Chapter 7, Problem 7.7P

Consider flow over a flat plate for which it is desired to determine the average heat transfer coefficient over the short span $x_1$ to $x_2,{\bar{h}}_{1-2},$ where $\left(x_2-x_1\right)\ll L.$

Provide three different expressions that can be used to evaluate ${\bar{h}}_{1-2}$ in terms of (a) the local coefficient at $x=\left(x_1+x_2\right)/2,$ (b) the local coefficients at $x_1$ and $x_2,$ and (c) the average coefficients at $x_1$ and $x_2.$ Indicate which of the expressions is approximate. Considering whether the flow is laminar, turbulent, or mixed, indicate when it is appropriate or inappropriate to use each of the equations.