## What is the peclet number?

The peclet number is defined as the ratio of heat flow rate by convection to the heat flow rate by conduction for a uniform temperature gradient.

Peclet number is denoted by the symbol **Pe**.

## Peclet number equation:

Mathematically peclet number is given by the following equation,

Pe=`\frac{Lu}{\alpha }`

Where,

L = Characteristic length

u = Fluid velocity

α = Thermal diffusivity

The peclet number can also be written in the form of Reynold and Prandtl number.

Pe = Re. Pr

## Significance of peclet number in heat transfer:

The significances of peclet number are given below:-

1) The peclet number gives the relation between conduction and convection heat transfer.

2) The flow with a higher peclet number indicates that the heat transfer by convection is dominant over conduction heat transfer.

3) For lower peclet number the heat transfer by conduction is dominant over convection heat transfer.

4) The peclet number also helps to find the relation between Reynolds and Prandtl number.

## Numericals on peclet number:

*1] A fluid with thermal diffusivity of 0.148 × 10^(-6) m²/s flows at a velocity of 1 m/s with characteristic length of 3.5 m. If the Reynolds number of the flow is 2500 then, find the value for Prandtl number.*

**Solution:**

Given:

α = 0.148 × 10^(-6) m²/s

L = 3.5 m

u = 1 m/s

Re = 2500

The peclet number is given by,

Pe=`\frac{Lu}{\alpha }`=`\frac{3.5\times 1}{0.148\times 10^{-3}}`

Pe = 23.64 × 10³

Now by using the relation between Pe, Pr, and Re,

Pe = Re .Pr

(23.64 × 10³) = 2500 × Pr

**Pr = 9.456**

*2) The particular fluid flow has the following properties. find the relation between heat transfer by conduction and heat transfer by convection.u = 1.5 m/sα = 0.19 × 10^(-3) m²/sCharacteristics length, L = 7 m*

**Solution:**

The peclet number is given by,

Pe=`\frac{Lu}{\alpha }`=`\frac{7\times 1.5}{0.19\times 10^{-3}}`

Pe = 55263

Now the relation between Qconduction and Qconvection is given by,

Qconvection = 55263 × Qconduction