During winter, the average temperature in Calgary is $-5C,$ with a relative humidity of $75\%,$ while the average temperature in Amsterdam is $5C,$ with a relative humidity of $90\%.$ The skin temperature of a person is $34\mathrm{.}2C,$ and this is only dependent on the internal body processes, and thus not dependent on the outside temperature. Overall, the heat transfer from a human body can be described by the following equation:

$Q=hA(T_{\text{s}\text{k}\text{i}\text{n}}-T_{\text{a}\text{i}\text{r}})$

In this equation $Q$ is the total heat transferred per unit of time, $A$ is the area of a person, $h$ is the heat transfer coefficient and $T_i$ are the respective temperatures.

a$)$ What is the unit of the heat transfer coefficient in the SI system? Show how you derived this from the equation without looking it up$.$

b$)$ The heat transfer coefficient is dependent on external factors such as the air velocity $v,$ the humidity of the air $RH($ranging from $0$ to $1)$ and the temperature difference between the air and the body $T.$ If the following equation can be used to estimate the heat transfer coefficient, explain why you feel colder in Amsterdam than in Calgary during the winter, when there is a $0\mathrm{.}1\frac{m}{s}$ breeze.

$h=186\mathrm{.}7R{H}^{0\mathrm{.}6}\frac{v^{0\mathrm{.}257}}{T^{1\mathrm{.}28}}$