Page 143 - Analysis and Design of Energy Geostructures

Heat and mass transfers in the context of energy geostructures 115

3.14 Boundary layers in flow problems
An essential feature of convection phenomena is the development of so-called
boundary layers. Addressing two particular boundary layers is paramount for the anal-
ysis and design of energy geostructures, with particular reference to problems of
internal and external flows: the velocity boundary layer and the thermal boundary layer.
The presence of boundary layers results in two distinct regions in convection phe-
nomena. In one region, located relatively close to a bounding surface, significant gra-
dients of the characteristic variable of the flow occur. In another region, located
relatively far from a bounding surface, negligible gradients of the characteristic variable
of the flow occur.
The velocity boundary layer develops as a consequence of the viscosity of the
moving fluid, which generates shear stresses close to the surface wall (cf. Fig. 3.20A).
Due to the presence of such shear stresses, the fluid velocity is equal to zero at the sur-
face wall in the boundary layer. The velocity increases within the boundary layer as a
consequence of the decreasing influence of the shear stresses acting on the fluid parti-
cles and remains constant at a velocity (different from zero) outside the boundary layer
that is usually termed the free stream velocity, v N . The thickness of the velocity
boundary layer, δ h , is usually considered to correspond to a fluid velocity of
v δ 5 0:99v N . The significance of the velocity boundary layer thus depends on the

Figure 3.20 The development of velocity and thermal boundary layers. Redrawn after
Bergman, T., Incropera, F., Lavine, A., DeWitt, D., 2011. Fundamentals of Heat and Mass Transfer. Wiley,
Hoboken, NJ.