## A theoretical study of the transference of heat and momentum across turbulent incompressible boundary layers

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A survey and evaluation of some models of turbulence
for isothermal turbulent flows is made. Models such as mixing length,
one-equation, two-equations and three-equations are
solved with the aid of a high speed computer for annular
turbulent flows. The results are compared with each other and
with experiment and the significance is discussed. The three equation
model (three transport equations plus the mean
velocity equation) emerges as the most accurate and capable of
the widest application: one set of constants only is sufficient
to solve a number of turbulent flows. Also, this model does not
require the prescription of any arbitrary length scale.
A study of the effect of varying the constants in the
three-equation model shows that the velocity and shear stress
profiles are insensitive to the variation of the constants. A variation of up to 50%, in the value of the constants produces,
at most, less than 2% variation in the velocity and shear
stress profiles. Only the turbulence energy distribution shows
some sensitivity. The position of maximum velocity for smooth
annuli with different radius ratios, as well as friction
factors for a number of wall conditions are calculated with the
three-equation model. The comparison between predictions and
experimental data shows a fairly good agreement.
Starting from this three-equation model, an extended
model, capable of predicting turbulent, two-dimensional, incompressible thermal boundary layers is developed. Three
more equations are incorporated in the isothermal model,
namely, (1) mean temperature equation (T), (2) convective heat
flux equation (uyT') and (3) equation for the intensity of
temperature fluctuation (1/2T'2). Appropriate approximations are
introduced and the new model of parabolic differential
equations is solved simultaneously with the equations for the
isothermal flow. The new five-equations model (five transport
equations plus mean velocity and mean temperature equations)
is applied to a number of real flows, with and without the
presence of walls. Both rough and smooth walls are considered.
Generally, good agreement is obtained when predicted results
are compared with the available experimental data.

##### Authors

Dieguez, Jose Antonio Diaz Dieguez##### Collections

- Theses [2005]