laminar

[logistic_guy]

For laminar flow over a flat plate, the local heat transfer coefficient \(\displaystyle h_x\) is known to vary as \(\displaystyle x^{-1/2}\), where \(\displaystyle x\) is the distance from the leading edge \(\displaystyle (x = 0)\) of the plate. What is the ratio of the average coefficient between the leading edge and some location \(\displaystyle x\) on the plate to the local coefficient at \(\displaystyle x\)?

 

[logistic_guy]

Understanding the problem is half the solution. We are given that \(\displaystyle h_x\) varies as \(\displaystyle x^{-1/2}\). In other words, \(\displaystyle h_x\) is directly proportional to \(\displaystyle x^{-1/2}\).

Or

\(\displaystyle h_x \propto x^{-1/2}\)

Or

\(\displaystyle h_x = ax^{-1/2}\)

And they want us to find the ratio \(\displaystyle \frac{\overline{h}}{h_x} = \frac{\overline{h}}{ax^{-1/2}}\)

All remained is to find \(\displaystyle \overline{h}\), and that will be our job in the next post.