions are different from those on the external surface of the pellet. The logical sequence of calculations is as follows ... 

Neglecting the thermal resistance of the coil wall, the overall heat transfer coefficient based on the external area of the coil, U is given by ... 

The container considered is painted on its surfaces and the thermal resistance of the metal is negligible compared with the resistance between the metal and the air-steam mixture on one hand and external air or water of the external spray system on the other. With these assumptions and in the case where the external spray is not operating, the formulae giving the amount of heat exchanged in the generic time interval and the metal temperature at the end of the same interval are given in Equations A2.11-A2.15. 

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