Thin-body heat conduction

To determine whether the thin body approximation may be used, one should compare the surface heat transfer coefficient, and the thermal conductance of the solid, ksom/8. Their ratio is the Biot number,... 

D. Physical Interpretation of the Asymptotics of the Solution Heat Conduction in Thin Bodies... 

X. HEAT CONDUCTION IN THIN BODIES A. Statement of the Problem... 

A body is called thin if one (or more) of its characteristic dimensions is much smaller than the others. A thin rod and a thin plate are examples of such bodies. We consider a boundary value problem describing a heat conduction process in a thin rod, where the ratio e of the thickness of the rod to its length is a small parameter. To simplify the presentation, we consider the problem for a planar rod, that is, in the thin rectangle (OsjfSl) X (0[Pg.166]

The above algorithm for the construction of the asymptotics of the solutions of heat conduction problems in this bodies can also be applied to some more complicated problems, for example, to problems of thermoelasticity in thin bodies. The corresponding system of equations for the displacement vector u(x, y, z, t) and temperature (x, y, z, t) in a domain G in the linear approximation has the form (see [48])... 

We may note that the thermal boundary layer in this case is asymptotically thin relative to the boundary layer for a solid body. This is a consequence of the fact that the tangential velocity near the surface is larger, and hence convection is relatively more efficient. From a simplistic point of view, the larger velocity means that convection parallel to the surface is more efficient, and hence the time available for conduction (or diffusion) normal to the surface is reduced. Thus, the dimension of the fluid region that is heated (or within which solute resides) is also reduced. Indeed, if we define Pe by using a characteristic length scale lc and a characteristic velocity scale uc, heat can be conducted a distance... 

When radiation falls on a solid body, a definite fraction p may be reflected and the remaining fraction 1 — p enters the solid to be either transmitted or absorbed. Most solids (other than glasses, certain plastics, quartz, and some minerals) absorb radiation of all wavelengths so readily that, except in thin sheets, the transmissivity T is zero, and all nonreflected radiation is completely absorbed in a thin surface layer of the solid. The absorption of radiation by an opaque solid is therefore a surface phenomenon, not a volume phenomenon, and the interior of the solid is not of interest in the absorption of radiation. The heat generated by the absorption can flow into or through the mass of an opaque solid only by conduction. 

Fully Laminar Nusselt Number Nu,. As the next step in the correlation method, the thin-layer solution is corrected to account for thick-layej" effects [175,223]. The body is surrounded by a uniform layer of stationary fluid of thickness A, and outside that thickness the fluid temperature is taken to be T . The heat transfer that would occur across this layer is determined by a conduction analysis and converted to a Nusselt number, and this Nusselt number is Nu,. 

Another type of thermotropic liquid crystals is called cholesteric liquid crystals. The color of cholesteric liquid crystals changes with temperature and therefore they are suitable for use as sensitive thermometers. In metallurgy, for example, they are used to detect metal stress, heat sources, and conduction paths. Medically, the temperature of the body at specific sites can be determined with the aid of liquid crystals. This technique has become an important diagnostic tool in treating infection and mmor growth (for example, breast tumors). Because locahzed infections and tumors increase metabolic rate and hence temperature in the affected tissues, a thin film of liquid crystal can help a physician see whether an infection or tumor is present by responding to a temperature difference with a change of color. 

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