Thermal conduction of metals

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

As described above, quantum restrictions limit tire contribution of tire free electrons in metals to the heat capacity to a vety small effect. These same electrons dominate the thermal conduction of metals acting as efficient energy transfer media in metallic materials. The contribution of free electrons to thermal transport is very closely related to their role in the transport of electric current tlrrough a metal, and this major effect is described through the Wiedemann-Franz ratio which, in the Lorenz modification, states that... 

R.L. Powell, W.A. Blaupied Thermal Conductivity of Metal and Alloys at Low Temperatures, Nat. Bureau of Standards Circular 556, US Govt. Print. Office, Washington, DC (1954)... 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

Figure 5.2 shows the temperature gradients in the case of heat transfer from fluid 1 to fluid 2 through a flat metal wall. As the thermal conductivities of metals are greater than those of fluids, the temperature gradient across the metal wall is less steep than those in the fluid laminar sublayers, through which heat must be transferred also by conduction. Under steady-state conditions, the heat flux q (kcal In m 2 or W m ) through the two laminar sublayers and the metal wall should be equal. Thus,... 

The electron-sea model affords a simple qualitative explanation for the electrical and thermal conductivity of metals. Because the electrons are mobile, they are free to move away from a negative electrode and toward a positive electrode when a metal is subjected to an electrical potential. The mobile electrons can also conduct heat by carrying kinetic energy from one part of the crystal to another. Metals are malleable and ductile because the delocalized bonding extends in all... 

How does the electron-sea model account for the electrical and thermal conductivity of metals ... 

The thermal conductivity of metals is much greater than that of all polyurethanes. The impact of this is that in the case of metals the heat is readily removed by the coolant into the stock and machine. The lower thermal conductivity of the polyurethane means that the heat remains near the surface of the part. Without proper care, the part can melt quite easily. Most polyurethanes start softening at about 135°C and melt to a gummy state by 180°C. 

Suda, S., Komazaki, Y., Kobajashi, N. (1983) Effective thermal conductivity of metal hydride beds, J. Less-Common Met., 89, 317-324. 

Metals, on the other hand, have an additional mechanism of conductive heat transfer—electron motion—which can be envisioned to transfer heat in an analogous fashion to that of the kinetic behavior a gas. Good electrical conductors tend to be good thermal conductors. However, the thermal conductivity of metals decreases with increasing temperature because of increased electron-electron scattering. 

TABLE 9.9 Thermal Conductivity of Metals, Oxides, and Conductive Adhesives at 25°C18... 

Thermal conductivity Everyone knows that touching a metallic surface at room temperature produces a colder sensation than touching a piece of wood or plastic at the same temperature. The very high thermal conductivity of metals allows them to draw heat out of our bodies very efficiently if they are below body temperature. In the same way, a metallic surface that is above body temperature will feel much warmer than one made of some other material. The high thermal conductivity of metals is attributed to vibra-... 

Electrical and Thermal Conductivity of Metallic K over its Entire Liquid Range. J. Inorg. Nucl. Chem. 28, 795 (1966). 

Asakuma, Y., Miyauchi, S., Yamamoto, T., Aoki, H., Miura, T. (2004). Homogenization method for effective thermal conductivity of metal hydride bed. Int.. Hydrogen Energy 29, 209-216. 

This can only be decided by experiment, or, failing that, by a suitable hypothesis whose consequences are in agreement with experiment. Properties which appear to approach infinity at the absolute zero are, for example, the electrical and thermal conductivity of metals and the thermal conductivity of crystals (Eucken ), while the thermal conductivity of amorphous bodies, the specific heat, and the coefficient of expansion appear to approach zero. 

Peierls has recently put forward a theory of the thermal conductivity of metals and its relationship to the electrical conductivity which leads to the following important results ... 

The bond electrons in covalent bond are very locked in the hybrid orbitals which gives very poor electrical conductance. This is in contrast to the bonds in metals. These bonds can be described by an electron sea model that tells us that the valence electrons freely can move around in the metal structure. The band theory tells us that the valence electrons move around in empty anti-bond orbitals that all lie very close in energy to the bond orbitals. The free movement of electrons in metals explain the very high electrical and thermal conductivity of metals. Metal atoms are arranged in different lattice structures. We saw how knowledge about the lattice structure and atomic radius can lead to calculation of the density of a metal. 

Thermal conductivities of metals cover a wide range of values, from about 10 Btu/ft-h- F (17 W/m- C) for stainless steel to 240 Btu/ft-h- F (415 W/m- C) for silver. For glass and most nonporous minerals the thermal conductivities are much... 

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