Page 268 - Fluid mechanics, heat transfer, and mass transfer

CONVECTIVE HEAT TRANSFER 249

. Under what circumstances the term (m b /m w ) 0.14 is of . Give an equation for Nusselt number for turbulent
significance? flow through tubes as function of friction factors, N Re
& Viscosity of liquids decreases with increase in and N Pr .
temperature. When viscosity of the liquids is high, & Petukhov–Kirillov equation for turbulent flow
for example, oils, there will be considerable var- through tubes:
iation in temperature of the bulk of the liquid and 1=2 2=3
N Nu ¼ðf=2Þ N Re N Pr =½1:07 þ 12:7ðf=2Þ ðN Pr 1ފ:
that of the wall. In other words, viscosities differ
significantly with this temperature variation from ð9:22Þ
bulk of the liquid and tube wall and the ratio
differs significantly from unity. For low-viscosity & Friction factor, f, can be calculated from
liquids like water, this temperature gradient will be
2
very small and therefore viscosity ratio tends to f ¼ð1:58 ln N Re 3:28Þ : ð9:23Þ
unity.
& This equation is claimed to predict heat transfer
. Is the above equation applicable for laminar flow
conditions? coefficients with 5–6% error in the range between
4
6
10 < N Re < 5 10 and 0.5 < N Pr < 200 and in the
& No. This equation, called Dittus–Boelter equation,
range 0.5 < N Pr < 2000, with 10% error.
is for turbulent flow inside pipes. For laminar flow
conditions, similar equation with different con- . What are the dimensionless groups involved in
stant and exponent terms, Seider–Tate equation, Seider–Tate equation? State its applications.
is used. & Gz and m/m W .
& Laminar flow inside pipes/tubes.
& Dittus–Boelter equation is applicable for N Re
> 6000. It should not be used for flow of liquid . Write Seider–Tate equation.
metals, which have abnormally low values of N Pr . 1=3 0:14
N Nu ¼ 1:86ðN Gz Þ ðm =m Þ ; ð9:24Þ
b
w
& It is applicable for fully developed flow conditions.
Local values of h near entrance to tubes are much
where N Gz , Graetz number ¼ N Re N Pr D/L as given in
higher than those for fully developed flow.
Equation 9.2.
& It must be recognized that local values of h differ
& Seider–Tate equation is satisfactory for small dia-
from average values given by the equation as tem-
meters and small temperature differences.
peratures and hence fluid properties differ from point
. Give Hausen correlation for heat transfer in laminar
to point along the length of the tube.
flow.
& For gases effect of temperature on fluid properties are
much less than for liquids as increase in k and C p with hD=k ¼½3:65 þf0:0668N Re N Pr ðD=LÞg=
temperature offset the increase in m, giving a slight 2=3 0:14
f1 þ 0:04 þ N Re N Pr ðD=LÞ gŠðm=m Þ : ð9:25Þ
w
increase in h.
& This equation is one of the widely recommended
& For liquids effect of temperature is much greater as
equations for laminar flow inside tubes.
variation in m is much more rapid than k and C p .
& h is the mean coefficient for the entire length of the
& In practice unless the tube is very long with variation
tube. Examination of the equation shows that the
of local value of h is more than 2:1, using average
mean coefficient decreases with increasing length of
value of h in the calculation of overall heat transfer
the tube, L. This is a consequence of the build up of an
coefficient, U, is adequate.
adverse temperature gradient in laminar flow.
. Why higher coefficients are found when a liquid is being
& Thevalue of L to be used is the length of a single pass,
heated rather than cooled?
or in a U-tube bundle, the length of the straight tube
& Reason is because of viscosity increases while
from the tube sheet to the tangent point of the bend.
cooling. For low-viscosity fluids, the ratio of m/m w
In other words, the adverse temperature gradient is
is not very important. However, for viscous
assumed to be completely destroyed by the strong
fluids, for example, oils, m w and m bulk may differ by
secondary flow induced in the U-bend.
10-fold.
. Give an equation for liquid natural convection outside
. ‘‘Local heat transfer coefficients in flow through tubes
single horizontal tubes.
are higher near the entrance region than those in regions
of fully developed flow.’’ True/False? N Nu ¼ hD o =k
& True. Reason is that turbulence effects are more near
3 2 2 1=4 ;
the entrance than inside tubes. ¼ 0:53½ðD r gb DT=m ÞðC p m=kފ ð9:26Þ
o