Atmospheric air at a temperature of 300 K flows parallel to a smooth and flat surface with a velocity of U ∞ = 3 m/s. The surface temperature of the plate varies with distance from the leading edge x...

Atmospheric air at a temperature of 300 K flows parallel to a smooth and flat surface with a velocity of U_∞
= 3 m/s. The surface temperature of the plate varies with distance from the leading edge x according to,

where T_s
is in Kelvins. Derive an analytical expression that can be used for calculating the convective heat transfer coefficient up to the point at which the surface temperature reaches 350 K.