## What is stanton number?

Stanton number is the ratio of heat transfer in the fluid to the heat capacity of the fluid.

Stanton number is denoted by the symbol **St** and mathematically it is expressed as,

`S_{t}=\frac{h}{\rho \times U\times C_{P}}`

Where,

h = Convective heat transfer coefficient

U = Velocity of the fluid flow

Cp = specific heat of fluid

ρ = density of the fluid

Stanton number is also written as,

`S_{t}=\frac{h}{\rho \times U\times C_{P}}`X` \frac{\mu KL}{\mu KL}`

`S_{t}=\frac{\frac{hL}{K}}{\frac{\rho \times U\times L}{\mu}\times \frac{\mu C_{P}}{K}}`

`S_{t}=\frac{Nu}{Re\times Pr}`

Therefore this form of standard number provides a relation between Nusselt number, Reynolds number, and Prandtl number.

Stanton number can be also written as,

`S_{t}=\frac{Nu}{Pe}` [∵ Pe = Re x Pr]

Therefore Stanton number is also considered as the ratio of nusselt number to the peclet number.

## Significance of stanton number in heat transfer:

The significance of Stanton number are given below,

1) Stanton number is used to analyze forced convection flow.

2) In heat transfer the Stanton number gives the relation between heat transfer rate and heat capacity of the fluid.

3) The Stanton number also finds the relation between nusselt number, Reynolds number, and Prandtl number.

4) It gives the relation between nusselt number and peclet number.

5) In boundary layer flow the Stanton number is used to find the relation between shear force at wall and heat transfer at a wall.

## Numerical on stanton number:

*The fluid is flowing at a velocity of 0.1 m/s and has a density of 650 Kg/m³ and specific heat of 700 J/Kg.K. The convective heat transfer coefficient is 60 W/m².K. Find the Prandtl number, if Re=10000 and Nu=8*0.

**Solution:-**

Given:-

h = 60 W/m².K

ρ = 650 Kg/m³

U = 0.1 m/s

Cp = 700 J/Kg.K

Re = 10000

Nu = 80

The stanton number is given by,

`S_{t}=\frac{h}{\rho \times U\times C_{P}}`=`\frac{60}{650\times 0.1\times 700}`

`S_{t}=1.38\times 10^{-3}`

Now the relation between Stanton number (St), Reynolds number (Re), Nusselt number (Nu), Prandtl number (Pr) is given by,

`S_{t}=\frac{Nu}{Re\times Pr}`

`1.318\times 10^{-3}=\frac{80}{10000\times Pr}`

Pr = 6.06

**Prandtl number** = Pr = 6.06 **— Answer**