(V semester Sec A/B)
By
Dr.M.SUBAS CHANDRA BOSE(Assistant Prof)(BT34),
&
Mrs.SABARUNISHA BEGUM(Assistant Prof)(BT29)
Bio Technology, REC
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
MASS TRANSFER
● Transfer of material from one homogeneous phase to
another. With or without phase change.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
UNIT - I DIFFUSION & MASS TRANSFER
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
DIFFUSION
The term mass transfer Diffusion is used to denote the transference of a component in a
mixture
from a region where its concentration is high to a region where the concentration is lower.
Mass transfer process can take place in a gas or vapour or in a liquid, and it can result
from the random velocities of the molecules (molecular diffusion) or from the circulating
or eddy currents present in a turbulent fluid (eddy diffusion).
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
A simple example of a mass transfer process is that occurring in a box consisting of
two compartments, each containing a different gas, initially separated by an impermeable
partition. When the partition is removed the gases start to mix and the mixing process
continues at a constantly decreasing rate until eventually (theoretically after the elapse of
an infinite time) the whole system acquires a uniform composition. The process is one
of molecular diffusion in which the mixing is attributable solely to the random motion
of the molecules. The rate of diffusion is governed by Pick's Law, first proposed by
FlCK(I) in 1855 which expresses the mass transfer rate as a linear function of the molar
concentration gradient. In a mixture of two gases A and B, assumed ideal, Pick's Law
for steady state diffusion may be written as:
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
DIFFUSION IN BINARY GAS MIXTURES
10.2.1, Properties of binary mixtures
If A and B are ideal gases in a mixture, the ideal gas law, equation 2.15, may be applied
to each gas separately and to the mixture:
PAV = nART
PBV = nRRT
PV = nRT
where nA and HB are the number of moles of A and B and n is the total number of
moles in a volume V, and PA , PB and P are the respective partial pressures and the total
pressure.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Equimolecular counterdiffusion
When the mass transfer rates of the two components are equal and opposite the process is
said to be one of equimolecular counterdiffusion. Such a process occurs in the case of the
box with a movable partition, referred to in Section 10.1. It occurs also in a distillation
column when the molar latent heats of the two components are the same. At any point
in the column a falling stream of liquid is brought into contact with a rising stream of
vapour with which it is not in equilibrium. The less volatile component is transferred from
the vapour to the liquid and the more volatile component is transferred in the opposite
direction. If the molar latent heats of the components are equal, the condensation of
a given amount of less volatile component releases exactly the amount of latent heat
required to volatilise the same molar quantity of the more volatile component. Thus at
the interface, and consequently throughout the liquid and vapour phases, equimolecular
counterdiffusion is taking place.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Mass transfer through a stationary second component
In several important processes, one component in a gaseous mixture will be transported
relative to a fixed plane, such as a liquid interface, for example, and the other will undergo
no net movement. In gas absorption a soluble gas A is transferred to the liquid surface
where it dissolves, whereas the insoluble gas B undergoes no net movement with respect
to the interface. Similarly, in evaporation from a free surface, the vapour moves away
from the surface but the air has no net movement.
The concept of a stationary component may be envisaged by considering the effect of
moving the box, discussed in Section 10.1, in the opposite direction to that in which B is
diffusing, at a velocity equal to its diffusion velocity, so that to the external observer B
appears to be stationary. The total velocity at which A is transferred will then be increased
to its diffusion velocity plus the velocity of the box.
For the absorption of a soluble gas A from a mixture with an insoluble gas B, the
respective diffusion rates are given by:
NA = - D AB
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Mass transfer velocities
It is convenient to express mass transfer rates in terms of velocities for the species under
consideration where:
As a result of the diffusional process, there is no net overall molecular flux arising from
diffusion in a binary mixture, the two components being transferred at equal and opposite
rates. In the process of equimolecular counterdiffusion which occurs, for example, in a
distillation column when the two components have equal molar latent heats, the diffusional
velocities are the same as the velocities of the molecular species relative to the walls of
the equipment or the phase boundary.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Thermal diffusion
If a temperature gradient is maintained in a binary gaseous mixture, a concentration
gradient is established with the light component collecting preferentially at the hot end
and the heavier one at the cold end. This phenomenon, known as the Soret effect, may be
used as the basis of a separation technique of commercial significance in the separation
of isotopes.
Conversely, when mass transfer is occurring as a result of a constant concentration
gradient, a temperature gradient may be generated; this is known as the Dufour effect.
