# 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}

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