Fourier’s Law of Conduction

  • Thread starter Bassalisk
  • Start date
  • #1
948
2
Hello,

Can anybody explain to me how does this:

dQ=-X*dS*grad(T)*dt

t being time and T being TD temperature.

transforms into this:

Q=-X*S*(T2-T1)*delta(t)/d

delta(t) being time interval

d being thickness length of material
X being heat conductivity

Thanks
 

Answers and Replies

  • #2
479
32
Maybe I don't quite get the form you have it in...S is what exactly?
 
  • #3
948
2
Maybe I don't quite get the form you have it in...S is what exactly?

S=Surface or Area
 
  • #4
5,441
9
Is S area ?
 
  • #6
5,441
9
The one dimensional form of the law is

[tex]\frac{{dQ}}{{dt}} = - kS\frac{{dT}}{{dx}}[/tex]

Where dQ/dt is the rate of heat flow which is directly proportional to the cross sectional area and the temperature gradient.
T is temperature
You only need use grad (T) for 3 D where grad(T) is the direction of max gradient.
t is time
S is area cross section
k is the constant of proportionality (thermal conductivity) -I don't like X because x is the axis variable.
 
  • #7
5,441
9
You can integrate this if you assume the temperature fall to be a linear function of x through the material to obtain your second formula.

That is dT = ax and integrate between limits x =0 and x = thickness to eliminate constant of integration.
 
  • #9
948
2
Thanks all, I got it now.
 

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