# 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

`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
- 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

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

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

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