Solution Paper - II

Question1:-

A triple effect forward feed evaporator is used to concentrate a liquid which has
marginal elevation in boiling point. The temperature of the stream to the first
effect is 105°C, and the boiling point of the solution within third effect is 45°C. The
overall heat transfer coefficients are,

2,200 W/m2: in the Ι-effect,

1,800 W/m2: in the ΙΙ-effect,
1,500 W/m2: in the ΙΙΙ-effect.

Find out at what temperatures the fluid boils in the Ι and ΙΙ effects.

Answer:-

Assumptions

1. We may assume that there is no elevation in boiling point in the evaporators.

2. Area of all the three evaporators are same (AΙ = AΙI = AΙII = A)
Total temperature drop = (105-45) °C = 60 °C
Using eq. 9.5, the temperature drop across Ι-effect,

Similarly, the temperature drop across ΙΙ-effect,

And the temperature drop across ΙΙΙ-effect,

Therefore, the boiling point in the first effect will be = (105 – 15.2) °C = 89.8 °C
Similarly, the boiling point in the second effect will be = (89.8 – 18.6)°C = 71.2 °C.

Question2:-

What is heat transfer coefficient?

Answer:-

The correlation used in the boiling and condensation may be used here. If the evaporator operates at very
high liquid velocity so that the boiling occurs at the top end of the tube, the following correlation (eq. 9.1)
may be used,

(9.1)

where, D is the inner diameter of the tube, k is the thermal conductivity of the liquid or solution.

Fig: Temperature profiles in an evaporator

Fouling is a concern in the evaporator; therefore the following equation (eq.9.2) may be used for the
overall heat transfer coefficient with time,

(9.2)
where, t is the time for where the evaporator is the operation, α is a constant for a particular liquid,
Udirty and Uclean all the overall heat transfer coefficient of the dirty and clean evaporator.

Question3:-

Discuss the effect of temperature on thermal conductivity.

Answer:-

The atoms and molecules in all substances are moving -- either vibrating in solids or actually moving in
liquids and gases. Temperature measures their average kinetic energy or energy of motion. Thermal
conductivity changes with temperature.

Effects
Thermal conductivity is relatively constant over a narrow temperature range. As the temperature
increases, however, the rate at which particles in the substance are moving increases, and the rate at
which heat is transferred typically increases as well.

Question4:-

In the oven door described in illustration 5.1 is subjected to an upward flow of air
(that is forced convection). What would be the minimum free stream velocity for
which natural convection may be neglected?

Answer:-

The following condition shows the effect of natural convection may be neglected,

The value of Gr number calculated in the previous illustration was 1.16 X 108

Thus,

U >> 0.24 m/s

Therefore, the bulk velocity of the air should be far greater that 0.24 m/s.

Question5:-

Explain Dühring rule.

Answer:-
Dühring's rule states that a linear relationship exists between the temperatures at which two solutions
exert the same vapor pressure The rule is often used to compare a pure liquid and a solution at a
given concentration.
Dühring's plot is a graphical representation of such a relationship, typically with the pure liquid's boiling
point along the x-axis and the mixture's boiling point along the y-axis; each line of the graph represents a
constant concentration.

Question6:-

What is Leidenfrost phenomenon?

Answer:-

Leidenfrost phenomenon was observed by Leidenfrost in 1756. When water droplets fall on a very hot
surface they dance and jump on the hot surface and reduces in size and eventually the droplets
disappear. The mechanism is related to the film boiling of the water droplets. When water droplet drops
on to the very hot surface, a film of vapour forms immediately between the droplet and the hot surface.
The vapour film generated provide and up-thrust to the droplet. Therefore, the droplet moves up and
when again the droplet comes in the contact of the hot surface, the vapour generated out of the water
droplet and the phenomenon continues till it disappears.

The effectiveness of nucleate boiling depends primarily on the ease with which bubbles form and free
themselves from the heating surface. The important factor in controlling the rate of bubble detachment is
the interfacial tension between the liquid and the heating surface. If this interfacial tension is large the
bubbles tends to spread along the surface and blocked the heat transfer area, rather than leaving the
surface, to make room for other bubbles. The heat transfer coefficient obtained during the nucleation
boiling is sensitive to the nature of the liquid, the type and condition of the heating surface, the
composition and purity of the liquid, agitation, temperature and pressure.
Question
n7:-

D
Define Grash
hof numberr?

Answer::-

The Gras shof number is a dime

ensionless nuumber in fluid dynamics an nd heat transffer which
approxima ates the ratio of the buoyancyto viscouss force acting on a fluid. It frequently ariises in the stu
udy of
situations involving nattural convection. It is name
ed after the German
G engineer Franz Gra ashof.

for vertical flat platess

for pip
pes

for blu
uff bodies
where the
e L and D sub
bscripts indica
ates the length scale basis for the Grash
hof Number.

g = acceleratio
on due to Eartth's gravity
β = volumetric thermal expa
ansion coefficcient (equal to
o approximate
ely 1/T, for ide
eal fluids, whe
ere T
iss absolute tem
mperature)
Ts = surface te
emperature
T∞ = bulk temp
perature
L = length
D = diameter
ν = kinematic viscosity
v

The transition to turbulent flow occuurs in the rang

ge for natural convection
c fro
om
vertical fla
at plates. At higher
h Grasho
of numbers, thhe boundary layer
l is turbullent; at lower Grashof nummbers,
the bound dary layer is la
aminar.

The produ
uct of the Gra
ashof number and the Pran
ndtl number gives
g the Raylleigh number, a dimension
nless
number th
hat characterizes convectio
on problems in
i heat transffer.

There is an
a analogous form of the Grashof
G num
mber used in cases
c of naturral convection
n mass
transfer problems.

w
where

and
 g = acceleration due to Earth's gravity
Ca,s = concentration of species a at surface
Ca,a = concentration of species a in ambient medium
L = characteristic length
ν = kinematic viscosity
ρ = fluid density
Ca = concentration of species a
T = constant temperature
p = constant pressure

Question8:-

A pipe having 10 cm of diameter is carrying saturated steam at 8 bar of absolute

pressure. The pipe runs through a room. The wall of the room is at 300 oK. A
portion around 1 m of the pipe insulation is damaged and exposed to the room
atmosphere. Calculate the net rate of heat loss from the pipe by radiation.

Answer:-

The emissivity of the pipe surface is not given so it may be considered black. Moreover, since the room
may be big compared to the surface area of the pipe, the room may also be considered to be a
blackbody.
We can write F11 + F12 = 1.
The value of F11 = 0, as the pipe cannot see itself.
Thus F12, the view factor (1-pipe, 2-room) will be 1.
The net rate heat loss due to radiation,

Tpipe can be obtained by the temperature of the steam at the prevailing pressure with the help of steam
table = 450 K.
σ (= 5.67 X 10-8 W/m2/K4)
On putting the value,
Q12 = {π(0.1)(1)}(1)(1)(5.67 X 10-8){4504 - 3004}
Q12 = 586 W