Stanton number: Definition, Formula, Significance, Example

What is Stanton number?

Stanton number is the ratio of heat transfer in the fluid to the heat capacity of the fluid. It is also calculated by taking ratio of the Nusselt number to the product of Reynold number and Prandtl number. This unitless number is useful for analyzing heat transfer by forced convection.

Stanton number is denoted by the symbol St and can be calculated using the below formula.

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 the fluid
ρ = density of the fluid

The formula of Stanton number is also written as,

S_t = `\frac{h}{\rho \times U\times C_{P}} \times \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 formula provides a relation between the Nusselt number, Reynolds number, and the Prandtl number.

The equation can be also written as,

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

Therefore Stanton number is also considered as the ratio of the Nusselt number to the Peclet number.

Significance of stanton number in heat transfer:

The significance of Stanton number are given below,

1. It is used to analyze forced convection flow.
2. In heat transfer, the Stanton number gives the relation between the heat transfer rate and the heat capacity of the fluid.
3. The Stanton number also finds the relation between the Nusselt number, Reynolds number, and Prandtl number.
4. It gives the relation between the Nusselt number and the Peclet number.
5. In boundary layer flow, the Stanton number is used to find the relation between shear force at a wall and heat transfer at a wall.

Solved Numericals:

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=80.

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 = 1.318 × 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

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