chap.1. fundamentals of heat transfer heat transfer by conduction conduction of heat means transport...

2CH204 Heat Transfer Op. Chemical Engineering Department, IT

- 1 -

Lecture 1 Chap.1. Fundamentals of Heat Transfer

HEAT: It is energy in a transit form, which moves from high to low temperature level. It is that quantity which is transferred between bodies due to the difference in

temperatures existing between them. TEMPERATURE: The temperature is a thermal State of a body, which distinguishes a hot body from a cold body. The temperature of a body is proportional to the stored molecular energy i.e., the average molecular kinetic energy of the molecules in a system. (A particular molecule does not have a temperature, it has energy; the gas as a system has temperature). “It is a thermal state of body differentiating hot and cold body.” THERMODYNAMICS: It is that branch of engineering science, which deals with transformation of energy from one form to another. Zeroth law of Thermodynamics deals with thermal equilibrium and

establishes a concept of Temperature. First law of Thermodynamics throws light on concept of internal energy. Second law of Thermodynamics indicates the limit of converting heat into

work and introduces the principle of increase of entropy. Third law of Thermodynamics defines absolute zero of entropy.

THERMODYNAMIC EQUILIBRIUM: Thus for attaining a state of thermodynamic equilibrium the following three types of equilibrium states must be achieved.

1. Thermal Equilibrium The temperature of the system does not change with time and has same value at all points of the system.

2. Mechanical Equilibrium: There are no unbalanced forces within the system

or between the surroundings. The pressure in the system is same at all points and does not change with respect to time.

3. Chemical Equilibrium: No chemical reaction takes place in the system and

the chemical composition which is same throughout the system does not vary with time.

HEAT TRANSFER PROCESS:

Difference Between Heat Transfer And Thermodynamics IMPORTANCE OF HEAT TRANSFER IN ENGINEERING: Reference: Introduction to Heat Transfer, by C.B.Gupta & R.Prakash


- 2 -

Lecture 2 BASIC LAWS GOVERNING HEAT TRANSFER: The following are the basic laws, which govern heat transfer.

First law of Thermodynamics: It is merely one statement of the law of the conservation of energy with particular reference to heat energy and work. 1. Second law of thermodynamics: It states that "Heat will flow naturally from

one reservoir to another at a lower temperature but not in opposite direction without assistance." This law established the direction of energy transport.

2. Law of Mass Conservation: This law is used to determine the parameters of flow.

3. Newton's laws of motion: These laws are used to determine fluid flow parameters

4. Rate Equations: depends on mode of heat transfer MODES OF HEAT TRANSFER: Heat transfer, which is defined as the transmission of energy from one region to another as a result of temperature gradient takes place by following three different modes:

1. Conduction 2. Convection 3. Radiation

VARIATION IN HEAT TRANSFER WITH REFERENCE TO TIME:

STEADY STATE HEAT TRANSFER: ‘Steady State’ means the state of the system that does not change with time. In the case of heat transfer, in particular, it means that both the temperature and the heat flux at any location remains constant or invariant with respect to time. UNSTEADY STATE HEAT TRANSFER: When temperature at any point in a system changes with time, process is unsteady state heat transfer. Eg.: Cooling of castings in a foundary. Internal energy changes in such a process. QUASI OR PERIODIC STEADY STATE HEAT TRANSFER: When variation in temperature of unsteady state system undergoes a particular cycle, it is known as periodic steady state heat transfer. Eg: Heating or cooling of a building wall during 24 hours cycle of the day. BASIC LAWS OF HEAT TRANSFER: 1. FOURIER’S LAW:

The fundamental conditions for heat transfer by conduction within a solid are: i) Temperature gradient must exist ii) Heat flows in the direction of decreasing temperature

Consider that one-dimensional heat is conducted across a solid wall. Reference: Introduction to Heat Transfer, by C.B.Gupta & R.Prakash


- 3 -

Lecture 3 THERMAL CONDUCTIVITY: From Fourier’s law,

q = lkA t or q = -k . A. dt/dx

let dx = 1 m, A = 1 m2, dt = 10C, then q = k. Thermal Conductivity of a material depends upon: a. Material structure b. Density of the material c. Moisture content d. Pressure and temperature

Following points regard thermal conductivity – its variation for different materials and under different conditions are worth noting:

