Page 416 - Introduction to Continuum Mechanics

400 Concept of a Boundary Layer

where 0 is temperature and «, the thermal diffusivity, is related to conductivity /c, density p
and specific heat per unit mass c by the formulas a = K/pc.
Suppose now we have the problem of a uniform stream flowing past a hot body whose
temperature in general varies along the boundary. Let the temperature at large distance from
the body be Ooo, then defining 0' = B-Q^, we have

2
with ©' = 0 at x +y -* °°. On the other hand, the distribution of vorticity around the body is
governed by

2 2
with£ = Oat x +y -»«>, where the variation of £, being due to vorticity generated on the solid
boundary and diffusing into the field, is much the same as the variation of temperature, being
due to heat diffusing from the hot body into the field.

Fig. 6.14

Now, it is intuitively clear that in the case of the temperature distribution, the influence of the
hot temperature of the body in the field depends on the speed of the stream. At very low speed,
conduction dominates over the convection of heat so that its influence will extend deep into
the fluid in all directions as shown by the curve C\ in Fig. 6.14, whereas at high speed, the heat
is convected away by the fluid so rapidly that the region affected by the hot body will be
confined to a thin layer in the immediate neighborhood of the body and a tail of heated fluid
behind it, as is shown by the curve C^ in Fig. 6.14.