A coolant fluid at 30°C flows over a heated flat plate

A coolant fluid at 30°C flows over a heated flat plate maintained at a constant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated as T = 30 + 70 expt(-y) where y(in m) is the distance normal to the plate and fis in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m²K) at that location will be

Under steady state conditions
Heat transfer by conduction = Heat transfer by convection

∴ -kA	dT	= h AΔT
	dy

or -k	dT	= h ΔT
	dy

or -k	dT	(30 + 70e^-y) = h (100 - 30°)
	dy

or -k	δ	(- 70e^-y) = h × 70
	δy

or – k
∴ -k (– 70 e⁰) = 70h
or 70 k = 70 h
But k = 1
∴ h = 1W/m²k
Alternately

hAΔ = kA	dT
	dy

or h(100 – 30) = k × (100 – 30)
or h = k = 1 W/m²K