heatexchangers

heat exchanger

A heat exchanger is a device built for efficient heat transfer from one medium to another
Heat transfer also known as heat flow as transfer of thermal energy is the movement of heat from one place to another
When an object is at adifferent temperature from its surroundings heat transfer occurs so that the body and the surroundings reach the same temperature at thermal equilibrium
Such heat transfer always occurs from a region of high temperature to another region of lower temperature
So, a heat exchanger is a component that allows the transfer of heat from one fluid ( liquid or gas) to another fluid
Heat transfer is usually required
To heat a cooler fluid by means by a hotter fluid
To reduce the temperature of a hot fluid by means of a cooler fluid
To boil a liquid by means of a hotter fluid
To condense a gaseous fluid by means of a cooler fluid
To boil a liquid while condensing a hotter gaseous fluid
In aheat exchanger the media may be separated by asolid wall , as that they never mix or they may be in direct contact.
In heat exchangers wher the media is separated by a solid wall , the heat is transferred from the hot fluid to the metal isolating the two fluids and then to the cooler fluid
The basic design of a heat exchanger normally has two fluids of different temperatures separated by some conducting medium
Types of heat exchangers
Based on the direction of flow , heat exchangers are of 3 types
1) parallel flow: in parallel flow heat exchangers the two fluids enter the heat exchanger from the same end with a large temperature difference
As the fluids transfer heat , hotter to cooler , the temperature of the two fluids approach each other
Thus they have a large temperature difference at the inlet and a small temperature difference at the inlet and a small temperature difference at the outlet .

---------------àfluid 1
--------------àfluid 2

2) counter flow : this exists when the two fluids flow in opposite directions . each of the fluids enter the heat exchangers at the opposite ends because the cooler fluid exits the counter flow heat exchanger , the cooler fluid will approach the inlet temperature of the hot fluid .
These type of heat exchangers have temperature difference along the heat transfer length . these are used for liquid – liquid condensing and gas cooling applications
Units are usually mounted vertically when condensing vapour and mounted horizontally when handling high concentrations of solids

--------------à
<-------------- 
3) Cross flow :
This exists when one fluid flows perpendicular to the second fluid
That is one fluid flows through tubes and the second fluid passes around the tubes at 90 degrees.it is generally used as a condenser. These are applicable when one of the fluid changes state .
Eg: steam condenser , the steam existing the turbine enters the condenser shell side , and the cool water flowing in the tube absorbs the heat from the steam , condesing it into water
Large volumes of vapor may be condensed using this type of heat exchangers flow
Among the 3 types of heat exchangers counter current flow is most efficient when compared with other because the average temperature difference between the two fluids over the length of the heat exchanger is maximized.
At the same operating conditions , operating the 3 heat exchangers the counter flow heat exchanger will result in a greater haeat transfer rate than operating in parallel flow

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Based on the flow heat exchangers are classified into two types as such
1) single pass heat exchangers - when a heat exchanger fluid passes only once
2) multipass heat exchangers - when a heat exchanger fluid passes more than once

Based on the function heat exchangers are classified into two types
1) regenerative : these heat exchangers use the same fluid for heating and cooling
The same fluid is both cooling fluid and cooled fluid . that is the hot fluid leaving a system gives up its heat to regenerate or heat up the fluid returning to the system.
These are found in high temperature systems where a portion of systems fluid is removed form the main process and then returned.
Because the fluid removed from the main process contain energy , the heat from the fluid leaving the main system is sued to reheat the returning fluid instead of being rejected to an external cooling medium to improve efficiency.

2) non regenerative: the hot fluid is cooled by fluid from a separate system and the enrgy removed is not returned to the system.
The most commonly used heat exchangers are
1) plate heat exchangers
2) shell tube heat exchangers
Plate heat exchangers :
Thes consists of thin plates joined together with a small amount of space between each plate typically mainatained by a small rubber gasket .
This consists of plates inside tubes to separate hot and cold fluids.
These set of tubes is called the tube bundles and can be made up of several types of tubes .
Shell and tube exchangers are typically used for high pressure applications
Several thermal design features should be t5aken into account when designing the tubes in this type of heat exchangers .

Tube diameter , tube thickenss, tube length , tube pitch , tube layout , baffle design play a major role.
Shell and tube heat exchangers :
These comprises of multiple tubes through which liquid flows
Set of tubes in a container called shell
The fluid flowing inside the tube is called tube side fluid and the fluid flowing on the outside of the tube is shell side fluid .
The tunes are divided into two sets
First set contains the liquid to be heated or cooled
Second set contain the liquid responsible for triggering the heat exchange



Selection of heat exchangers:
This depends on the heat transfer rate
Size and weight
Cost
Pumping power
Material of construction



keywors: heat . exchangers, heat exchangers, shell and tube heat exchangers, plate heat exchangers, heat transfer equipment

fourierslaw

Fouriers law of heat conduction;

Rate of heat conduction through uniform material ids directly proportional to area which is normal to the direction of heatflow and the temperature gradient which is in the direction of heat flow

Q α a dt/dy

Q= -k a dt/dy
Q /a = -k dt /dy
Q’ = -k dt /dy

Q = heat flow
A = area of crosssection
,dt/dy = temperature gradient

K= thermal conductivity



Thermal conductivity :

It is the rate of heat transfer per unit area

K = Q’ dy/dt



Q’ = heat flux

Units of thermal conductivity

Watt /m.kelvin



Fouriers law of heat conduction for a plane wall

Let the thermal conductivity be = k
Let the thickness of the wall be = x m
Let the hot surface temperature be = t1
Let the temperature of cold surface be = t2