In a binary mixture consisting of two gaseous components A and B subject to a temperature
gradient, the flux due to thermal diffusion is given by GREW and IBBS
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
UNIT - II GAS LIQUID OPERATIONS
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Gas absorption principles
Liquid/Gas Absorption ops
includes absorption, stripping and desorption
soluble vapour absorbed from mixture with a liquid (solute), solute is
then regenerated  can also have gas absorption with reaction.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
The removal of one or more selected components from a mixture of gases
by absorption into a suitable liquid is the second major operation of
chemical engineering that is based on interphase mass transfer controlled
largely by rates of diffusion. Thus, acetone can be recovered from an
acetone–air mixture by passing the gas stream into water in which the
acetone dissolves while the air passes out. Similarly, ammonia may be
removed from an ammonia–air mixture by absorption in water. In each of
these examples the process of absorption of the gas in the liquid may be
treated as a physical process, the chemical reaction having no appreciable
effect
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
The transfer unit
The group (dy/ye − y), which is used in Chapter 11, has been
defined by CHILTON and
COLBURN(52) as the number of overall gas transfer units NOG.
The concept of the transfer
unit is also introduced in Volume 1, Chapter 10. The application
of this group to the
countercurrent conditions in the absorption tower is now
considered.
Over a small height dZ, the partial pressure of the diffusing
component A will change
by an amount dPAG.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
UNIT - III VAPOUR LIQUID OPERATIONS
Total condenser
Distillation
Overhead vapor
Reflux drum
1
Rectifying section stages
Feed
Stripping section stages
Distillate
Reflux
2
f
Feed Stage
Boilup
N
Partial reboiler
Bottoms
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Distillation and V-L Equilibria
Types of Distillation
Action on an Ideal Plate
Mass Balance in a Distillation Column
Determination of Ideal Number of Plates – McCabe –
Thiele Analysis
Differential or batch distillation
Flash or equilibrium distillation
Continuous Rectification – Binary systems
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MASS TRANSFER 0PERATIONS
Differential distillation:
The simplest examples of batch distillation at a single stage.
Starting with a still pot, initially full, heated at a constant rate. In this
process the vapour formed on boiling the liquid is removed at once from
the system.
Since this vapour is richer in the more volatile component, with this result
the composition of the product progressively alters.
Thus, whilst the vapour formed over a short period is in equilibrium with
the liquid
At the end of the process the liquid, which has been vaporized, is removed
as the bottom product.
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MASS TRANSFER 0PERATIONS
Let S be the number of mols of material in the still and x be the mol fraction
of component A.
Suppose an amount dS, containing a mol fraction y of A, be vaporised.
Then a material balance on component A gives:
ydS = d (Sx)
= S dx + x Ds
The integral on then right-hand side can be solved graphically if the
equilibrium relationship between y and x is available.
Thus, if over the range concerned the equilibrium relationship is a straight
line of the form y= m x + c
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
This process consists of only a single stage, a complete
separation is impossible unless the relatively volatility is
finite. Application is restricted to conditions where a
preliminary separation is to be followed by a more
rigorous distillation, where high purifies is not required, or
where the mixture is very easily separated
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Flash & continuous distillation
This method is frequently carried out as a continuous process.
Consist of vaporizing a definite fraction of liquid feed in such a way that the
vapour evolved is in equilibrium with the residual liquid.
The feed is usually pumped through a fired heater and enters the still through a
valve where the pressure is reduced.
The still is essentially a separator in which the liquid and vapour produced is
reduced by reduction in pressure with sufficient time to reach equilibrium. The
vapour is removed from the top of the separator and is then usually condensed,
while the liquid leaves from the bottom.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Flash & continuous distillation
It is used in petroleum refining, in which petroleum fractions are heated in pipe stills
and the heated fluid flashed in to vapour and residual streams, each containing many
components.
Flash distillation is used most for separating components that boil at widely different
temperatures.
It is not effective separating components of comparable volatility, which requires the use
of distillation with reflux
By definition a vapour leaving a plate are brought into equilibrium.
Assume that the plates are numbered serially from top down and that the plate under
consideration is the nth plate from the bottom.
Then the immediately above plate n is plate n-1, and the immediately below is n+1.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Material Balance diagram for plate n:
Vn-1,yn-1
Ln-2,Xn-2
Vn,yn
Plate n -1
Plate n
Ln-1,Xn-1
Vn+1,yn+1
Ln ,xn
Plate n+1
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
For example if two fluid enter plate n and two leave it, the liquid, Ln-1 mol/h, from plate
n-1 and the stream of vapour, Vn+1 mol/h, from plate n+1 are brought into intimate
contact.
