Chapter 7, Problem 7.8P

A flat plate of width 1 m is maintained at a uniform surface temperature of $T_s=150°\text{C}$ by using independently controlled, heat-generating rectangular modules of thickness $a=10\text{mm}$ and length $b=50\text{mm}\text{.}$ Each module is insulated from its neighbors, as well as on its back side. Atmospheric air at 25°C flows over the plate at a velocity of 30 m/s. The thermophysical properties of the module are $k=5.2\text{W/m}\cdot \text{K,}{c}_p=320\text{J/kg}\cdot \text{K,}$ and $\rho =2300{\text{kg/m}}^{\text{3}}.$

1. Find the required power generation, $\stackrel{.}{q}\left({\text{W/m}}^{\text{3}}\right)$, in a module positioned at a distance 700 mm from the leading edge.
2. Find the maximum temperature $T_{\max }$ in the heat- generating module.