ABSTRACT
Prandtl number represents the ratio of the shear component
of diffusivity for momentum (m/r) to the diffusivity for heat (k/rCp). In simple terms, Pr represents the ratio of kinematic viscosity () to thermal diffusivity (a) of a fluid. Mathematically, the Prandtl number may be expressed as
follows for Newtonian fluids:
Pr ¼ mCp k
¼ m=r k=rCp
¼ v a
(1)
For non-Newtonian fluids flowing through circular tubes,
five different forms of the Prandtl number corresponding to
five definitions of the Reynolds number have been used
by researchers:[3] 1) generalized Reynolds number (GRe);
2) Reynolds number based on the apparent viscosity at
the wall (Rea); 3) Reynolds number derived from the non-
dimensional momentum equation (Regen); 4) Reynolds
number based on the solvent viscosity (Res); and
5) Reynolds number based on the effective viscosity
(Reeff). For experimental or analytical studies on drag and
heat transfer for non-Newtonian fluids under laminar flow
conditions, GRe and Rea with their corresponding Prandtl
numbers are recommended, while the Rea, Pra combination
is more practical for turbulent pipe flow, as it allows
comparison of experimental data with analytical predic-
tions.[3] The generalized Prandtl number (GPr) can be
expressed as follows to conform with Eq. 1:
GPr ¼ Cpm ð3nþ 1Þ=n½ n 2n3ðD=VÞ1n
kf
" # (2)
where n, m (Pa secn), D (m), and V (m sec-1) are the fluid
behavior index, consistency coefficient, tube diameter,
and average velocity, respectively. The average velocity
V ¼ 4Q/(pD2), while Q (m3 sec-1) represents the volumetric through flow rate. For conventional canning of
foods in rotary autoclaves, the apparent viscosity has
been calculated at a shear rate commensurate with the
rotation speed of the autoclave,[4,5] with the diameter of
rotation representing the characteristic dimension.
