For flow of gas over a flat surface that has been artificially roughened by sand-blasting, the local heat transfer by convection can be correlated by the dimensionless reactionNux = 0.05 Rex0.9(a) Derive a relationship for the average heat transfer coefficient in flow over a plate of length L.(b) Assuming the analogy between heat and momentum transfer to be valid, derive a relationship for the local friction coefficient.(c) Assuming the gas to be air at a temperature at 400 K flowing at a velocity of 50 m/s, estimate the heat flux 1 m from the leading edge for a plate surface temperature of 300 K.GIVENGas flow over a roughened flat surfaceLocal Nusselt number Nux = 0.05 Rex0.9ASSUMPTIONSSteady stateshe analogy between heat and momentum transfer isvalid

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Gas T- U.