HIGHLIGHTS OF EIGHTH SESSION

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HIGHLIGHTS OF EIGHTH SESSION

• Convective Heat Transfer
• Equation governing convective heat transfer
• Natural Convection
• Forced Convection

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HEAT EXCHANGERS
In a heat exchanger, heat energy is transferred
from one body or fluid stream to another. In the
design of heat exchanger equipment, heat transfer
equations are applied to calculate this transfer
of energy so as to carry it out efficiently and
under controlled conditions. The equipment goes
under many names, such as boilers, pasteurizers,
jacketed pans, freezers, air heaters, cookers,
ovens and so on.
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Continuous-flow Heat Exchangers
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cpGdT U(T - Tb)dA   Therefore (U/cpG) dA
dT/(T Tb) If this is integrated over the length
of the tube in which the area changes from A 0
to A A, and T changes from T1 to T2, we
have           U/(cpG) A ln(T1 Tb)/(T2 -
Tb)               
(where ln loge)                                 
                      ln (? T1/ ? T2)       in
which ?T1 (T1 Tb) and ?T2 (T2 -
Tb) therefore       cpG UA/ ln (?T1/ ?T2)
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From the overall equation, the total heat
transferred per unit time is given
by                        q UA ?Tmwhere ? Tm
is the mean temperature difference, but the total
heat transferred per unit is also                
        q cpG(T1 T2)  so q UA ?Tm cpG(T1
T2) UA/ ln (?T1/ ?T2) x (T1 T2) but (T1
T2) can be written (T1 Tb) - (T2 -
Tb)          so (T1 T2) (?T1 - ?T2) therefore
UA?Tm UA(? T1 - ?T2) / ln (? T1/ ? T2)
                                  so that 
         ? Tm   (? T1 - ? T2) / ln (?T1/?T2)
                      where ?Tm is called the
log mean temperature difference
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Scraped Surface Heat Exchanger One type
of heat exchanger, that finds considerable use in
the food processing industry particularly for
products of higher viscosity, consists of a
jacketed cylinder with an internal cylinder
concentric to the first and fitted with scraper
blades, as illustrated in Figure. The blades
rotate, causing the fluid to flow through the
annular space between the cylinders with the
outer heat transfer surface constantly scraped.
Coefficients of heat transfer vary with speeds of
rotation but they are of the order of 900-4000 J
m-2 s-1 C-1. These machines are used in the
freezing of ice cream and in the cooling of fats
during margarine manufacture.
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Scraped Surface Heat Exchanger
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Jacketed Pans
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Jacketed Pan In a jacketed pan, the liquid to be
heated is contained in a vessel, which may also
be provided with an agitator to keep the liquid
on the move across the heat-transfer surface, as
shown in Figure.
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The source of heat is commonly steam condensing
in the vessel jacket. Practical considerations of
importance are 1. There is the minimum of air
with the steam in the jacket. 2. The steam is
not superheated as part of the surface must then
be used as a de-super heater over which low gas
heat-transfer coefficients apply rather than high
condensing coefficients. 3. Steam trapping to
remove condensate and air is adequate. The
action of the agitator and its ability to keep
the fluid moved across the heat transfer surface
are important. Some overall heat transfer
coefficients are shown in Table .
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Heating Coils Immersed in Liquids
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In some food processes, quick heating is required
in the pan, for example, in the boiling of jam.
In this case, a helical coil may be fitted inside
the pan and steam admitted to the coil as shown
in figure. This can give greater heat transfer
rates than jacketed pans, because there can be a
greater heat transfer surface and also the heat
transfer coefficients are higher for coils than
for the pan walls. Examples of the overall heat
transfer coefficient U are quoted as  1)
300-1400 for sugar and molasses solutions heated
with steam using a copper coil, 2)
1800 for milk in a coil heated with water
outside,  3) 3600 for a boiling aqueous
solution heated with steam in the
coil.
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Plate Type Heat Exchanger A popular heat
exchanger for fluids of low viscosity, such as
milk, is the plate heat exchanger, where heating
and cooling fluids flow through alternate
tortuous passages between vertical plates as
illustrated in Figure
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The plates are clamped together, separated by
spacing gaskets, and the heating and cooling
fluids are arranged so that they flow between
alternate plates. Suitable gaskets and channels
control the flow and allow parallel or counter
current flow in any desired number of passes.
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A substantial advantage of this type of heat
exchanger is that it offers a large transfer
surface that is readily accessible for
cleaning. The banks of plates are arranged so
that they may be taken apart easily. Overall
heat transfer coefficients are of the order of
2400-6000 J m-2 s-1 C-1.
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Problem Milk is flowing into a pipe cooler and
passes through a tube of 2.5 cm internal diameter
