Introduction:

This problem deals with the determination of the local heat transfer coefficient on a flat plate subjected to a uniform flow of air. The local skin friction coefficient is given, and we are required to determine the local heat transfer coefficient at that point.

Given:

- Velocity of air flow over the plate = 50 m/s
- Local skin friction coefficient at the point = 0.004

Solution:

The local heat transfer coefficient can be calculated using the relation:

h = (k / L) * Nu

where h is the local heat transfer coefficient, k is the thermal conductivity of air, L is the characteristic length of the flow, and Nu is the Nusselt number.

The Nusselt number can be determined using the relation:

Nu = (0.332 * Re^0.5 * Pr^(1/3)) / (1 + (0.047 / Pr)^(2/3))^(1/4)

where Re is the Reynolds number and Pr is the Prandtl number.

Re = (rho * V * L) / mu

where rho is the density of air, V is the velocity of air, L is the characteristic length of the flow, and mu is the dynamic viscosity of air.

Pr = (Cp * mu) / k

where Cp is the specific heat capacity of air at constant pressure.

Substituting the given values, we get:

- rho = 1.225 kg/m^3 (density of air at standard conditions)
- mu = 1.7894 * 10^-5 Pa*s (dynamic viscosity of air at standard conditions)
- Cp = 1005 J/kg*K (specific heat capacity of air at constant pressure)
- k = 0.0263 W/m*K (thermal conductivity of air at standard conditions)
- V = 50 m/s (velocity of air flow over the plate)
- L = ? (characteristic length of the flow)

From the given data, we do not have the value of the characteristic length of the flow. Therefore, we cannot calculate the Reynolds number, Prandtl number, and Nusselt number. Hence, we cannot determine the local heat transfer coefficient at the given point.

Conclusion:

In conclusion, we cannot determine the local heat transfer coefficient at the given point as we do not have the value of the characteristic length of the flow.