Conduction, of heat

Siace the pores ia an aerogel are comparable to, or smaller than, the mean free path of molecules at ambient conditions (about 70 nm), gaseous conduction of heat within them is iaefficient. Coupled with the fact that sohd conduction is suppressed due to the low density, a siUca aerogel has a typical thermal conductivity of 0.015 W/(m-K) without evacuation. This value is at least an order of magnitude lower than that of ordinary glass and considerably lower than that of CFC (chloro uorocarbon)-blown polyurethane foams (54). 

Overcuring is encountered to some degree in all compounds of any thickness because of the slow conductance of heat through mbber. Earthmover tires may have tire shoulder gauges in excess of 0.3 m (- 12 in.). The outside/inside are overcured to effect a satisfactory state-of-cure in the tread mbber. 

Example The equation 9T/9t = K(d T/dx ) represents the unsteady onedimensional conduction of heat. 

When q is zero, Eq. (5-18) reduces to the famihar Laplace equation. The analytical solution of Eq. (10-18) as well as of Laplaces equation is possible for only a few boundary conditions and geometric shapes. Carslaw and Jaeger Conduction of Heat in Solids, Clarendon Press, Oxford, 1959) have presented a large number of analytical solutions of differential equations apphcable to heat-conduction problems. Generally, graphical or numerical finite-difference methods are most frequently used. Other numerical and relaxation methods may be found in the general references in the Introduction. The methods may also be extended to three-dimensional problems. 

Conduction with Change of Phase A special type of transient problem (the Stefan problem) involves conduction of heat in a material when freezing or melting occurs. The liquid-solid interface moves with time, and in addition to conduction, latent heat is either generated or absorbed at the interface. Various problems of this type are discussed by Bankoff [in Drew et al. (eds.). Advances in Chemical Engineering, vol. 5, Academic, New York, 1964]. 

The conduction of heat by liquid metals is directly related to tire electronic structure. Heat is caiTied tlrrough a metal by energetic electrons having... 

Carslaw and Jaeger. 1947. Conduction of Heat in Solids. Oxford University Press, New York. 

In the finite-difference appntach, the partial differential equation for the conduction of heat in solids is replaced by a set of algebraic equations of temperature differences between discrete points in the slab. Actually, the wall is divided into a number of individual layers, and for each, the energy conserva-tk>n equation is applied. This leads to a set of linear equations, which are explicitly or implicitly solved. This approach allows the calculation of the time evolution of temperatures in the wall, surface temperatures, and heat fluxes. The temporal and spatial resolution can be selected individually, although the computation time increa.ses linearly for high resolutions. The method easily can be expanded to the two- and three-dimensional cases by dividing the wall into individual elements rather than layers. 

Pick s law States that the molecular diffusion of water vapor in a gas without appreciable displacement of the gas is analogous to the conduction of heat, and is governed by a similar type of law. 

Warme-leiter, m. conductor of heat, -leit-fahigkeit, /. thermal conductivity, heat conductance. -leitung, /. conduction of heat, -leitvermdgen, n., -leitzahl, /. thermal conductivity. 

Thermal conductivity of heat transfer fluid (liquid), BTU/(hr)(ft2)( F/ft)... 

The heat transfer area. A, can be greatly increased by using finned tubes, but care must be taken to ensure good conduction of heat away from the fin into the tube and subsequently into the water. Some common fin types are shown in Figure 25.3 while Figure 25.4 shows some of the attachment methods employed to ensure satisfactory fin to tube heat transfer. 

Conduction of heat through plain surfaces under steady-state conditions is given by the product of the area, temperature difference, and overall conductance of the surface (see Section 1.8) ... 

Discuss the conduction of heat by copper (a metal) and by glass (a network solid) in terms of the valence orbital occupancy and electron mobility. 

Conduction of Heat.-—Let the quantity of the heat SQ pass by conduction from a body at temperature Ti to a body at temperature T2. Suppose that an auxiliary medium at temperature T0 is available. 

Conditions of equilibrium, 92 Conduction of heat, 48, 84, 454 Configuration, 22, 107 Connodal curve, 243 Conservation of energy, 35 Contact potential differences, 470 Continuity of states, 174 Corresponding states, 228, 237 Creighton. See Southern. 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

Figure 9.5. Conduction of heat through a plane wall...

The low conductivity of heat insulating materials, such as cork, glass wool, and so on, is largely accounted for by their high proportion of air space. The flow of heat through such materials is governed mainly by the resistance of the air spaces, which should be sufficiently small for convection currents to be suppressed. 

In the problems which have been considered so far, it has been assumed that the conditions at any point in the system remain constant with respect to time. The case of heat transfer by conduction in a medium in which the temperature is changing with time is now considered. This problem is of importance in the calculation of the temperature distribution in a body which is being heated or cooled. If, in an element of dimensions dr by dy by dr (Figure 9.9), the temperature at the point (x, y, z) is 9 and at the point (x + dx, y + dy, r. + dr) is (9 4- d6>), then assuming that the thermal conductivity k is constant and that no heat is generated in the medium, the rate of conduction of heat through the element is ... 

For a thick-walled cylinder, the rate of conduction of heat through lagging is given by equation 9.21 ... 

Forster, H.K. J. Appl. Phys. 25 (1954) 1067. On the conduction of heat into a growing vapor bubble. 

The heating of the liquid can be approximated by the transient conduction of heat to a slab of finite thickness 8, with the conventional differential equation,... 

The burning of a column of delay composition takes place by the passage of a reaction front along the column. The temperature profile of this reaction front can be measured by the use of suitable thermocouples and recording instruments. By analysing the shape of the front it can be shown that the reaction is a solid/solid reaction initiated by thermal conduction of heat through the unreacted material. It follows that to obtain reproducible reaction rates there must be (1) constant amount of solid to solid contact and (2) constant thermal conductivity. 

---