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Chemically Reacting Flows
Published in Greg F. Naterer, Advanced Heat Transfer, 2018
The rate equation for a chemical reaction is used to relate the rate of the reaction to the concentration of each reactant. It is typically expressed as follows: r=kCAnCBm where k is the reaction rate coefficient or rate constant, and the exponents n and m are called reaction orders. For gas phase reactions, the reaction rate is often expressed instead in terms of partial pressures of each constituent. The rate constant includes the effects of all parameters (except concentration) on the reaction rate. Usually, temperature is the most significant factor.
Battery Energy Storage
Published in Iqbal Husain, Electric and Hybrid Vehicles, 2021
where kf and kr are the forward and reverse rate constants, respectively. The rate constants are the proportionality factors linking the concentration of the species to the reaction rates. The concentration of species undergoing oxidation at a distance x from the surface and at time t will be denoted as CO(x, t); hence, the surface concentration is CO(0, t). Similarly, the surface concentration for the species undergoing reduction is CR(0, t).
Basic Principles
Published in Kathleen Sellers, Fundamentals of Hazardous Waste Site Remediation, 2018
The reaction rate constant must be determined experimentally. Data may be collected in a batch reactor or continuous-flow reactor; often, reaction rates are determined in laboratory tests using beakers or flasks, which are essentially batch reactors. Beginning with different values of Co, the experimenters measure C at various times t after the reaction begins. The data may be evaluated using various methods;94,95 the integral method is described below as it applies to a first-order reaction.
A numerical investigation of bio-convective electrically conducting water-based nanofluid flow on the porous plate with variable wall temperature
Published in Numerical Heat Transfer, Part A: Applications, 2023
Shuhe Sun, Shuguang Li, Sidra Shaheen, Muhammad Bilal Arain, Khalid Ali Khan
The least amount of energy needed for a particle to undergo various chemical alterations or reactions is called activation energy, or Ea. Mechanochemistry, food processing, chemical engineering, geothermal, and oil storage all use activation energy. The impression of activation energy upon the outlines of concentration is portrayed in Figure 8. The amount of nanofluid within the boundary layer augments as the activation energy rises. As a result, energy flow encounters more resistance. Figure 9 shows how the chemical reaction constant affects concentration boundary layer thickness. The proportionality constant, known as the rate constant, links the rate of a chemical reaction to the concentrations of reacting components in an equation. Looking at the equilibrium constant allows us to determine whether a response tends to have a higher concentration of products or reactants at equilibrium. The concentration boundary layer’s thickness is observed to decrease as chemical reaction constant rises.
Kinetics of reduction of Banded Haematite Jasper ore with coal
Published in Mineral Processing and Extractive Metallurgy, 2021
Sanjeev Kumar Das, Ranjit Prasad, Rajendra Prasad Singh, Srinivasan Ranganathan
At 1273 K, none of the expressions above could satisfactorily describe the kinetics of reduction. At 1323 K, the data were best describe by expression (2), indicating that the reaction was controlled by ‘chemical reaction’ kinetics. At 1373 and 1473 K, the reduction kinetics was controlled by diffusion, expression (5), above. The reduction kinetics are illustrated in Figures 9–11, for the three temperatures. The Arrhenius equation k = A.e–Q/RT (where ‘k’ is the rate constant; t, time Q, the activation energy; ‘R’ universal gas constant and ‘T’ the temperature) correlates the relation between the reaction rate constant and the activation energy. Assuming that the Arrhenius equation would describe the kinetics of reduction in the temperature range 1373–1473 K, the value of the activation energy was estimated, through a solution of the following set of simultaneous equations:
Statistical optimization and kinetic study on biodiesel production from a potential non-edible bio-oil of wild radish
Published in Chemical Engineering Communications, 2019
Chokkalingam Senthilkumar, Chandrasekaran Krishnaraj, Pandian Sivakumar, Anirbid Sircar
Figure 3 represents the experimental results obtained for biodiesel conversion at different temperatures (40 to 60 °C) with respect to time. The other process parameters like methanol to oil molar ratio (9:1) and catalyst concentration (1.0 wt%) were kept constant as obtained from optimization results. The ME conversion percentage reaches maximum at 50 °C which is optimum to ME yield during optimization and this ensures that the reaction attains maximum conversion. Kinetic rate constant and root mean square value (R2) are determined and tabulated in Table. 7. The reaction rate constant shows that the rate of the reaction increases with respect to temperature proving that the reaction is sensitive to temperature.