Assuming the steady state
According to fouriers law of heat conduction



q/a = -k dt /dx



x t2
∫dx = -ka /q ∫dt
0 t1

x-0 = -ka /q(t2-t1)

q = t1-t2/(x/ka)
q= ^t/R
r = x/ka
thermal conductivity is the function of property of the material and its temperature or themal energy
k of solids > liquids>gases

keywords: thermal conductivity , fouriers law of heat conduction, fouriers law of heat conduction in plane wall,

fluiddynamis

Fluidmechanics:



Study of fluid and its behaviour and properties is called fluid mechanics
Fluidmechanics is basically classified into two types like
1) fluid statics : study of fluid at rest
2) fluid dynamics: study of fluid at motion
Based on the shear rate fluids are classified into two types
1) Newtonian
2) non Newtonian
Based on the relation ship with temperature and pressure drop fluids are classified into two types they are
1) compressible: these fluids are sensitive to pressure and temperature drop
2) incompressible fluids: fluids which are insensitive to temperature and pressure dropn is called an incompressible fluid

Fluid properties:

Density : mass unit volume
Units kg/m3
Specific weight : weight /unit volume
Relative density :
Mass density /standard density
Surface tension :
Amount of force required to maintain a unit length of film in equilibrium
Viscosity:
When fluid is subjected to shearstress it undergoes certain deformation offering a certain resistance called viscosity

Newtons law of viscosity
Let the area of the fluid film is a sq.m
Let the distance between the top and bottom layers be y m
Let the fluid be flowing between the two layers
Let the velocity of the fluid be v m/sec2
Let the viscosity of the fluid be u
Let the shear stress = T
T= F/A
Let the net force acting be F newtons

According to newtons law of viscosity

F∞ vA/y
F= u A dv/dy
F/A = u dv/dy

T = u dv/dy
Therefore shearstress is directly proportional to velocity gradient
Viscosity is the constant introduces
The fluids which obey the newtons law of viscosity are called Newtonian fluids
Which does not obey are considered as the no Newtonian fluid
Types of non Newtonian fluids and the graphs concerned are given as

Pseudoplastics: are those for which the viscosity decreases with the velocity gradient

Ex: blood , rubber

Bhingam plastics: these fluids undergo continuous deformation.
Ex: toothpaste , paint , jelly

Dilatant fluids : are those for which the viscosity increases with the velocity gradient
Ex: organic fluids, biological fluids
Starch

Time dependent non Newtonian fluids

Shear thinning : viscosity decreases with increase of time
Viscoplastic : acts both as elastic aswell viscous substance
Shear thickening : viscosity increases with increase of time



keywords: fluidmechanics, fluid statics, fluid dynamics, newtons law of viscosity , non newtonain fluids, graphs of non newtonain fluids,

pseudoplastics, bingham plastics, dilatent fluids , time dependent fluids

dimensinlessnumbers

Dimensionless numbers

Heat transfer dimensionless numbers:



Prandtl number = momentum diffusivity / thermal diffusivity

V/k
V = u/ ſ
‘ſ ‘ replaced by 1/cp

Pr = CpU/K



Grasshoff number = gβ(T-T’)L*L*L/V*V

Grasshoff number for pipes = gβ(T-T’)D*D*D/V*V

Rayleighs number =
Ra= prandtl * grasshoff

Nusslets number = hx/k

Stanton number =
St=C’/2

C’ = coefficient of friction



Mass transfer dimensionless numbers



Schmidt number : momentum diffusivity / mass diffusivity

Sc= u/ ſ D

Reynolds number = inertial forces /viscous forces
Dv ſ/u

keywords: schmidt number , reynolds number , stanton number ,rayleighs number, nuslets number, prandtl number , grasshoff number,

heat transfer dimensionless numbers, mass transfer dimensionless numbers

bernoulisequation

Bernoulis equation:

It denotes the interconversion of energies

Forces that at includes

Rate of work done by pressure from surroundings
Rate of energy obtained from internal energy reversible conversion
Rate of energy obtained due to reversible conversion of energy
Rate of work done by mechanical forces
Consider a pipe with an inlet and out let
With pressure p1, area a1, velocity of fluid be v1 at inlet
P2, a2,v2 be at the outlet



P1,a1,v1 -------------------- p2,a2,v2,
--------------------

Total energy = kinetic energy+ potential enrgy

TE1 = KE1+PE1

TE1 = ½ mv1*v1 +mgz1
,m (v1*v1/2 +gz1)
TE2 = ½ mv2*v2 +mgz2
,m(v2*v2/2 +gz2)
W = ,m(v1*v1/2 +gz1)-,m(v2*v2/2 +gz2)
,m [(v2*v2/2- v12/2)+g(z2-z1)]

W = W2-W2
(P2*m/ſ)+(P1*m/ ſ)
,m(p2-p1)/ ſ

m(p2-p1)/ ſ = m [(v2*v2/2- v1*v1/2)+g(z2-z1)]

(p2-p1)/ ſ = [(v2*v2/2- v12/2)+g(z2-z1)]

(p2-p1)/ ſ - [(v2*v2/2- v12/2)+g(z2-z1)] = constant



Correction factors

1) kinetic correction factor = ά

To eliminate the problem of integration it must be introduced

(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)] = constant



2)Pump work correction factor

ή= wp – Hfs / wp
wp – Hfs = ήwp

ήwp +(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)] = constant

3)Friction correction factor:

ήwp +(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)]+ hf = constant



limitations of bernoulis equation

1) applicable only for ideal fluids
2) Total heat cannot be transferd from one point to another completely



keywords: bernoulis equation , limitations of bernoulis equation, correction factors in bernoulis equation