Critical insulation thickness

In certain instances, the heat loss from an insulated pipe may exceed that from an uninsulated one. In these systems, the insulator has a relatively high thermal conductivity and its resistance to heat flow is insufficient to compensate for the additional heat loss resulting from the increased exposed area. The heat loss increases to a maximum, then it decreases with an increase in thickness. The thickness of the insulator which corresponds to the maximum heat loss is called the critical insulation thickness Xcr, ft.). It is verified by the following equation ... 

Equation (2-18) expresses the critical-radius-of-insulation concept. If the outer radius is less than the value given by this equation, then the heat transfer will be increased by adding more insulation. For outer radii greater than the critical value an increase in insulation thickness will cause a decrease in heat transfer. The central concept is that for sufficiently small values of h the convection heat loss may actually increase with the addition of insulation because of increased surface area. 

A 1.0-mm-diameter wire is maintained at a temperature of 400°C and exposed to a convection environment at 40°C with h = 120 W/m2 °C. Calculate the thermal conductivity which will just cause an insulation thickness of 0.2 mm to produce a "critical radius." How much of this insulation must be added to reduce the heat transfer by 75 percent from that which would be experienced by the bare wire ... 

The pipe in Prob. 2-51 is covered with a layer of asbestos [k = 0.18 W/m °C] while still surrounded by a convection environment with h = 12 W/m2 °C. Calculate the critical insulation radius. Will the heat transfer be increased or decreased by adding an insulation thickness of (a) 0.5 mm, (b) 10 mjn ... 

For small diametor pipes there is a critical thickness of insulation that produces the minimum thermal resistance. To be effective insulation thicknesses must be greater than this value. In this problem the critical thickness of insulatitm is O.OOSm as shown on the figure. This can be verified by differentiating the sum of the conductive and convective resistance with respect to the outside radius and setting the result equal to uao. Thus... 

EXAMPLE 43-5. Insulating an Electrical Wire and Critical Radius An electric wire having a diameter of 1.5 mm and covered with a plastic insulation (thickness = 2.5 mm) is exposed to air at 300 K and =... 

Fig. 2. Criticality of arrays of 113.6-litre containers with various Celotex insulator thicknesses.

The electronic insulation of these electrodeposited polymer layers must hold to a two-terminal voltage of 4 V if lithium (or lithium ion) anodes are to be used in the 3-D nanobattery. Because the polymers must also be thin, high dielectric strengths are critical. As seen in Table 2, diminishing the thickness of the dielectric to the nanoscale exacts a higher standard in terms of the quality of the dielectric. For example. 

All the results were confirmed by investigations with both back- and front-side illumination [37]. In this study, which also describes theoretical aspects, a final resolution of 17 pm for an epi-structure was achieved, which consisted of a thin layer (3 pm, specific resistance of lOQcm) and a thick silicon substrate (0.38 pm, with low specific resistance of 0.005-0.02 Q cm). Instead of using a pattern grid on the front-side to study the smallest possible resolution, in this work the sensor chip was coated half with a metal layer. This forms on the covered side a metal-insulator-semiconductor (MIS) structure. The light pointer was moved from the metallised area to the uncovered area and the resolution was determined at the borderline by measuring the photocurrent that depends on the diffusion length of the carriers. Since, for the assumption that the diffusion length is the main decisive and critical parameter for the amount of carriers which could reach the metal-covered part of the semiconductor substrate from a specific distance, the calculation of the minimal resolution was experimentally observed. 

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