A stream of vapour, Vn mol/h, rises to plate n-1 and a stream of liquid, Ln mol/h,
descends to plate n+1.
Since the vapour streams are the V phase, their considerations are denoted by y; the
liquid streams are the L phase and their concentrations are denoted by x. Then the
concentrations of the streams entering and leaving the nth plate are as follows:
Vapour leaving plate, yn
Liquid leaving plate, xn
Vapour entering plate, yn+1
Liquid entering plate, xn-1
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Boiling-Point Diagram showing rectification on ideal plate:
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Number of Plates Required in a Distillation Column:
To develop a method for the design of distillation units to give the desired
fractionation, it is necessary to determine the numbers of trays.
Before that the heat and material flows over the trays, the condenser and
the reboiler must be established
Thermodynamic data is required to establish how much mass transfer is
needed to establish equilibrium between the stream leaving each tray.
The diameter of the column will be dictated by the necessity to
accommodate the desired flow rates, to operate within the available drop
in pressure, while at the same time affecting the desired degree of mixing
of the stream on each tray.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Summary of the material balances for two components systems:
Let the process be analysed simply for a binary mixture of A and B as follows:
Let F be the number of mols per unit of feed of mol fraction xf of A.
D be the number of mols per unit time of vapour formed with y the mol fraction of A and
B be the number of mols per unit time of liquid with x the mol fraction of A. Then an
overall mass balance gives:
F=D+B
Component A balance
FxF = D xD + B xB
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Eliminating B and D from these equations give the follow:
D xF  xB

F xD  xB
B xD  xF

F xD  xB
Net flow rates. Quantity D is the difference between the flow rates of the streams
entering and leaving the top of the column. A material balance around the condenser
and accumulator in the gives:
D  Va  La
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Eliminating B and D from these equations gives the following:
The difference between the flow rates of vapour and liquid anywhere in the upper
section of the column is also equal to D. This surface includes the condenser and all
plates above n+1. A total material balance around this control surface gives:
D  Vn 1  Ln
Similar material balances for A give the following equations:
Dx D  Va Ya  La xa  Vn 1 yn 1  Ln xn
Quantity D xD is the net flows rate of the component A upward in the upper section of
the column. It too is constant throughout this part of the equipment. In the lower
section of the column the net flow rates are also constant but, are in a downward
direction.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
The net flow of total material equals B; that of the component A is BxB. The following
equations apply:
B  Lb  Lb  Lm  Vm1
Bx B  Lb xb  Vb yb  Lm xm  Vm1 ym1
Operating lines:
There are two sections in the column; there are also two operating lines, one for the
rectifying section and other for the stripping section.
yn 1
Ln
Va ya  La xa

xn 
Vn 1
Vn 1
For the first section (rectifying section) the operation line is represented by:
y n 1 
Ln
Dx D
xn 
Ln  D
Ln  D
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Substituting for DxD in the equation above and eliminating Vn+1
Vm1 ym1  Lm xm  Bx B
For the section below the feed plate, a material balance over control surface II gives
yn 1 
Ln
Dx D
xn 
Ln  D
Ln  D
Rearranging this equation and taking into account that the slope is the ratio of liquid
flow to the vapour flow, and also eliminating Vm+1
ym 1 
Lm
Bx B
xm 
Lm  B
Lm  B
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Feed Line:
The conditions of the vapour rate or the liquid rate may change depending of the thermal
condition of the feed.
It is related to the heat to vaporize one mole of feed divided by molar latent
heat (q)
Various type of feed conditions:
Cold feed, q>1
Feed at bubble point (saturated liquid), q=1
Feed partially vapour, 0<q<1
Feed at dew point (saturated vapour), q=0
Feed superheated vapour q<0
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Feed Line - Diagram:
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Feed Line:
Cold feed : It is assumed that the entire feed stream adds to the liquid flowing down the
column.
Feed at bubble point: no condensation is required to heat the feed.
Feed partial vapour: the liquid portion of the feed becomes part of the L and the vapour
portion becomes part of V
Feed saturated vapour the entire feed becomes part of the V
Feed superheated: part of the liquid from the rectifying column is vaporized to cool the
feed to a state of saturated vapour.
Feed Line Equation:
If xq = xF, and yq =xF then;
The point of intersection of the two operating lines lies on the straight line of slope
(q/q -1) and intercept (xF, yF)
yq 
q
xF
xq 
q 1
q 1
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Reflux Ratio:
The analysis of fractionating columns is facilitated by the use of a quantity called reflux
ratio.
