# Arrhenius Number

on . Posted in Dimensionless Numbers

Arrhenius equation, abbreviated as Ar, a dimensionless number, is where the temperature dependance of the reaction rate constant which is the rate of chemical reaction.  Chemical reactions are typically expected to preceed faster at higher temeratures and slower at lower temperatures.  As the temperature rises, molecules move faster and collide, greatly increasing their likelyhood to bond.  This results in a higher kinetic energy, which has an affect on the activation energy of the reaction.  It used in heat transfer and fluid dynamics to characterize the relative importance of thermal diffusion to convective heat transfer.

The Arrhenius number helps to determine whether conduction or convection dominates in a heat transfer process.  When the Arrhenius number is much smaller than 1, thermal diffusion (conduction) is dominant.  On the other hand, when the Arrhenius number is much greater than 1, convective heat transfer is dominant.

The Arrhenius number provides insight into the balance between conduction and convection in heat transfer processes and is particularly relevant in situations where both mechanisms are at play, such as in fluid flow over a heated surface.

## Arrhenius equation

$$\large{ Ar = \frac{E_a}{R \; T} }$$
Symbol English Metric
$$\large{ Ar }$$ = Arrhenius number $$\large{dimensionless}$$
$$\large{ E_a }$$ = activation energy $$\large{ft-lbf}$$ $$\large{J}$$
$$\large{ R }$$ = universal gas constant $$\large{ \frac{lbf-ft}{lbmol-R} }$$ $$\large{ \frac{J}{kmol-K} }$$
$$\large{ T }$$ = temperature $$\large{F}$$ $$\large{K}$$ Tags: Mass Equations