# Peclet Number

on . Posted in Dimensionless Numbers

Peclet number, abbreviated as Pe, a dimensionless number, describes the ratio of the rate of convection of a substance by fluid flow to the rate of diffusion of that substance.  It is used to determine whether convection or diffusion dominates in a given system.  It used in fluid dynamics to characterize the relative importance of convection and diffusion processes.

If the Peclet number is much less than 1 (Pe << 1), it indicates that diffusion is dominant, and the flow is characterized by slow mixing and high thermal or mass transfer resistance.  In such cases, the concentration or temperature gradients will diminish rapidly due to diffusion.  If the Peclet number is much greater than 1 (Pe >> 1), it suggests that convection is dominant, and the flow is characterized by fast mixing and low thermal or mass transfer resistance.  In these cases, the concentration or temperature gradients will be maintained and advected by the fluid flow.

The Peclet number is commonly used in various fields of study, including fluid dynamics, heat transfer, and mass transfer, to analyze and predict the behavior of fluids and the transport of heat or mass within them.

## Peclet Number formula

$$\large{ Pe = \frac { v \; \rho \; C \; l_c }{ k } }$$     (Peclet Number)

$$\large{ v = \frac{ Pe \; k }{ \rho \; C \; l_c } }$$

$$\large{ \rho = \frac{ Pe \; k }{ v \; C \; l_c } }$$

$$\large{ C = \frac{ Pe \; k }{ v \; \rho \; l_c } }$$

$$\large{ l_c = \frac{ Pe \; k }{ v \; \rho \; C } }$$

$$\large{ k = \frac{ v \; \rho \; C \; l_c }{ Pe } }$$

### Solve for Pe

 velocity, v density, ρ heat capacity, C characteristic length, lc thermal conductivity, k

### Solve for v

 Peclet number, Pe thermal conductivity, k density, ρ heat capacity, C characteristic length, lc

### Solve for ρ

 Peclet number, Pe thermal conductivity, k velocity, v heat capacity, C characteristic length, lc

### Solve for C

 Peclet number, Pe thermal conductivity, k velocity, v density, ρ characteristic length, lc

### Solve for lc

 Peclet number, Pe thermal conductivity, k velocity, v density, ρ heat capacity, C

### Solve for k

 velocity, v density, ρ heat capacity, C characteristic length, lc Peclet number, Pe

Symbol English Metric
$$\large{ Pe }$$ = Peclet number $$\large{dimensionless}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ C }$$ = heat capacity $$\large{\frac{Btu}{F}}$$  $$\large{\frac{kJ}{K}}$$
$$\large{ l_c }$$ = characteristic length $$\large{ft}$$ $$\large{m}$$
$$\large{ k }$$ = thermal conductivity $$\large{\frac{Btu-ft}{hr-ft^2-F}}$$ $$\large{\frac{W}{m-K}}$$ 