at a rate of 0.4 kg s-1. Its initial temperature
is 49C and it is wished to cool it to 18C using
a stirred bath of constant 10C water round the
pipe. What length of pipe would be required?
Assume an overall coefficient of heat transfer
from the bath to the milk of 900 J m-2 s-1 C-1,
and that the specific heat of milk is 3890 J kg-1
C-1.
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Now            q cpG (T1 T2)                 
        3890 x 0.4 x (49 - 18)       
48,240 J s-1 Also                       q
UA?Tm                  ?Tm (49 - 10) - (18
10) / ln(49 -10)1(18 - 10)                   
      19.6C.Therefore 48,240 900 x A x
l9.6                      A 2.73
m2                but A pDLwhere L is the
length of pipe of diameter D                Now
D 0.025 m.                      L 2.73/(p x
0.025)                          34.8 m
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Factors affecting rate of evaporation The basic
factors that affect the rate of evaporation are
the  1) rate at which heat can be transferred
to the liquid,  2) quantity of heat required to
evaporate each kg of water,  3) maximum
allowable temperature of the liquid,  4)
pressure at which the evaporation takes place,
 5) changes that may occur in the foodstuff
during the course of the evaporation
process.
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Important practical considerations in Evaporators
     1) Maximum allowable temperature, which
may be substantially below 100C.
     2) promotion of circulation of the liquid
across the heat transfer surfaces, to
attain reasonable high heat  transfer
coefficients and to prevent any local
overheating,      3)viscosity of the fluid
which will often increase
substantially as the concentration of the
dissolved materials increases,
4) Tendency to foam which makes separation of
liquid and vapour difficult.
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Parts Of Typical Evaporator Typical evaporator
is made up of three functional sections 1)
The heat exchanger 2) The evaporating section,
where the liquid boils and evaporates.
3) The separator in which the vapour leaves the
liquid and passes off to the condenser or
to other equipment.
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Vacuum Evaporation
For the evaporation of liquids that are
adversely affected by high temperatures, it may
be necessary to reduce the temperature of boiling
by operating under reduced pressure. The
relationship between vapor pressure and boiling
temperature, for water is as shown in figure.
When the vapor pressure of the liquid reaches the
pressure of its surroundings, the liquid boils.
The reduced pressures required to boil the liquor
at lower temperatures are obtained by mechanical
or steam jet ejector vacuum pumps, combined
generally with condensers for the vapors from the
evaporator.
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Vacuum Evaporation
Mechanical vacuum pumps are generally cheaper in
running costs but more expensive in terms of
capital than are steam jet ejectors. The
condensed liquid can either be pumped from the
system or discharged through a tall barometric
column in which a static column of liquid
balances the atmospheric pressure
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Single effect evaporator steam usage and heat
transfer surfaceA single effect evaporator is
required to concentrate a solution from 10
solids to 30 solids at the rate of 250 kg of
feed per hour. If the pressure in the evaporator
is 77 kPa absolute, and if steam is available at
200 kPa gauge, calculate the quantity of steam
required per hour and the area of heat transfer
surface if the overall heat transfer coefficient
is 1700 J m-2 s-1 C-1. Assume that the
temperature of the feed is 18C and that the
boiling point of the solution under the pressure
of 77 kPa absolute is 91C. Assume, also, that
the specific heat of the solution is the same as
for water, that is 4.186 x 103 J kg-1C-1, and
the latent heat of vaporization of the solution
is the same as that for water under the same
conditions.
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Mass balance (kg h-1)
From steam tables condensing temperature of steam
at 200 kPa (gauge)300 kPa absolute is 134C and
latent heat 2164 kJ kg-1 the condensing
temperature at 77 kPa (abs.) is 91C and latent
heat is 2281 kJ kg-1.
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Heat balanceHeat available per kg of
steam         latent heat sensible heat in
cooling to 91C        2.164 x 106 4.186 x
103(134 - 91)         2.164 x 106 1.8 x
105        2.34 x 106 J Heat required by the
solution           latent heat sensible heat
in heating from 18C to 91C          2281 x
103 x 167 250 x 4.186 x 103 x (91 - 18)       
3.81 x 108 7.6 x 107         4.57 x 108 J
h-1
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Now, heat from steam        heat required by
the solution,Therefore quantity of steam
required per hour
(4.57 x 108)/(2.34 x 106)               
                        195 kg h-1Quantity of
steam/kg of water evaporated 195/167           
                            1.17 kg steam/kg
water. Heat-transfer areaTemperature of
condensing steam 134C.Temperature difference
across the evaporator (134 - 91)
43C.Writing the heat transfer equation for q in
joules/sec,                                   
 q UA ?T               (4.57 x 108)/3600 1700
x A x 43                                     A
1.74 m2
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MULTIPLE EFFECT EVAPORATION
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End of 9th Session