Conduction, heat quasi-stationary

A quasi-stationary reaction condition is assumed when accumulation of heat in the system is small relative to the heat conducted away. 

The temperature distribution in a reacting mixture is stabilized when the rate of loss of heat by conduction or convection from any volume element is equal to that produced by the reaction itself in that volume element. In the case that the rate of heat loss cannot compensate for the rate of heat production, a stationary or quasi-stationary temperature distribution is impossible and the temperature of the reaction mixture increases exponentially, causing the reaction rate to do likewise, and a thermal explosion results. This is illustrated in Fig. XIV. 1, which follows... 

First, we shall use a quasi-stationary approach already mentioned earlier, based on the assumption that characteristic times of heat and mass transfer in the gaseous phase are much shorter than in the liquid phase, since the coefficients of diffusion and thermal conductivity are much greater in the gas than in the liquid. Therefore the distribution of parameters in the gas may be considered as stationary, while they are non-stationary in the liquid. On the other hand, small volume of the drop allows us to assume that the temperature and concentration distributions are constant within the drop, while in the gas they depend on coordinates. Another assumption is that the drop s center does not move relative to the gas. Actually, this assumption is too strong, because in real processes, for example, when a liquid is sprayed in a combustion chamber, drops move relative to the gas due to inertia and the gravity force. However, if the size of drops is small (less than 1 pm) and the processes of heat and mass exchange are fast enough, then this assumption is permissible. As usual, we assume the existence of local thermodynamic equilibrium at the drop s surface, as well as equal pressures in both phases. The last condition was formulated at the end of Section 6.7. 

QUASI-STATIONARY MEASUREMENTS OF THE HEAT CONDUCTIVITY OF SYNTHETIC MATERIALS IN THE TEMPERATURE RANGE -180 TO +90 C. //ENGLISH TRANSLATION OF KOLLOID-ZEITSCHRIFT AND ZEITSCHRIFT FUER POLYMERE, 174/2/ 134-42,1961.//... 

Obviously Eqs.(l-3) cannot be integrated readily for r t) because Td is not known. An additional equation is required. Neglecting the work of formation of the droplets surface and keeping the droplet temperature Td unchanged for a short time interval of computation (quasi-stationary treatment) means that the latent heat of condensation ft L has to be conducted away from the droplet by the heat flux... 

In order to identify EPHs of the cell or electrode reactions from the experimental information, there had been two principal approaches of treatments. One was based on the heat balance under the steady state or quasi-stationary conditions [6,11, 31]. This treatment considered all heat effects including the characteristic Peltier heat and the heat dissipation due to polarization or irreversibility of electrode processes such as the so-call heats of transfer of ions and electron, the Joule heat, the heat conductivity and the convection. Another was to apply the irreversible thermodynamics and the Onsager s reciprocal relations [8, 32, 33], on which the heat flux due to temperature gradient, the component fluxes due to concentration gradient and the electric current density due to potential gradient and some active components transfer are simply assumed to be directly proportional to these driving forces. Of course, there also were other methods, for instance, the numerical simulation with a finite element program for the complex heat and mass flow at the heated electrode was also used [34]. 

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