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Difficulty in theoretical understanding of Newton's law of cooling

Physics Asked on June 22, 2021

Newton’s law of cooling states that the rate of heat loss of a body is directly proportional to the
difference between the body’s temperature and that of the surroundings when there is a breeze.
I can see how this would follow from Fourier’s law of heat conduction (we can consider $frac{kA}{Delta x}$ to be the constant of proportionality) but what I do not understand is why is it specified that there is a breeze? Is it just a way to set the temperature range, or to prevent local heat exchange? I am a bit confused.

2 Answers

but what I do not understand is why is it specified that there is a breeze?

Without seeing the statement in context, it looks like they are only talking about forced convection. But Newton's Law of Cooling also applies when there is no breeze, which is natural convection due to the natural movement of air when it is heated or cooled.

That aside, the main difference between the constant of proportionality in Newton's Law of Cooling and Fourier's Law of Conduction, is that $h$, the convection heat transfer coefficient of the former is a variable whereas $k$, the material thermal conductivity of the latter is a property of the material, a constant.

$h$ depends on the movement of the fluid (e.g, natural convection vs forced convection) and the physical characteristics of surface (e.g., rough vs smooth).

Hope this helps.

Correct answer by Bob D on June 22, 2021

Newton's law of cooling assumes that the entire resistance to heat transfer resides in the fluid thermal boundary layer at the surface of the object, and that heat conduction within the object is very rapid (high thermal conductivity) so that the entire object (right up to the surface) is at a uniform temperature. The faster the fluid surrounding the object is moving relative to the surface of the object, the thinner the thermal boundary layer, and the more rapid the heat conduction through the layer. The cooler fluid from behind washes over the surface, and washes away the heated fluid near the surface.

Answered by Chet Miller on June 22, 2021

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