Important parameter for Transient Heat Conduction

In this blog we are going to talk about important parameter that are used to do calculation in transient heat conduction

1. Characteristic Length

It is defined as the ratio of volume of the body to the surface area of the body. It is denoted by `L_{c}`

The formula to find characteristic length is 
`L_{c} = \frac{V}{A}`

where V =  Volume of the body

A = surface area of the body

 `L_{c}`  = Characteristic Length

Characteristic Length of for Various Bodies

• Plane Wall
  
  
  
  

  Characteristic Length,
  `L_{c}=\frac{V}{A} = \frac{AL}{2A} = \frac{L}{2}`
  
  
• Sphere of  radius R:
  `L_{c}=\frac{V}{A} = \frac{\frac{4}{3}\pi R^{3}}{4\pi R^{3}} = \frac{R}{3}`
• Cylinder of Radius R and Length L
  `L_{c}=\frac{V}{A} = \frac{\pi R^{2}L}{2\pi R^{2}+2\pi RL} = \frac{R}{2(1+\frac{R}{L})}`
  
  if L>>R ,then  (1 + R/L) nearly equal to 1
  
  Hence the cylinder characteristic length in this case will be R/2

2. Biot Number

It is defined as the ratio of the internal resistance of the body to the convective resistance of the body. It is a dimensionless Number

`B_{i}=\frac{Internal Resistance}{Convective Resistance}`

`B_{i}=\frac{\frac{L_{c}}{kA}}{\frac{1}{hA}}`

`B_{i}=\frac{hL_{c}}{k}`

Here 

`B_{i}` is Biot Number

h = heat transfer coefficient of the ambient

k = thermal conductivity of the  body

`L_{c}` characteristic length of the body V/A

V = volume of the body

A = surface area

Meaning and Significance of Biot Number:
Suppose Bi number is small . It means that system has small conduction (internal resistance). Small temperature gradient exists it means temperature is uniform throught the system and vice versa

3. Fourier Number

`F_{o}=\frac{\alpha \tau }{l^{2}}`

`\alpha` = thermal diffusivity

l = characteristic Length

It tells about the degree of penetration of heating or cooling effect through solid