Main Question or Discussion Point
Newton's law of cooling is: dQ/dt = KA(θ - θo). Then where does the equation dQ/dt = KA(dT/dx) come from?
This generally applies to the surface interface between two materials.Newton's law of cooling is: dQ/dt = KA(θ - θo).
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.Then where does the equation dQ/dt = KA(dT/dx) come from?
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.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.