Chapter 6, Problem 6.38P

Consider parallel flow over a flat plate for air at 300 K and engine oil at 380 K. The free stream velocity is $u_{\infty }=2\text{m/s}\text{.}$ The temperature difference between the surface and the free stream is the same in both cases, with $T_s>T_{\infty }.$

1. Determine the location where transition to turbulence occurs, $x_c,$for both fluids.
2. For laminar flow over a flat plate, the velocity boundary layer thickness is given by
$\frac{\delta }{x}=\frac{5}{\sqrt{{\mathrm{Re}}_x}}$
Calculate and plot the velocity boundary layer thickness $\delta$ over the range $0\le x\le x_c$ for each fluid.
3. Calculate and plot the thermal boundary layer thickness ${\delta }_t$ for the two fluids over the same range of x used in part (b). At an x-location where both fluids experience laminar flow conditions, explain which fluid has the largest temperature gradient at the plate surface, ${-\delta T/\delta y|}_{y=0}.$ Which fluid is associated with the largest local Nusselt number Nu? Which fluid is associated with the largest local heat transfer coefficient h?