Heat conduction definition

CA 42, 5229(1948)(Theory of propagation of flame. States conditions in an expl chem reaction necesssry for propagation of the flame at a const rate. Calcs this rate for a definite relationship between diffusion and heat conductance. Evaluates the effect of chain reactions on the propagation of the flame) 4) B. Karlovitz, JChemPhys 19, 541-46(1951) Sc CA 45, 9341 (1951)(Theory of turbulent flames) 5) G. Klein, Phil-TransRoySocLondon 249, 389—415 (1957)... 

The direct-effect a and T) must be positive definite because of Fourier s law of heat conduction (where the thermal conductivity is always positive, according to... 

Coefficient of Thermal Conductivity or Specif, ic Heat Conductivity ( is the quantity of heat transmitted per second thru a plate of material 1cm thick and 1cm2 in area, when the temp difference between the two sides of the plate is one degree centigrare. Some values are given in Ref and under individual compds described in this Encyclopedia Ref Clift Fedoroff, Vol 2(1943), Table of Physical Constants of Compounds Used in Explosives Industry and Definition of Terms Used in Table of Physical Constants [See also S. Nagayama Y.Mizushima KKK 21, 8-11 (I960) CA 55, 9877 (1961) Explosivst 1964, 2l]... 

Although, in general, transports are not reversible, we can idealize them as being reversible from the point of view of the system. This is because, by definition, we are not interested in the details of the processes that occur in the surroundings. Thus, we can imagine heat transfer to occur from a heat reservoir, which is constructed of a material with infinite heat conductivity, so that it maintains a uniform temperature as heat is withdrawn from it. Moreover, the reservoir is in contact with the boundary of the system sufficiently long so that the boundary is at the temperature of the reservoir. In this case, the decrease of the entropy of the reservoir is exactly equal to the entropy transported to the system ... 

Criticism of the Stosszahlansatz and its corollaries arose as soon as it was recognized as paradoxical that the completely reversible gas model of the kinetic theory was apparently able to explain irreversible processes, i.e., phenomena whose development shows a definite direction in time. These nonstationary,51 irreversible processes were brought into the center of interest by the //-theorem of Boltzmann. In order to show that every non-Max-wellian distribution always approaches the Maxwell distribution in time, this theorem synthesizes all the special irreversible processes (like heat conduction and... 

Ignition processes often are characterized by a gradual increase of temperature that is followed by a rapid increase over a very short time period. This behavior is exhibited in the present problem if a nondimensional measure of the activation energy E is large, as is true in the applications. Let tc denote an ignition time, the time at which the rapid temperature increase occurs a more precise definition of arises in the course of the development. In the present problem, during most of the time that t < tc, the material experiences only inert heat conduction because the heat-release term is exponentially small in the large parameter that measures E. The inert problem, with w = 0, has a known solution that can be derived by Laplace transforms, for example, and that can be written as... 

The basis of the solution of complex heat conduction problems, which go beyond the simple case of steady-state, one-dimensional conduction first mentioned in section 1.1.2, is the differential equation for the temperature field in a quiescent medium. It is known as the equation of conduction of heat or the heat conduction equation. In the following section we will explain how it is derived taking into account the temperature dependence of the material properties and the influence of heat sources. The assumption of constant material properties leads to linear partial differential equations, which will be obtained for different geometries. After an extensive discussion of the boundary conditions, which have to be set and fulfilled in order to solve the heat conduction equation, we will investigate the possibilities for solving the equation with material properties that change with temperature. In the last section we will turn our attention to dimensional analysis or similarity theory, which leads to the definition of the dimensionless numbers relevant for heat conduction. 

Thermal radiation differs from heat conduction and convective heat transfer in its fundamental laws. Heat transfer by radiation does not require the presence of matter electromagnetic waves also transfer energy in empty space. Temperature gradients or differences are not decisive for the transferred flow of heat, rather the difference in the fourth power of the thermodynamic (absolute) temperatures of the bodies between which heat is to be transferred by radiation is definitive. In addition, the energy radiated by a body is distributed differently over the single regions of the spectrum. This wavelength dependence of the radiation must be taken as much into account as the distribution over the different directions in space. 

Snow is a porous medium formed of air, ice crystals and small amounts of chemical impurities. Because ice has a high vapor pressure (165 Pa at -15°C, 610 Pa at 0°C), the vertical temperature gradient that is almost always present within the snowpack generates sublimation and condensation of water vapor that change the size and shape of snow crystals. This results in changes in physical variables such as density, albedo, heat conductivity, permeability and hardness. These physical changes have formed the basis for the definition of snow metamorphism. ... 

Solution calorimetry involves the measurement of heat flow when a compotmd dissolves into a solvent. There are two types of solution calorimeters, that is, isoperibol and isothermal. In the isoperibol technique, the heat change caused by the dissolution of the solute gives rise to a change in the temperature of the solution. This results in a temperature-time plot from which the heat of the solution is calculated. In contrast, in isothermal solution calorimetry (where, by definition, the temperature is maintained constant), any heat change is compensated by an equal, but opposite, energy change, which is then the heat of solution. The latest microsolution calorimeter can be used with 3-5 mg of compound. Experimentally, the sample is introduced into the equilibrated solvent system, and the heat flow is measured using a heat conduction calorimeter. 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volume Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (heat-impermeable) or diathermic (heat-conducting). However, because the concept of heat has not yet been introduced, the definitions of adiabatic and diathermic need to be considered carefully. Both kinds of walls are impermeable to matter a permeable wall will be introduced later. 

Unfortunately, there are severalthings about the above derivation that can be criticized. Both and N contain the temperature T, yet the temperature is different at different positions. Since the simple law of heat conduction is correct only if T2 — is small compared with either of the two temperatures, it is sufficient to use the average temperature in computing N and . A more serious objection is that we use quantities such as N and derived from the equilibrium distribution function and apply them to a nonequilibrium situation. The fact of the matter is that if a nonequilibrium distribution is used, the mathematical complication introduced is enormous. Happily, the result of the more accurate treatment is not substantially different but only changes the numerical constant 5 in Eq. (30.17), assuming the absence of attractive forces. Finally, the distance X has been introduced in a somewhat arbitrary way. To understand Eq. (30.17) we must have a more definite idea about X. 

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