Current Attempt in Progress

Generally laminar flow will continue on a smooth flat plate until a critical Reynolds number is reached. However, the flow can be tripped by adding roughness or a wire to the leading edge of the plate, causing the flow to be turbulent. Consider expressions for the local heat transfer coefficients for laminar and turbulent conditions:

$h_{\text{l}\text{a}\text{m}}(x)=(1\mathrm{.}74\frac{W}{m^{1\mathrm{.}5}}*(K))x^{-0\mathrm{.}5}$

$h_{\text{t}\text{u}\text{r}\text{b}}(x)=(3\mathrm{.}98\frac{W}{m^{1\mathrm{.}8}}*(K))x^{-0\mathrm{.}2}$

Find the average heat transfer coefficients, in $\frac{W}{m^2}*K,$ for laminar and turbulent conditions for the following cases.

Case A: Plate is $L_A=1\mathrm{.}4m$ in length.

Case B: Plate is $L_B=0\mathrm{.}7m$ in length.

Laminar conditions:

Case A:

$\frac{?}{\text{b}\text{a}\text{r}}(h{)}_{\text{l}\text{a}\text{m}\text{,}{L}_A}=\frac{W}{m^2}*K$

Case B:

$\frac{?}{\text{b}\text{a}\text{r}}(h{)}_{\text{l}\text{a}\text{m}\text{,}{L}_B}=\frac{W}{m^2}*K$