Q$3.$ In an experimental setup, engine oil flows over a horizontal plate and the oil temperature is best obtained according to the following function

$T=320-20[1-$exp$(-250y)]$

where $T$ is the temperature in Kelvin and $y$ is the vertical distance in $m.(20$ points$)$

$($a$)$ Determine the value of the local convection heat transfer coefficient at this position.

$($b$)$ Determine the approximate thickness of the thermal boundary layer at this position.