Two ratios are used, one is the ratio of the reflux to the overhead product and the other
is the ratio of the reflux to the vapour.
Both ratios refer to quantities in the rectifying section. The equations for those ratios are
RD 
L V D

D
D
and
RV 
L
L

V LD
If the operation lines equations are divided D, the result is, for constant molar overflow,
RD
xD
yn 1 
xn 
RDline
of
1the rectifying
RDsection
1
This equation is an operation
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Reflux Ratio:
The y intercept of this line is xD/(RD+1).
The concentration xD is set by the conditions of the design.
RD, the reflux ratio, is an operating variable that can be controlled at will by adjusting the
split between reflux and overhead product or by changing the amount of vapour formed
in the reboiler for a given flow rate of the overhead product.
A point at the upper end of the operating line can be obtained by setting xn equal to xD in
the equation above.
A point at the upper end of the operating line can be obtained by setting xn equal to xD in
the previous equation.
yn 1 
RD
xD
x R  1
xD 
 D D
RD  1
RD  1
RD  1
or
yn 1  xD
The operating line for the rectifying section then intersects the diagonal at point (xD, xD).
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
The operation lines represented by those two equations are plotted with the equilibrium
curve on the x-y diagram.Those equations also show that unless Ln and Lm are constant,
the operating lines are curved.The lines can be plotted only if the change in these
internal streams with concentration is known.
Minimum
Reflux
a
e
b
Total
(Maximum)
Reflux
xF
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Influence of the Number of Reflux Ratio:
Any change in R will therefore modify the slope of the operation line as can be seen from
the Figure
Minimum
Reflux
e
b
xF
Dr.M.SUBAS.C.BOSE
a
MASS TRANSFER 0PERATIONS
If no product is withdrawn from the still (D=0), the column is said to operate under
conditions of total reflux and, as seen from equation , the top operating line has its
maximum slope of unity, and coincides with the line x=y.
Minimum
Reflux
The step become very close to the plate above, these
conditions are known as minimum
reflux and Rm denotes the reflux ratio.
a
e
Any small increase in R beyond Rm will give a workable system, though a large numbers
of plate will be required.
b
The minimum number of plates is required for a given separation at conditions of total
reflux
There is a minimum reflux ratio below which it is impossible to obtain the desired
enrichment, however many plates are used.
xF
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Calculation of Minimum Reflux Ratio Rm
Based on the previous figure, the slope of the line ad is given by
Rm
x  xF
 D
or
Rm  1
xD  xF
Rm
Minimum
xD Reflux
 yF
y F  xF
e
b
xF
Dr.M.SUBAS.C.BOSE
a
MASS TRANSFER 0PERATIONS
McCabe -Thiele principles
Construction the operation lines:
Locate the feed line Calculate the y-axis intercept xD/(RD + 1) of
the rectifying line and plot that line through the intercept and
the point (xD, xD)
Draw the stripping line through point (xB,xB) and the
intersection of the rectifying line with the feed line.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Effect the feed condition on feed line:
If the feed is a cold liquid, the feed line slopes will be
upward and to the right;
if the feed is a saturated liquid, the line is vertical;
if the feed is a mixture of liquid and vapour, the lines
slopes upward and to the left and the slope is the negative of
the ratio of the liquid to the vapour;
if the feed is saturated vapour the line is horizontal and
if the feed is superheated vapour. The lines slope
downward and to the left.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Feed Plate location
After the location of the feed plate the construction of the
number of ideal trays is found by the usual step-by step
construction. The process can begin at the top and also a total
condenser is used.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
UNIT - IV EXTRACTION OPERATIONS
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Liquid–Liquid Extraction
13.1. INTRODUCTION
The separation of the components of a liquid mixture by treatment with a solvent in
which one or more of the desired components is preferentially soluble is known as
liquid–liquid extraction—an operation which is used, for example, in the processing
of coal tar liquids and in the production of fuels in the nuclear industry, and which
has been applied extensively to the separation of hydrocarbons in the petroleum
industry. In this operation, it is essential that the liquid-mixture feed and solvent are
at least partially if not completely immiscible and, in essence, three stages are
involved:
(a) Bringing the feed mixture and the solvent into intimate contact,
(b) Separation of the resulting two phases, and
(c) Removal and recovery of the solvent from each phase.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Stage wise Extraction
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Continuous Extraction
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
General principles of Leaching
Leaching is concerned with the extraction of a soluble constituent from a
solid by means
of a solvent. The process may be used either for the production of a
concentrated solution
of a valuable solid material, or in order to remove an insoluble solid, such
as a pigment,
from a soluble material with which it is contaminated. The method used for
the extraction
is determined by the proportion of soluble constituent present, its
distribution throughout
the solid, the nature of the solid and the particle size.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Factors influencing the rate of extraction
The selection of the equipment for an extraction process is influenced by
the factors which
are responsible for limiting the extraction rate. Thus, if the diffusion of the
solute through
the porous structure of the residual solids is the controlling factor, the
material should be
of small size so that the distance the solute has to travel is small. On the
other hand, if
diffusion of the solute from the surface of the particles to the bulk of the
solution is the
controlling factor, a high degree of agitation of the fluid is required.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
EQUIPMENT FOR LEACHING
Processes involved
Three distinct processes are usually involved in leaching operations:
(a) Dissolving the soluble constituent.
