Problem $3.(30$ pts $)$ A gas flows over a strand of hair with a diameter of $150$ micrometers $(150{10}^{-6}m)$ and the flow has a free stream velocity of $0\mathrm{.}20\frac{m}{s}.$

$($a$)$ Determine the friction factor.

$($b$)$ Determine the convection heat transfer coefficient for the flow over the hair.

Use the following gas properties for the analysis:

Use the following gas properties for the analysis:

$c_p=1010\frac{J}{k}g*K,k=0\mathrm{.}0260\frac{W}{m}*K,=1\mathrm{.}90{10}^{-5}k\frac{g}{m}*s,=1\mathrm{.}20k\frac{g}{m^3},Pr=0\mathrm{.}74$