Insulation optimum

The selection of a material having the right balance of ablation and insulation properties is needed to produce optimum heatshield performance. 

The carbon black in semiconductive shields is composed of complex aggregates (clusters) that are grape-like stmctures of very small primary particles in the 10 to 70 nanometer size range (see Carbon, carbon black). The optimum concentration of carbon black is a compromise between conductivity and processibiUty and can vary from about 30 to 60 parts per hundred of polymer (phr) depending on the black. If the black concentration is higher than 60 phr for most blacks, the compound is no longer easily extmded into a thin continuous layer on the cable and its physical properties are sacrificed. Ionic contaminants in carbon black may produce tree channels in the insulation close to the conductor shield. 

Cooling is most effectively accompHshed with a tandem arrangement of two extmders, as shown ia Figure 12, whereia the first extmder ensures complete dissolution of the blowiag ageat, and the second extmder is operated at slow speed for optimum cooling. Additional information on extmsion of foams is contaiaed ia Reference 28 (see FoAAffiD plastics Insulation, thermal). 

An example in support of the first point is the case of optimum insulation thickness. A tank, optimally insulated when first installed, can fall below optimal if the value of heat is quadmpled. This change can justify twice the old iasulation thickness on a new tank. However, the old tank may have to function with its old iasulation. The reason is that there are large costs associated with preparation to iasulate. This means that the cost of an added increment of iasulation is much greater than assumed ia the optimum iasulation thickness formulas (Fig. 15). 

For insulators, Z is very small because p is very high, ie, there is Htde electrical conduction for metals, Z is very small because S is very low. Z peaks for semiconductors at - 10 cm charge carrier concentration, which is about three orders of magnitude less than for free electrons in metals. Thus for electrical power production or heat pump operation the optimum materials are heavily doped semiconductors. 

The optimization of heat-transfer surfaces also plays a role. At the optimum, the lifetime cost of a surface is approximately equal in value to the lifetime cost of power used to overcome the temperature differential in the condenser and evaporator. Additionally, condensation on insulation is a sign of questionable insulation (see Insulation, thermal). Frost is a certain signal that insulation can be improved. 

Optimal economic insulation thickness may be determined Iw various methods. Two of these are the minimum-total-cost method and the incremental-cost method (or marginal-cost method). The minimum-total-cost method involves the actual calculations of lost energy and insulation costs for each insulation thickness. The thickness producing the lowest total cost is the optimal economic solution. The optimum thickness is determined to be the point where the last dollar invested in insulation results in exactly 1 in energy-cost savings ( ETI— Economic Thickness for Industrial Insulation, Conservation Pap. 46, Federal Energy Administration, August 1976). The incremental-cost method provides a simplified and direcl solution for the least-cost thickness. 

Multilayer Insulation Miiltilayer insulation consists of alternating layers of highly reflec ting material, such as aluminum foil or aluminized Mylar, and a low-conduc tivity spacer material or insulator, such as fiberglass mat or paper, glass fabric, or nylon net, all under high vacuum. When properly applied at the optimum density, this type of insulation can have an apparent thermal conduc tivity as low as 10 to 50 jlW/m-K between 20 and 300 K. 

Optimum comfort would be in the center of each zone. Moving away from the center, some people would be expected to have thermal sensations approaching - 0.5 and -i-0.5 at the cooler and warmer ET borders. The zones of Fig. 5.7b are for sedentary or slightly active ( M 1.2 met) people. If the activity level is higher than that, then the ET" line borders can be shifted about 1.4 K lower per met of increased activity. Similarly, if the clothing is different than the 0.9 and 0.5 do vales of Fig. 5.7a, the temperature boundaries can be decreased about 0.6 K for each 0.1 do increase in clothing insulation. Another, similar way to adjust the comfort zone for both different activity levels and do values is to shift the zone centered on the optimum temperature at... 

Typical dimensions for the /5-alumina electrolyte tube are 380 mm long, with an outer diameter of 28 mm, and a wall thickness of 1.5 mm. A typical battery for automotive power might contain 980 of such cells (20 modules each of 49 cells) and have an open-circuit voltage of lOOV. Capacity exceeds. 50 kWh. The cells operate at an optimum temperature of 300-350°C (to ensure that the sodium polysulfides remain molten and that the /5-alumina solid electrolyte has an adequate Na" " ion conductivity). This means that the cells must be thermally insulated to reduce wasteful loss of heat atjd to maintain the electrodes molten even when not in operation. Such a system is about one-fifth of the weight of an equivalent lead-acid traction battery and has a similar life ( 1000 cycles). 

There will be exceptions to this rule, such as thicker insulation where electric power is expensive, or thinner insulation for a chamber only used infrequently. Ceiling panels may be thicker to give added structural strength. In cases of doubt, the insulation costs must be resolved as the optimum owning cost. 

Diamond is an electrical insulator with the highest thermal conductivity at room temperature of any material and compares favorably with beryllia and aluminum nitride. P3]-P5] jg undoubtedly the optimum heat-sink material and should allow clock speeds greater than 100 GHz compared to the current speed of less than 40 GHz. 

Estimate the optimum thickness of insulation for the roof of a house, given the following information. The insulation will be installed flat on the attic floor. Overall heat transfer coefficient for the insulation as a function of thickness, U values (see Chapter 12) ... 

The effect of insulation thickness on total cost (x = optimum thickness). Insulation can be purchased in 0.5-in. increments. (The total cost function is shown as a smooth curve for convenience, although the sum of the two costs would not actually be smooth.)... 

In specifying the insulation thickness for a cylindrical vessel or pipe, it is necessary to consider both the costs of the insulation and the value of the energy saved by adding the insulation. In this example we determine the optimum thickness of insulation for a large pipe that contains a hot liquid. The insulation is added to reduce heat losses from the pipe. Next we develop an analytical expression for insulation thickness based on a mathematical model. 

In Example 3.3 we developed an objective function for determining the optimal thickness of insulation. In that example the effect of the time value of money was introduced as an arbitrary constant value of r, the repayment multiplier. In this example, we treat the same problem, but in more detail. We want to determine the optimum insulation thickness for a 20-cm pipe carrying a hot fluid at 260°C. Assume that curvature of the pipe can be ignored and a constant ambient temperature of 27°C exists. The following information applies ... 

A Case of a Composite Wall Optimum Insulation Thickness for a Steam Line... 

The optimum thickness of insulation can be established by economic analysis when all of the cost data are available, but in practice a rather limited range of thicknesses is employed. Table 8.22 of piping insulation practice in one instance is an example. 

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