Accuracy of Newton's law of cooling

Question

I've made an experiment to verify Newtn's law of cooling, but while doing the analysis, my results don't fit accurately with the data collected (303 data using a sensor). According with my initial conditions such as $T_R=21.8°C$ (room temperature) and $T_o=80°C$ (initial temperature) I should obtain something like:

$\ln(T-21.8)=-kt+\ln(52.8)$

Instead, I obtain the following:

$\ln(T-21.8)=-6.061\times10^{-4}t+\ln(46.63)$

So, I was wondering if something's missing or maybe Newton's law is not enough to describe the cooling of an object.

Answer 1

There are two heat transfer resistances involved here: the heat transfer resistance outside, from the surrounding fluid to the surface, and the heat transfer resistance inside the object, from the surface to the internal region. Newton's law assumes that the overall resistance is dominated by the outside resistance (which is typically nearly constant). However, the inside resistance varies from a low value to a higher asymptotic value over time, and, if this resistance is significant, it results in a higher overall resistance that varies with time.