(b) Separating the solution, so formed, from the insoluble solid residue.
(c) Washing the solid residue in order to free it of unwanted soluble matter or to obtain
as much of the soluble material as possible as the product.
Leaching has in the past been carried out mainly as a batch process although many
continuous plants have also been developed. The type of equipment employed depends on
the nature of the solid—whether it is granular or cellular and whether it is coarse or fine.
The normal distinction between coarse and fine solids is that the former have sufficiently
large settling velocities for them to be readily separable from the liquid, whereas the
latter can be maintained in suspension with the aid of only a small amount of agitation.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
UNIT - V SOLID FLUID OPERATIONS
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MASS TRANSFER 0PERATIONS
INTRODUCTION - ADSORPTION
Although adsorption has been used as a physical-chemical process for many years, it is
only over the last four decades that the process has developed to a stage where it is now
a major industrial separation technique. In adsorption, molecules distribute themselves
between two phases, one of which is a solid whilst the other may be a liquid or a gas.
The only exception is in adsorption on to foams, a topic which is not considered in this
chapter.
Unlike absorption, in which solute molecules diffuse from the bulk of a gas phase to
the bulk of a liquid phase, in adsorption, molecules diffuse from the bulk of the fluid to
the surface of the solid adsorbent forming a distinct adsorbed phase.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
The adsorption which results from the influence of van der Waals forces is
essentially
physical in nature. Because the forces are not strong, the adsorption may be easily
reversed.
In some systems, additional forces bind absorbed molecules to the solid surface.
These are chemical in nature involving the exchange or sharing of electrons, or
possibly molecules
forming atoms or radicals. In such cases the term chemisorption is used to describe
the phenomenon. This is less easily reversed than physical adsorption, and
regeneration may be a problem. Chemisorption is restricted to just one layer of
molecules on the surface, although it may be followed by additional layers of
physically adsorbed molecules.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
MOISTURE CONTENT RELATIONSHIPS:
MOISTURE/SOLID EQUILIBRIUM RELATIONSHIPS DEFINED ON THE BASIS OF
RELATIVE HUMIDITY AT A SPECIFIC TEMPERATURE EQUILIBRIUM AMOUNT
OF MOISTURE TENDS TO DECREASE WITH INCREASING TEMPERATURE.
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
MOISTURE CONTENT VARIABLES BASED ON THE MASS OF MOISTURE
RELATIVE TO THE MASS BONE DRY SOLID
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MASS TRANSFER 0PERATIONS
DRYING RATE CURVES:
DEPEND ON WHETHER HEAT ORMASS TRANSFER CONTROLS FREE MOISTURE VS.
TIME DRYING RATE VS. MOISTURE CONTENT
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MASS TRANSFER 0PERATIONS
DRYING REGIMES CONSTANT RATE - NO LIMIT TO MASS TRANSFER IN SOLID PHASE
SURFACE MOISTURE TRANSFER NEAR SURFACE FALLING RATE – MOISTURE FLUX
THROUGH THE SOLID IS HINDERED CRITICAL POINTS OCCUR BETWEEN CONSTANT
RATE AND FALLING RATE WITH A CHANGE IN THE FALLING RATE DRYING
MECHANISM.
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MASS TRANSFER 0PERATIONS
FALLING RATE EXAMPLE:
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
FALLING RATE EXAMPLE:
Dr.M.SUBAS.C.BOSE
MASS TRANSFER 0PERATIONS
Dr.M.SUBAS.C.BOSE