Heat transfer

Convection
When fluid flows over a solid body or inside a channel while temperatures of the fluid
and the solid surface are different, heat transfer between the fluid and the solid surface takes place
as a consequence of the motion of fluid relative to the surface; this mechanism of heat transfer is
called convection.
In forced convection the fluid is artificially induced, by a pump, blower or a fan that
forces the fluid flow over the surface. Natural (or free) convection, by contrast, occurs when the
fluid motion is set up by buoyancy effects resulting from density difference caused by
temperature difference in the fluid. For example, a hot plate vertically suspended in stagnant cool
air causes a motion in the air layer adjacent to the plate surface because the temperature gradient
in the air gives rise to a density gradient, which in turn sets up the air motion. As the temperature
field in the fluid is influenced by the fluid motion, the determination of temperature distribution
and of heat transfer in convection for most practical situations is a complicated matter. In
engineering applications, to simplify the heat transfer calculations between a hot surface at T w
and cold fluid flowing over it at a bulk temperature T f as illustrated in Fig.3, a heat transfer
coefficient h is defined as:
q  h(Tw  T f ) ……………………………………….3

Where q represent the heat flux from the hot wall to the cold fluid (in watts per square
meter). Alternatively, for heat transfer from the hot fluid to the cold wall, the equation above is
written as:
q  h(T f  Tw ) ………………………………………..4

Where q is the heat flux from the hot fluid to the cold wall. Historically, the form given
by equation 3 was first used as a law of cooling as heat is removed from a body to a liquid
flowing over it, and it is generally referred to as “Newton’s law of cooling”. If the heat flux in
equations 3 and 4 is given in watts per square meter and the temperature are in degrees Celsius
(or Kelvin’s), then the heat transfer coefficient h in equations 3and 4 must have the dimensions
W /( m 2  C ) if the equations are dimensionally correct.
y

Tf
Fluid flow

Fluid flow profile

T
0
Wall at Tw Tw

Fig.3: Heat transfer by convection from a hot wall at Tw to a cold fluid.

To calculate the rate of convection between an object and the surrounding fluid, using the
heat transfer coefficient h, unlike the thermal conductivity, the heat transfer coefficient is not a
material property and it is depend on:
1. Type of flow (i.e., laminar or turbulent),
2. Geometry of the body,
3. Flow passage area,
4. The physical properties of the fluid,

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5. The average temperature,

6. The position along the surface of the body,
7. Mechanism of heat transfer (forced or free convection).

When heat transfer coefficient varies with the position along the surface of the body, for
convenience in engineering applications, its average value hm over the surface is considered
instead of its local value h. Equations 3 and 4 are also applicable for such cases by merely
replacing h by hm; then q represents the average value of the heat flux over the region considered.
The heat transfer coefficient can be determined analytically for flow over bodies having a
simple geometry such as a flat plate or inside a circular tube. For flow over bodies having
complex configurations, the experimental approach is used to determine h. There is a wide
difference in the range of the values of the heat transfer coefficient for various applications. Table
1 lists typical values of h encountered in some applications.

Type of flow h, W /( m 2  C )
Free convection,  T=24  C
0.25 m vertical plate:
Atmospheric air 5
Engine oil 37
Water 440
0.02 m outer diameter, horizontal cylinder in:
Atmospheric air 8
Engine oil 62
Water 741
0.02 m diameter sphere in:
Atmospheric air 9
Engine oil 60
Water 606
Forced convection

Atmospheric air at 25 °C with U  = 10 m/s over a flat plate:

L=0.1 m 39
L=0.5 m 17
Flow at 5 m/s across 1 cm outside cylinder of:
Atmospheric air 85
Engine oil 1,800
Water at 1 kg/s inside 2.5 cm inner diameter of tube 10,500
Boiling of water at 1 atm
Pool boiling in a container 3,000
Pool boiling at peak heat flux 35,000
Film boiling 300
Condensation of steam at 1 atm
Film condensation on horizontal tube 9,000-25,000
Film condensation on vertical surfaces 4,000-11,000
Drop-wise condensation 60,000-120,000

Table 1: Typical values of the convective heat transfer coefficient h.

Radiation
All bodies continuously emit energy because of their temperature, and the energy thus
emitted is called thermal radiation. The radiation energy emitted by a body is transmitted in the
space in the form of electromagnetic waves according to Maxwell’s classic electromagnetic wave
theory or in the form of discrete photons according to Planck’s hypothesis. Both concepts have
been utilized in the investigation of radiative heat transfer. The emission or absorption of

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radiation energy by a body is a bulk process; that is, radiation originating from the interior of the
body is emitted through the surface. Conversely, radiation incident on the surface of a body
penetrates to the depths of the medium where it is attenuated. When a large proportion of the
incident radiation is attenuated within a very short distance from the surface, we may speak of
radiation as a being absorbed or emitted by the surface. For example, thermal radiation incident
on a metal surface is attenuated within a distance of a few angstroms from the surface; hence
metals are opaque to thermal radiation.
The solar radiation incident on a body of water is gradually attenuated by water as the
beam penetrates to the depths of water. Similarly, the solar radiation incident on a sheet of glass
is partially reflected and the remaining is transmitted. Therefore, water and class are considered
semitransparent to the solar radiation.
It is only in vacuum that radiation propagates with no attenuation at all. Also the
atmospheric air contained in a room is considered transparent to thermal radiation for all practical
purposes, because the attenuation of radiation by air is insignificant unless the air layer is several
kilometers thick. However, gases such as carbon dioxide, carbon monoxide, water vapor and
ammonia absorb thermal radiation over certain wavelength bands; therefore they are
semitransparent to thermal radiation.
It is apparent from the previous discussion that a body at a temperature T emits radiation
owing to its temperature; also a body absorbs radiation incident on it.

Emission and absorption of radiation

The maximum radiation flux emitted by a body at temperature T is given by the Stefan-
Boltzmann law:
Eb    T 4 (W/m2) ………………………….……..5
Where:
T: the absolute temperature in Kelvin’s,
 : the Stefan –Boltzmann constant = 5.6697  10-8 W/(m2.K4),
Eb: the blackbody emissive power.

Only an ideal radiator or the so-called blackbody can emit radiation flux according to
equation 5. The radiation flux emitted by a real body at an absolute temperature T is always less
than that of the blackbody emissive power Eb; it is given by:

q    Eb    T 4 ………………………………………6

Where the emissivity  lies between zero and unity; for all real bodies it is always less
than unity.

About absorption, if a radiation flux qinc is incident on a black body, it is completely

absorbed by the blackbody. However, if the radiation flux qinc is incident on a real body, then the
energy absorbed q abs by the body is given by:
qabs    qinc ……………………………………..7

Where the absorptivity  lies between zero and unity, for all real bodies it is always less
than unity.