Newton's Law of Cooling

1. Apr 9, 2015

andyrk

Newton's law of cooling is: dQ/dt = KA(θ - θo). Then where does the equation dQ/dt = KA(dT/dx) come from?

2. Apr 9, 2015

Orodruin

Staff Emeritus
This generally applies to the surface interface between two materials.

This is Fourier's law (or something reminiscent of it, you really should define what you mean by Q). It applies to the heat transfer within a material.

3. Apr 9, 2015

andyrk

How can dQ/dt have two different dimensions?

4. Apr 9, 2015

nasu

K means different things in the two formulas.

5. Apr 9, 2015

andyrk

I would say that Q means different things too. Q in newton's law of cooling is temperature whereas in Fourier's law it is heat.

6. Apr 10, 2015

Orodruin

Staff Emeritus
Well, Fourier's law is actually just a statement on the current. What appears in the left hand side is the heat transfer per unit time across a surface. This can be related to an actual change in temperature (or heat, they are related by heat capacity, volume, and density) through the continuity equation.