NEWTON’S LAW: Newton proposed the fundamental heat convection equation,

q = h . A . T = h . A (Ts - T) STEFAN BOLTZMANN’S LAW: “The maximum energy radiated by a body is proportional to the fourth power of its absolute temperature.”

q = . A . T4 THERMAL CONDUCTANCE & RESISTANCE: From Fourier’s law,

q = lkA (t1 – t2) = K (t1 – t2)

K is known as internal thermal conductance.W/0C CONVECTIVE AND RADIATIVE CONDUCTANCE / RESISTANCE Reference: Introduction to Heat Transfer, by C.B.Gupta & R.Prakash


- 4 -

Lecture 4 COMBINED HEAT TRANSFER PROCESS: In this case, the heat transfer modes which are acting in series are convection-conduction and convection. In steady-state conditions the rate of convection heat transfer qci, from the hot fluid to the inside surface of the container is equal to the rate of conduction heat transfer qb from the inside surface to the outer surface of the container wall, which is also equal to the convection heat transfer qco, from the outer surface of the container wall to the air. The heat transfer rates can be expressed as

co

oBoBcoBoco R

TTTTKTTAhq 0

At Steady State, qci = qb = qco

cokci RRRUA

1

THERMAL DIFFUSIVITY: It is the ratio of thermal conductivity to thermal storage capacity. It is denoted by .

= Thermal Conductivity / Thermal Storage Capacity = (k / . c) Thermal storage capacity is product of density and specific heat of material.

Thermal diffusivity of solid is property of material. It has dimensions of area divided by time such as m2/ sec or ft2/hr.

ANALOGIES BETWEEN VARIOUS TRANSPORT PROCESSES ANALOGY BETWEEN FLOW OF HEAT AND ELECTRICITY: When two physical systems are described by similar equations and have similar boundary conditions these are said to be analogous. ANALOGIES BETWEEN TRANSPORT PROCESSES: The three transport processes are Energy, Mass and Momentum

transport. The transfer of any of these entities is due to existence of driving force

or potential gradient. Transport process is governed by fundamental laws. Reference: Introduction to Heat Transfer, by C.B.Gupta & R.Prakash


- 5 -

Lecture 5

Chap.2 Heat Transfer By Conduction Conduction of heat means transport of heat energy in a medium from a region at a higher temperature to a region at a lower temperature without any macroscopic motion in the medium. The difference in temperature between the regions is responsible for the flow of heat and is called the temperature driving force. Heat conduction is also called diffusion of heat. The mechanism of heat conduction in a medium depends upon the state of the medium i.e. whether it is a solid, a liquid or a gas. In a solid, the molecular motion is restricted to variations about an equilibrium position. In the presence of a temperature gradient heat energy is transferred from one molecule to a neighboring molecule through molecular vibrations. In metals, however, conduction of heat occurs more through the drift of free electrons than by molecules in a gas (free electrons are often referred to as electron gas), and that is why a material having good electrical conductivity also possesses good thermal conductivity.

Steady State Heat Conduction In Plane Wall

21 TTkAQ

dxdTkq x

Steady State Heat Conduction In A Composite Wall: For a ‘single-layered’ plane wall, the rate of heat conduction Q can be calculated directly from Eq.2.1, if the surface area A, the wall thickness l, the thermal conductivity k, and the temperature difference are known. We can extend the same equation to the case of a composite or ‘multi-layer’ wall.

Akl

Akl

Akl

TTQ

3

3

2

2

1

1

41

The thermal resistance RT of the composite wall is given by

QTT

Akl

Akl

Akl

RRRRT41

3

3

2

2

1

1321

Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 6 -

Lecture 6 Steady State Heat Conduction In A Composite Wall With Parallel And Series Heat Flows:

In several practical applications, composite structures found containing a combination of series and parallel heat flows.An example of such a composite plane wall is shown in fig. In which the wall is made of three sections. First section of thickness l1 is made of material with thermal conductivity k1, The intermediate section of thickness l2 is made of two different materials with thermal conductivities k2 and k3. The material with thermal conductivity k2 has a breadth of b1 while the other material has a breadth of b2. The third section is made of a material with thermal conductivity k. Thermal resistance of each layers can be calculated as

AkR

.

As the second section contains two parallel sub sections in it.

