What is the difference between them?

 

from what I see:

 

Fourier’s law states that rate of heat flow is proportional to the gradient of temperature difference.

 

whereas:

 

Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings.

 

so fourier's:

heat flow (proportional) difference in temp between system and surroundings

newton's:

rate of heat loss (proportional) difference in temp between system and surroundings

 

but couldn't you call heat flow (fourier) - loss of heat from one part of the system (newtons) and gain in the other?

 

what is the precise difference between the two? or are they quite similar, in which case again what is the precise difference between them?

Are you sure it´s "the gradient of temperature difference" (what´s that supposed to be?) and not the temperature gradient?

In the latter case I´d say that statement one is the differential version of statement two, as where the integration from inside to outside means integration over something like the container walls.

 

EDIT: Great, I cannot find out how to put the missing backslash in for the lower boundary of my integral as I´m showed the equation as a bitmap and not as the raw tex-text when I try to edit.... and where did the "delete this post" option go ?

Are you sure it´s "the gradient of temperature difference" (what´s that supposed to be?) and not the temperature gradient?

yeah, ok, so "temperature gradient" or "temperature difference"

 

but I still cannot see the difference between the two...

 

what do you mean by: "statement one is the differential version of statement two" ?

with that I mean that you get statement one if you take the derivative of statement two or (otherwise round and as I tried to show) you get statement two if you integrate statement one. Or in other words: The two statements should basically be the same. The equation I wrote is however a bit shematic. I´m currently thinking of a better explanation.

The two statements should basically be the same..... I´m currently thinking of a better explanation.

yeah, I mean, I am assuming that there is a difference as they are both recognised seperate equations and laws... but what is that small difference that isn't quite clicking (assuming there is one)?

Newton's law tells you the cooling rate - how fast the temperature changes.

 

Fourier's law tells you heat transfer rate, which is how fast the energy is transferred.

 

The link between them is the heat capacity, which tells you how much energy a material can store for a given change in temperature.