Conduction Heat Transfer by Vedat S. Arpacı

By Vedat S. Arpacı

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56 LUMPED, INTEGRAL, DIFFERENTIAL FORMULATIONS [2-81 in Fig. 2-21. Again, for idealized intimate contact we may assume that the temperatures of the two continua are the same on the boundary, as expressed previously by Eq. (2-107). The friction brake is an important practical case of the foregoing boundary condition. However, wear and high temperatures make this boundary condition impractical for continuous operation. The obvious remedy, lubrication, is beyond the scope of the text and is not considered here.

Since a plate of L z = rn or 1c2 = 0 is physically impossible, the foregoing insulation may never be accomplished in the absolute sense. The larger the thickness or the smaller the thermal conductivity, however, the better the insulation will be. If the heat loss through plate 2 is to be completely eliminatcd, the use of another heater becomes necessary (Fig. 2-16). Then, by properly adjusting the Ambient FIG. 2-16 * The case of finite resistance of the ambient is introduced in (4). i The temperature drop (or temperature gradient) across a plate is immaterial for the conductive character of the plate.

Equation (2-101) is Newton's cooling law. I t is important, however, to note that this relation is not phenomenological like Fourier's law of conduction and Stefan-Boltzmann's law of radiation. Since it is based on an assumption only, it cannot be considered a natural (particular) law; it will therefore be referred to as the definition of the heat transfer coefficient. Despite its weak foundation, Eq. (2-101), being the only relation available for expressing the unspecified heat transfer to the ambient, plays a significant role in conduction problems.

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