Page 267 - Fluid mechanics, heat transfer, and mass transfer

CONVECTIVE HEAT TRANSFER BASICS
248
& For viscous fluids, & The relation between the heat transfer and the skin
friction coefficient is expressed in terms of Stanton
2=3 0:14 number and skin friction coefficient:
J H ¼ h=C p GðN Pr Þ ðm =m Þ : ð9:12Þ
b
w
➢ Stanton number is defined as
& Friction factor, f, is related to N Re by the following
h=C p G ¼ N Nu =ðN Re N Pr Þ: ð9:17Þ
equation, applicable in the range of 5000 < N Re
< 200,000: ➢ Skin friction coefficient C f is defined by
2
t w =½ð1=2Þðrv ފ, where t w is wall shear stress.
0:2
f ¼ 0:046ðN Re Þ : ð9:13Þ & Thus, heat transfer coefficient can be related to skin
friction coefficient by
& For transition region to turbulent flow, that is, 2100 <
N Re < 6000:
N St 1=2ðC f Þ or h C p GC f =2: ð9:18Þ
1=3 2=3
J H ¼ 1:86ðD=LÞ ðN Re Þ ; ð9:14Þ & This equation provides a useful estimate of h, based
on knowing the skin friction, or drag.
which is shown on a plot of N Re versus J H (See
& This relation is known as the Reynolds analogy
Figure 9.3)
between shear stress and heat transfer. The Reynolds
. What is the basis for the analogy between momentum
analogy is extremely useful in obtaining a first
and heat transfer?
approximation for heat transfer in situations in which
& Mechanism of diffusion of heat and diffusion of
the shear stress is known.
momentum are essentially the same.
& This can be written as
. Give the equations involved in Colburn analogy for
heat flux to wall momentum flux to wall
momentum and heat transfer. ¼
convected heat flux convected momentum flux:
2=3
J M ¼ J H or f=2 ¼½h=ðC p GފðN Pr Þ : ð9:15Þ
ð9:19Þ
& Where viscosity variation is considerable between
& A modified Reynolds analogy has been obtained to
wall and bulk fluid, the equation can be written as take into consideration the fact that Prandtl number
Pr is usually not equal to 1:
2=3 0:14
J H ¼½h=ðC p GފðN Pr Þ ðm =m Þ : ð9:16Þ
b
w
2=3
1=2ðC f Þ¼ N St N Pr ; 0:6 < N Pr < 60: ð9:20Þ
& The viscosity ratio factor can be neglected if fluid
properties are evaluated at the mean temperature & The following equation is often recommended for
between bulk fluid and fluid at wall. heat transfer in tubes:
. Write Reynolds analogy equation between transfer of
0:8 0:33 0:14
momentum and heat and name other analogies. N Nu ¼ 0:023ðN Re Þ ðN Pr Þ ðm =m Þ : ð9:21Þ
b
w

J H factors as function of N Re .
FIGURE 9.3