A fluid is flowing steadily under laminar conditions over a thin rectangular plate at temperature $T_s$ as shown in the figure below. The velocity and temperature of the free stream are $u_{\infty}$ and $T_{\infty}$, respectively. When the fluid flow is only in the $x$ direction, $h_\chi$ is the local heat transfer coefficient. Similarly, when the fluid flow is only in the $y$-direction, $h_y$ is the corresponding local heat transfer coefficient. Use the correlation $\mathrm{Nu}=0.332 \; (\mathrm{Re})^{1 / 2}(\mathrm{Pr})^{1 / 3}$ for the local heat transfer coefficient, where, $\mathrm{Nu}, \mathrm{Re}$, and $\mathrm{Pr}$, respectively are the appropriate Nusselt, Reynolds and Prandtl numbers. The average heat transfer coefficients are defined as $\bar{h}_l=\frac{1}{l} \int_0^l h_x d x$ and $\bar{h}_w=\frac{1}{w} \int_0^w h_y d y$. If $w=1 \mathrm{~m}$ and $l=4 \mathrm{~m}$, the value of the ratio of $\bar{h}_w$ to $\bar{h}_l$ is______________(in integer).
