Chapter 6, Problem 6.59P

An object of irregular shape has a characteristic length of $L=1\text{m}$ and is maintained at a uniform surface temperature of $T_s=325\text{K}\text{.}$ It is suspended in an airstream that is at atmospheric pressure $\left(p=1\text{atm}\right)$ and has a velocity of $V=100\text{m/s}$ and a temperature of $T_{\infty }=275\text{K}\text{.}$ The average heat flux from the surface to the air is $12,000{\text{W/m}}^{\text{2}}.$ Referring to the foregoing situation as case 1, consider the following cases and determine whether conditions are analogous to those of case 1. Each case involves an object of the same shape, which is suspended in an airstream in the same manner. Where analogous behavior does exist, determine the corresponding value of the average convection coefficient.

1. The values of $T_s,T_{\infty },$ and p remain the same, but $L=2\text{m}$ and $V=50\text{m/s}\text{.}$
2. The values of $T_s$ and $T_{\infty }$ remain the same, but $L=2\text{m,}V=50\text{m/s,}$ and $p=0.2\text{atm}\text{.}$
3. The surface is coated with a liquid film that evaporates into the air. The entire system is at 300 K, and the diffusion coefficient for the air-vapor mixture is $D_{\text{AB}}=1.12\times {10}^{-4}{\text{m}}^{\text{2}}\text{/s}\text{.}$ Also, $L=2\text{m},V=50\text{m/s,}$ and $p=1\text{atm}\text{.}$
4. The surface is coated with another liquid film for which $D_{\text{AB}}=1.12\times {10}^{-4}{\text{m}}^{\text{2}}\text{/s,}$ and the system is at 300 K. In this case $L=2\text{m,}V=250\text{m/s,}$ and $p=0.2\text{atm}\text{.}$