Search for question

Problem 2.11. In the 2-D flow field shown in Fig. P 2.11, an incompressible and constant-property fluid

flows parallel to an inclined surface. The heat flux at surface varies according to

9.(x)-qe

At any location along the surface a fraction y of the heat flux is absorbed at the surface, and the

remainder causes volumetric energy deposition in the fluid according to

4.(x,y)-q(x)(1-7) be

a) Write the momentum and energy conservation equations, and their boundary conditions, for

the flow field. Note that the equations should not include redundant terms.

b) Do velocity and temperature boundary layers form on this surface? If they do, assume that the

fluid has the properties of water at 300 K and U₂ =2.0 m/s, and calculate the thicknesses of

the boundary layers at a location where Re, -1.25×10¹.

c) Assume that the velocity profile near the surface approximately follows:

(1/6)-(1/6) for y/6 51

for y/8>1

"

U₂

Derive an expression which can be used to compare the volumetric energy deposition rate with

volumetric viscous dissipation rate.

d) Assume that the fluid has the properties of water at 300 K, and U-2.0 m/s. For the location

where Re, -1.25x10' and assuming that the velocity profile near the surface approximately

follows the above expression, calculate the volumetric viscous dissipation rate at a distance of

y = 8/2 from the wall.

Fig: 1