Using the integral relations from Problem 19.17, and assuming the velocity and temperature...

Using the integral relations from Problem 19.17, and assuming the velocity and temperature profiles of the form

where δ is the thickness of both the hydrodynamic and thermal boundary layers, show that the solution in terms of δ and vx from each integral equation reduce to

Next, assuming that both δ and vx vary with x according to

show that the resulting expression for δ becomes

and that the local Nusselt number is

Problem 19.17

Show that, for the case of natural convection adjacent to a plane vertical wall, the appropriate integral equations for the hydrodynamic and thermal boundary layers are