The grain growth is a thermal activation process, satisfying the well-known Arrhenius equation
And activation energy is calculated through the Arrhenius equation
Diffusion coefficient, D, the amount of a particular substance that diffuses across a unit area in unit time, often obeys the activated transition state theory and its temperature dependence can be expressed by the Arrhenius equation
, (22), (23) equation (1):
For the knock simulation, the parameters a, c and the activation energy [E.sub.A] must be determined as a reference point at a predefined knock rate limit and the Arrhenius equation
has to be transferred to the combustion process of the engine and its temperature and pressure history.
According to Arrhenius equation
, the ln A and [E.sub.a] for a given particle diameter can be obtained from the slope and intercept of the line, respectively (see Table 4).
(3), according to Arrhenius equation
, the expression of reaction rate constant k is as follows:
Here k [[s.sup.-1]] is the reaction rate constant expressed by the Arrhenius equation
(2) where A [[s.sup.-1]], E [J x [mol.sup.-1]] and R [J x [mol.sup.-1] x [K.sup.-1]] are pre-exponential factor, activation energy and gas constant.
From this Fig, it can be seen that increasing the reaction temperature strongly increases the leaching rate, as expected from the exponential dependence of the rate constant in the Arrhenius equation
The NO reduction under rich condition was assumed to follow the Arrhenius equation
, with the first-order dependence of the inlet NO concentration based on previous study [32-33].
Also, linear curve fitting was performed to calculate pre-exponential factor and activation energy in the Arrhenius equation
Calculating the viscosity of the Rapeseed oil at different temperature (170, 180 and 190[degrees]C) for the Arrhenius equation
The rule of thumb, based upon the Arrhenius equation
, is that a 10[degrees]C temperature rise translates to a twofold increase in reaction rate.