On the expedience for practice to search for a more accurate analytical solution of the integral in the Arrhenius equation in non-isothermal kinetics

The existing methods of approach to solve the integral in the Arrhenius equation (Coats-Redfern, Gorbachev, Zsakó, Balarin etc.), when the standard linearization method of the integral kinetic equation is applied in order to determine the value of the activation energyE, yield factually identical results. Hence attempts to find more accurate approaches have no practical sense.     

Algorism for the solution of the exponential integral in non-isothermal kinetics at linear heating

The solution of the exponential integral at linear heating for the general case that the activation energy linearly depends on temperature according toE(T)=E ₀+RBT is

Linear and hyperbolic temperature programming in non-isothermal kinetics

The method suggested by several authors for determining the mechanism of solid-phase transformations by linearizing the function Ing() vs. 1/T is more correct for a hyperbolic temperature change than for a linear temperature change. In the latter case, the method yields reliable results only under the condition that the relationship Ing()/T ² vs. 1/T is linear. The well-known Horowitz-Metzger method is essentially suited for processing thermokinetic curves obtained under hyperbolic heating or cooling.

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Zusammenfassung Die von mehreren Autoren vorgeschlagene Methode den Mechanismus von Umwandlungen in der Festphase durch Linearisierung der Funktion zwischen Ing() und 1/T zu bestimmen ist für hyperbolische TemperaturÄnderungen korrekter als für die lineare TemperaturÄnderung. In letzterem Falle ergibt die Methode nur unter der Bedingung zuverlÄssige Ergebnisse, da\ der Zusammenhang zwischen Ing()/T ² und 1/T linear ist. Die bekannte Methode nach Horowitz-Metzger eignet sich im Wesentlichen zur Bearbeitung thermokinetischer Kurven bei hyperbolischem Aufheizen oder Kühlen.

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Résumé La méthode proposée par plusieurs auteurs pour déterminer le mécanisme des transformations en phase solide en linéarisant la fonction reliant In g() et 1/T est plus correcte lorsque les variations de température suivent un régime hyperbolique qu'elle ne l'est pour les régimes linéaires. Dans ce dernier cas, la méthode ne fournit des résultats fiables qu'à la condition que la relation entre Ing()/T ² et 1/T soit linéaire. La méthode bien connue d'Horowitz — Metzger s'applique essentiellement au traitement des courbes obtenues avec des lois d'échauffement ou de refroidissement hyperboliques.

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ln g() vs 1/T , ln g()/T ² vs 1/T. — .

     

Evaporative cooling of air in an adiabatic channel with partially wetted zones

The paper deals with the numerical study of heat and mass transfer in the process of direct evaporation air cooling in the laminar flow of forced convection in a channel between two parallel insulated plates with alternating wet and dry zones along the length. The system of Navier–Stokes equations and equations of energy and steam diffusion are being solved in two-dimensional approximation. At the channel inlet, all thermal gas-dynamic parameters are constant over the cross section, and the channel walls are adiabatic. The studies were carried out with varying number of dry zones (n = 0–16), their relative length (s/l = 0–1) and Reynolds number Re = 50–1000 in the flow of dry air (φ₀ = 0) with a constant temperature at the inlet (_{T 0} = 30 °C). The main attention is paid to optimization analysis of evaporation cell characteristics. It is shown that an increase in the number of alternating steps leads to an increase in the parameters of thermal and humid efficiency. With an increase in Re number and a decrease in the extent of wet areas, the efficiency parameter reduces.     

To the problem of applying the equation of Kolmogorov,Erofeev, Kazeev,Avrami and Mampel to the kinetics of non-isothermal transformations

The possibility of applying the KEKAM equation -In (1?α)=kt ⁿ to the kinetics of non-isothermal transformations is discussed. The derived form of this equation in the shape $$\frac{{d\alpha }}{{dt}} = nk^{1/n} (1 - \alpha )[ - \ln (1 - \alpha )]^{1 - 1/n} ,$$ according to the logic of the reasoning, cannot be applied to kinetic curves under the conditions of programmed heating.