CHE 333
Heat and Mass Transfer: Fundamentals & Applications
Fourth Edition
Yunus A. Cengel, Afshin J. Ghajar
McGraw-Hill, 2011
Chapter 7
EXTERNAL FORCED
CONVECTION
Objectives
Distinguish between internal and external flow
Develop an understanding of friction drag and
pressure drag
Evaluate the drag and heat transfer associated
with flow over a flat plate for both laminar and
turbulent flow
Calculate the drag force exerted on cylinders
during cross flow, and the average heat transfer
coefficient
Determine the pressure drop and the average heat
transfer coefficient associated with flow across a
tube bank
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DRAG AND HEAT TRANSFER IN EXTERNAL FLOW
Fluid flow over solid bodies creates:
drag force on the automobiles, power lines, trees,
and underwater pipelines
lift on airplane wings
upward draft of rain, snow, hail, and dust particles in
high winds;
cooling of metal or plastic sheets, steam and hot
water pipes
Free-stream velocity:
Velocity of fluid relative to an immersed solid body
sufficiently far from body. It is usually taken to be
equal to the upstream velocity V (approach velocity)
The fluid velocity ranges from zero at the surface (the
no-slip condition) to the free-stream value away from
the surface.
Friction and Pressure Drag
Drag: The force a flowing fluid exerts on a
body in the flow direction.
The components of the pressure and wall
shear forces in the normal direction to flow
tend to move the body in that direction, and
their sum is called lift.
Both the skin friction (wall shear) and
pressure contribute to the drag and the lift.
The drag force FD depends on the density of the fluid, the upstream velocity
V, and the size, shape, and orientation of the body.
The drag characteristics of a body is represented by the dimensionless drag
coefficient CD defined as
The part of drag that is due directly to wall
shear stress w is called the skin friction
drag (or just friction drag) since it is
caused by frictional effects, and the part
that is due directly to pressure P is called
the pressure drag.
At low Reynolds numbers, most drag is
due to friction drag.
The friction drag is proportional to the
surface area.
The pressure drag is proportional to the
frontal area and to the difference
between the pressures acting on the
front and back of the immersed body.
The pressure drag is usually dominant for
blunt bodies and negligible for
streamlined bodies.
When a fluid separates from a body, it
forms a separated region between the
body and the fluid stream.
Separated region: The low-pressure
region behind the body here recirculating
and backflows occur.
The larger the separated region, the
larger the pressure drag.
Wake: The region of flow
trailing the body where the
effects of the body on velocity
are felt.
Viscous and rotational effects
are the most significant in the
boundary layer, the separated
region, and the wake.
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Heat Transfer
Local and average
Nusselt numbers:
Average Nusselt
number:
Film temperature:
Average friction
coefficient:
Average heat transfer
coefficient:
The heat transfer rate:
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PARALLEL FLOW OVER FLAT PLATES
The transition from laminar to turbulent flow depends on the surface
geometry, surface roughness, upstream velocity, surface temperature, and
the type of fluid, and is best characterized by the Reynolds number.
The Reynolds number at a distance x from the leading edge of a flat plate is
expressed as
A generally accepted value for the
Critical Reynold number
The actual value of the engineering
critical Reynolds number for a flat
plate may vary somewhat from 105 to 3
106, depending on the surface
roughness, the turbulence level, and
the variation of pressure along the
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surface.
Friction Coefficient
Combined laminar + turbulent flow:
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Heat Transfer Coefficient (isothermal plate)
Local Nusselt number at x over a flat plate may be obtained by solving
differential energy equation for laminar flow (chapter 6) and by
empirical works for turbulent flow. For isothermal and smooth surfaces:
The local Cfx and hx are higher in turbulent
flow than they are in laminar flow.
hx reaches its highest values when flow
becomes fully turbulent, and then
decreases by a factor of x0.2 in the flow
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direction.
Nusselt numbers for average heat
transfer coefficients
Laminar +
turbulent
For liquid metals
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13
Flat Plate with Unheated Starting Length
Local Nusselt numbers
Average heat transfer
coefficients
Flow over a flat plate with an
unheated starting length.
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Uniform Heat Flux
For a flat plate subjected to uniform heat flux
These relations give values that are 36 percent higher for
laminar flow and 4 percent higher for turbulent flow relative
to the isothermal plate case.
When heat flux is prescribed, the rate of heat transfer to or
from the plate and the surface temperature at a distance x are
determined from
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FLOW OVER CYLINDERS AND SPHERES
Flow over cylinders and spheres is frequently encountered in practice:
The tubes in a shell-and-tube heat; soccer, tennis, and golf balls.
Flows across cylinders and spheres, in general, involve flow
separation, which is difficult to handle analytically.
Flow across cylinders and spheres has been studied experimentally,
and several empirical correlations have been developed for the heat
transfer coefficient.
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For flow over
a cylinder
FLOW
OVER
CYLINDERS AND SPHERES
The fluid properties are evaluated at the film temperature
For flow over a sphere
The fluid properties are evaluated at the free-stream temperature T,
except for s, which is evaluated at the surface temperature Ts.
Constants C and m are
given in the table.
The relations for cylinders above are for single cylinders or
cylinders oriented such that the flow over them is not affected by
the presence of others. They are applicable to smooth surfaces.
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18
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FLOW ACROSS TUBE BANKS
Cross-flow over tube banks is commonly encountered
in practice in heat transfer equipment, e.g., heat
exchangers.
In such equipment, one fluid moves through the
tubes while the other moves over the tubes in a
perpendicular direction.
Flow through the tubes can be analyzed by
considering flow through a single tube, and
multiplying the results by the number of tubes.
For flow over the tubes the tubes affect the flow
pattern and turbulence level downstream, and thus
heat transfer to or from them are altered.
Typical arrangement: in-line or staggered
The outer tube diameter D is the characteristic length.
The arrangement of the tubes are characterized by the
transverse pitch ST, longitudinal pitch SL , and the
diagonal pitch SD between tube centers.
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diagonal
pitch
Arrangement of the
tubes in in-line and
staggered tube
banks (A1, AT, and
AD are flow areas at
indicated locations,
and L is the length of
the tubes).
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All properties except Prs are to
be evaluated at the arithmetic
mean temperature.
Correlations in Table 7-2
The average Nusselt number relations in Table 72 are for tube banks
with more than 16 rows. Those relations can also be used for tube
banks with NL < 16 provided that they are modified as
NL < 16
where F is a correction factor whose values are given in Table 73.
For ReD > 1000, the correction factor is independent of Reynolds number.
Log mean
temperature
difference
Exit temperature
Heat transfer
rate
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Pressure drop
f is the friction factor and
c is the correction factor.
The correction factor c
given is used to account
for the effects of deviation
from square arrangement
(in-line) and from
equilateral arrangement
(staggered).
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Example 7.5: A long 10-cmdiameter steam pipe whose
external surface temperature is
110C passes through some
open area that is not protected
against the winds
(Fig. 723). Determine the rate
of heat loss from the pipe per
unit of its length when the air is
at 1 atm pressure and 10C and
the wind is blowing across the
pipe at a velocity of 8 m/s.
Summary
Drag and Heat Transfer in External Flow
Friction and pressure drag
Heat transfer
Parallel Flow Over Flat Plates
Friction coefficient
Heat transfer coefficient
Flat plate with unheated starting length
Uniform Heat Flux
Flow Across Cylinders and Spheres
Effect of surface roughness
Heat transfer coefficient
Flow across Tube Banks
Pressure drop
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