In discussion of the other basic materials, iron and copper, mention has already been made of the energy losses which their use entails. These, of course, manifest themselves in the form of heat. This results in a rise in temperature of the system, be it core and windings, core frames, tank, or other ancillary parts. These will reach an equilibrium when the heat is being taken away as fast as it is being produced. For the great majority of transformers, this limiting temperature is set by the use of paper insulation, which, if it is to have an acceptable working life, must be limited to somewhere in the region of 100°C. Efficient cooling is therefore essential, and for all but the smallest transformers, this is best provided by a liquid.   For most transformers mineral oil is the most efficient medium for absorbing heat from the core and the windings and transmitting it, sometimes aided by forced circulation, to the naturally or artificially cooled outer surfaces of the transformer. The heat capacity, or specific heat, and the thermal conductivity of the oil have an important influence on the rate of heat transfer.   When the resistive and other losses are generated in transformer windings heat is produced. This heat must be transferred into and taken away by the transformer oil. The winding copper retains its mechanical strength up to several hundred degrees Celsius. Transformer oil does not significantly degrade below about 140oC, but paper insulation deteriorates with greatly increasing severity if its temperature rises above about 90oC. The cooling oil flow must, therefore, ensure that the insulation temperature is kept below this figure as far as possible.   The maximum temperature at which no degradation of paper insulation occurs is about 80oC. It is usually neither economic nor practical, however, to limit the insulation temperature to this level at all times. Insulation life would greatly exceed transformer design life and, since ambient temperatures and applied loads vary, a maximum temperature of 80oC would mean that on many occasions the insulation would be much cooler than this. Thus, apart from premature failure due to a fault, the critical factor in determining the life expectancy of a transformer is the working temperature of the insulation or, more precisely, the temperature of the hottest part of the insulation or hot spot. The designer’s problem is to decide the temperature that the hot spot should be allowed to reach. Various researchers have considered this problem and all of them tend to agree that the rate of deterioration or ageing of paper insulation rapidly increases with increasing temperature.

Figure 1   Figure 1   In situ measurements of conditions such as temperature can be used to infer the quality of the wafers being produced in thermal processes. In many types of thermal processing equipment, temperature is measured using a thermocouple embedded in the wafer holder (or susceptor). A thermocouple is a circuit consisting of a pair of wires made of different metals joined at one end (the “sensing junction”) and terminated at the other end (the “reference junction”) in such a way that the terminals are both at a known reference temperature. Leads from the reference junction to a load resistance (i.e., an indicating meter) complete the thermocouple circuit. Due to the thermoelectric effect (or Seebeck effect), a current is induced in the circuit whenever the sensing and reference junctions are different temperatures. This current varies linearly with the temperature difference between the junctions.   In some cases (such as in rapid thermal processes), the use of a thermocouple is not possible because there is no susceptor. Alternative temperature sensors used in such situations include thermopiles and optical pyrometers. A thermopile, which also operates via the Seebeck effect, consists of several sensing junctions made of the same material pairs located in close proximity and connected in series in order to multiply their output.   The second alternative method to the thermocouple is pyrometry. Pyrometers operate by measuring the radiant energy received in a certain band of energies, assuming that the source is a graybody of known emissivity. The input energy can then be converted to a source temperature using the Stefan–Boltzmann relationship. Most commercial systems monitor the mid-infrared band (3–6 m).   One major issue in using pyrometry is that the effective emissivity of the source must be accurately known. The effective emissivity includes both intrinsic and extrinsic contributions. Intrinsic emissivity is a function of the material, surface finish, temperature, and wavelength. Extrinsic emissivity is affected by the amount of radiant energy from other sources reflected back to the spot being measured (which can increase the apparent temperature). In addition, the presence of multiple layers of different thin-film materials can also alter the apparent emissivity due to interference effects.

Figure 1   Measurement, or measuring, is also the most important part of an experiment. Measuring is not absolute, as it does not define a quantity (standard) to be measured. Measuring is a relative effort and is made to compare and to evaluate. To be independent, a comparison requires a measure, a standard unit.   The art of measuring is at least as old as humanity itself. The human body performs measurements all the time. One of the most basic quantities continuously measured by the human body is the environment temperature. Feeling hot or cold is a consequence of this measuring. Although not descriptive (not quantified with a parameter such as temperature), the natural measuring of the environmental temperature by the human body is nevertheless a relative process. This process is based on a comparison of the environmental temperature with a certain standard, in this case the temperature at which the body feels neitherhot norcold—the null point of human thermal control. In heat transfer, temperature and heat flow are unquestionably the most important quantities to be measured. Other quantities of interest to heat transfer include fluid speed, pressure (force), mechanical stress, electric current, voltage, length, surface area, volume, and displacement. In this chapter the focus is on temperature and heat flow measurements.   General measuring concepts such as sensitivity, hysteresis, calibration, accuracy, and readability are presented first. Then the discussion turns to statistical concepts such as mean, deviation, standard deviation, normal distribution, Chauvenet’s criterion, and the chi-square test, related to the determination of precision, bias error, and measuring uncertainty. The final section of this chapter is devoted to a brief discussion of some common instruments for measuring temperature or heat flow.   Among the two possible alternatives for sensing devices, the most common are the contact sensing devices such as thermocouples that measure by physical contact. In general, contact sensing devices are rugged, economical, relatively accurate, and easy to use. Disadvantages commonly associated with contact sensing devices include susceptibility to wear (e.g., breaking of thermocouple junction). They also require accessibility forphysical contact. Because of the contact nature of these devices, they tend to interfere with the medium where measurement is to be taken, frequently affecting the state and the value of the quantity to be measured. The last disadvantage can be a serious problem. For instance, the conductive wires of a thermocouple will always provide a heat path when in contact with the medium where temperature is to be measured. This heat path can modify the state of the medium where temperature is to be measured by adding energy to, or extracting energy from, the medium.

Natural convection is generated by the density difference induced by the temperature differences within a fluid system. Because of the small density variations present in these types of flows, a general incompressible flow approximation is adopted. In most buoyancy-driven convection problems, flow is generated by either a temperature variation or a concentration variation in the fluid system, which leads to local density differences. Therefore, in such flows, a body force term needs to be added to the momentum equations to include the effect of local density differences.   Mixed convection involves features from both forced and natural flow conditions. The buoyancy effects become comparable to the forced flow effects at small and moderate Reynolds numbers. Since the flow is partly forced, a reference velocity value is normally known (Example: velocity at the inlet of a channel). Therefore, non-dimensional scales of forced convection can be adopted here. However, in mixed convection problems, the buoyancy term needs to be added to the appropriate component of the momentum equation. If we replace 1/P r with Re in the non-dimensional natural convection equations of the previous subsection, we obtain the non-dimensional equations for mixed convection flows. These equations are the same as for the forced convection flow problem except for the body force term, which will be added to the momentum equation in the gravity direction.   Forced convection heat transfer is induced by forcing a liquid, or gas, over a hot body or surface. Two forced convection problems will be studied in this section. The first problem is the extension of flow through a two-dimensional channel as discussed in the previous section and the second one is of forced convection over a sphere. The difference between the first problem and the one in the previous section is that the top and bottom walls are at a higher temperature than that of the air flowing into the channel.