Answer Happy

3. above we assumed adiabatic boundary condtions for the temperature field: i.e., we prescribed the temperature gradient (zero) at the wall and then calculated what the wall temperature (T) would need to be. Another common application is that of an isothermal wall, where we instead prescribe the wall temperature (T) and try to determine the temperature gradient and hence heat flux at the wall. Note that the stagnation temperature equation is still given by U To OT +v- dr Əy k To pC, By²
(c) By relating derivatives of To to those of 8, and dividing every term in the mo- mentum equation by U we can argue that 6 and u/U.. both satisfy the same differential equation and the same boundary conditions. Consequently, we can write = u/U amd hence, by re-arrangement, To = Twe+(10.00-Two) U (6) This also allows us to determine the static temperature, since in a boundary layer with u² > ², we can write T-To-u²/(20₂). (d) Using all the information above, and the expression q = -k(OT/Jy)|y, express the wall heat flux in terms of the velocity gradient at the wall, and hence the wall shear stress (7) asssuming a Newtonian fluid.