Thermal energy generation parameter

For small valnes of the thermal energy generation parameter /S, eqnation (27-56) is expanded in a Taylor series about = 0 ... 

Figure 27-1 Effect of the thermal energy generation paramete on dimensionless reactant concentration profiles as one travels inward toward the center of a porous catalyst with rectangular symmetry. The chemical kinetics are first-order and irreversible, and the reaction is exothermic. All parameters are defined in Table 27-4. The specific entries for P = 0.6 and = 1.0 are provided in Table 27-6.

Consider one-dimensional (i.e., radial) diffusion and multiple chemical reactions in a porous catalytic pellet with spherical symmetry. For each chemical reaction, the kinetic rate law is given by a simple nth-order expression that depends only on the molar density of reactant A. Furthermore, the thermal energy generation parameter for each chemical reaction, Pj = 0. 

Answer Two. The thermal energy balance is not required when the enthalpy change for each chemical reaction is negligible, which causes the thermal energy generation parameters to tend toward zero. Hence, one calculates the molar density profile for reactant A within the catalyst via the mass transfer equation, which includes one-dimensional diffnsion and multiple chemical reactions. Stoichiometry is not required because the kinetic rate law for each reaction depends only on Ca. Since the microscopic mass balance is a second-order ordinary differential eqnation, it can be rewritten as two coupled first-order ODEs with split boundary conditions for Ca and its radial gradient. 

Estimate the maximum temperature at the center of a catalytic pellet at large intrapellet Damkohler numbers in the diffusion-limited regime when the thermal energy generation parameter P = 2 (i.e., exothermic chemical reaction), the temperature on the external surface of the pellet is surface = 300 K, and the average pore size is greater than 1 tim. 

The thermal energy generated or absorbed by an electrochemical cell is determined first by the thermodynamic parameters of the cell reaction, and second by the overvoltages and efficiencies of the electrode processes and by the internal resistance of the cell system. While the former are generally relatively simple functions of the state of charge and temperature, the latter are dependent on many variables, including the cell history. 

After selective absorption of radiation, excited molecules may relax either by emission of radiation or by non-radiative processes (cf Chapter 3, Fig. 3.1). In photoacoustic measurements, the conversion of absorbed radiation into thermal energy is utilized. This type of conversion results in changes in the sample s thermodynamic parameters such as temperature or pressure. Changes in pressure generate acoustic waves, which eventually will be transferred to the surroundings of the sample (Fig. 5.12) where they can be measured by a sensitive microphone see Fig. 5.13 (photoacoustic spectroscopy (PAS)). 

An abuse model requires (i) materials (mass) balance for the exothermic side reactions, (ii) estimation of the reaction parameters (e.g., heat of reaction) from experimental measurements such as differential scanning calorimetry (DSC) and accelerated rate calorimetry (ARC), (iii) devising the kinetic expressions of the reactions, and (iv) incorporation of the thermal behavior due to these reactions in the energy balance equation (e.g., in terms of volumetric source terms). Specifically, the thermal energy conservation equation is duly modified to include the additional heat generation effects to reflect the specific abuse behavior in terms of heat generation due to side reaction kinetics and/or joule heating. The thermal boundary condition may also include radiative heat transfer to the ambient air. 

Control of sonochemical reactions is subject to the same limitation that any thermal process has the Boltzmann energy distribution means that the energy per individual molecule wiU vary widely. One does have easy control, however, over the energetics of cavitation through the parameters of acoustic intensity, temperature, ambient gas, and solvent choice. The thermal conductivity of the ambient gas (eg, a variable He/Ar atmosphere) and the overaU solvent vapor pressure provide easy methods for the experimental control of the peak temperatures generated during the cavitational coUapse. 

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