# Peclet Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Péclet number, abbreviated as Pe, a dimensionless number, defined as a ratio of heat transport by convection to heat transport by conduction.

## Peclet Number fromula

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

### Where:

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

### Solve For:

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