Chapter 6, Problem 6.8P

For laminar free convection from a heated vertical surface, the local convection coefficient may be expressed as $h_x=C{x}^{-1/4},$ where $h_x$ is the coefficient at a distance x from the leading edge of the surface and the quantity C, which depends on the fluid properties, is independent of x. Obtain an expression for the ratio ${\bar{h}}_x/h_x,$ where ${\bar{h}}_x$ is the average coefficient between the leading edge $\left(x=0\right)$ and the x-location. Sketch the variation of $h_x$ and ${\bar{h}}_x$ with x.