Newton's Law of Cooling and Heat Transfer Coefficient
Law
Suppose that at time $t$ the temperature of the surface of some object is $T(t)$, and the temperature of the system or the environment can be expressed as a constant $T_{\infty}$. The law stating that at time $t$ the heat flux $q$ between the object and the environment is proportional to the temperature difference $\Delta T (t) = T(t) - T_{\infty}$ is called Newton’s law of cooling. $$ q = h \Delta T (t) $$ Here, $h$ is called the heat transfer coefficient.
Explanation
For example, imagine dropping a red-hot iron ball into cold water. The iron ball is so hot that the water touching it vaporizes and boils in an instant, and the temperature of the iron ball drops sharply.
There is no need to think of Newton’s law of cooling as something difficult. Reading the formula as it is, it says that ’the hotter it is, the faster it cools’, or more precisely ’the larger the temperature difference between the object and the environment, the faster it cools’. Considering the sign of $\Delta T$, it does not actually have to be cooling; it could also be called heating.
Comparison of Thermal Conductivity and Heat Transfer Coefficient
The SI unit of thermal conductivity $k$ is as follows. $$ k \left[ {\frac{ \mathrm{W} }{ \mathrm{m} \cdot \mathrm{K} }} \right] $$ Meanwhile, the SI unit of the heat transfer coefficient $h$ is as follows. $$ h \left[ {\frac{ \mathrm{W} }{ \mathrm{m}^2 \cdot \mathrm{K} }} \right] $$ We can see that, unlike thermal conductivity, the heat transfer coefficient is expressed in units per area. The heat transfer coefficient is an indicator representing the heat transfer between the surface of an object and the environment; since the larger the surface area of the object, the more smoothly heat transfer can occur, expressing it in units per area is more intuitive.