Laminar flow normally persists on a smooth flat plate until a critical Reynolds number value is reached. However, the flow can be tripped to a turbulent state by adding roughness to the leading edge of the plate. For a particular situation, experimental results show that the local heat transfer coefficients for laminar and turbulent conditions are

\[\begin{aligned}& h_{\text {lam }}(x)=1.74 \mathrm{~W} / \mathrm{m}^{1.5} \cdot \mathrm{K} x^{-0.5} \\& h_{\text {turb }}(x)=3.98 \mathrm{~W} / \mathrm{m}^{1.8} \cdot \mathrm{K} x^{-0.2}\end{aligned}\]

Calculate the average heat transfer coefficients for laminar and turbulent conditions for plates of length \(L=\) \(0.1 \mathrm{~m}\) and \(1 \mathrm{~m}\).