So, cB RRR

111

2

And total R = RA + R2 + RD

= AkbkbkA

bbAk 4

3

2312

212

1

1

where, A = h x b

Examples based on Heat Transfer through Plain/ Composite Wall Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 7 -

Lecture 7 Steady State Heat Conduction Through Variable Area:

In the case of a plane wall the area for heat flow is constant. However, there are solids of other geometries in which the area for heat flow is variable. Two common geometries of practical importance are cylindrical and spherical, in both of which the area depends upon the radius or the radial position.

Steady State Heat Conduction In Hollow Cylinder:

Rate of heat flow through thick walled cylinder

Q= k(2πL) (T1-T2)/ ln (r2/ r1) --- (IV)

Heat Conduction through pipes and through pipe insulation is an example of heat conduction in a hollow cylinder.

Examples based on Steady State Heat Conduction In Hollow

Cylinder Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 8 -

Lecture 8 Combined Heat Transfer Through A (two layered) Composite Cylinder: Consider a thick walled hollow cylinder with inside radius r1, outside radius r2 ,

length ℓ & made up of material with thermal conductivity KA. The cylinder is

covered with a layer of material having thermal conductivity KB.

30

2

3

1

2

1

0

11.

1.1

2

rh

rrn

k

rrn

krh

ttLQ

BAi

i

Compare this equation with Q = UA t

Lrh

rrn

Lk

rrn

LkLrh

tttAUQ

BAi

i

30

2

3

1

2

1

0

21

21

2.1

21

Where U is the overall heat transfer coefficient. The overall heat transfer

coefficient can be defined based on any area A. Since it is more practical and convenient to measure the outside diameter of the pipe, the overall heat transfer coefficient is usually defined based on the outer surface area A.

0

2

33

1

23

1

3 1

1

hkr

rr

kr

rr

rhr

U

BAi

o

Similarly we can get


- 9 -

3

12

31

1

21.1

1

rhr

kr

rr

kr

rr

h

Ui

oBAi



- 10 -

Lecture 9 Logarithmic Mean Radius: If we open the cylindrical body, we will get the flat wall. It is considered

convenient to have an expression for the heat flow through a hollow cylinderof

the same form as that for a plane wall. Then the thickness will be equal to (r2-r1)

and the area A will be an equivalent area Am. we can correlate both equations as

follow :

1. Logarithmic Mean Radius of hollow cylinder

rm =

1

2

12

rr

rr

Logarithmic Mean Radius of hollow cylinder

It is radius which when applied to integrated equation for a flat wall, will give

correct rate of heat flow through a thick walled cylinder.

2. Logarithmic Mean Radius of hollow sphere Am=4 π rm

2 = 4π r1 r2 rm = 21 rr Logarithmic Mean Radius of hollow sphere

The Logarithmic Mean Radius is more convenient than arithmetic mean radius &

whereas Arithmetic Mean is used with appreciable error.



- 11 -

Lecture 10 Heat Transfer by Conduction Through Hollow Sphere: Of all the geometrical

configurations, a sphere has the largest volume per unit surface area. Since heat

losses are dependent on surface area, a hollow spherical vessel is usually used

to store fluids at low temp. (liquid nitrogen) to minimize heat losses and hence to

reduce the rate of evaporation. If the interior and exterior surfaces of a spherical

vessel are maintained at constant temperature, the conduction through the

spherical shell is a one-dimensional steady state process.

Q = 4K(T1-T2). r1 r2/(r2-r1)

Q = 4K.rm2(T1-T2)./(r2-r1)

Where rm = 21rr = mean radius which is geometric mean for sphere.

Combined Heat Transfer Through A (two layered) Composite Sphere

230322

23

211

122

1

0

1)()(1)(4

rhrrKrr

rrKrr

rh

ttQ

i

i

Examples based on Combined Heat Transfer Through A Hollow / (two layered) Composite Sphere



- 12 -

Lecture 11 Thermal Insulation: Insulation – General Aspects: Process equipments such

as reaction vessel, Reboiler, distillation column, evaporator etc. or a steam pipe

will lose heat to atmosphere by conduction, convection & radiation. In such

cases, conservation of heat i.e. usually of steam & coal is economic necessity &

therefore, some form of lagging should be applied to hot surface. In furnaces

surface temp. is reduced substantially by making use of series of insulating

bricks that are poor conductors of heat.

Insulation: A material, which retards the flow of heat with reasonable

effectiveness, is known as ‘Insulation’. Insulation serves the following two

purposes:

(I) It Prevents the heat flow from the system to surroundings

(II) It prevents the heat flow from the surroundings to the system.

Application: Factors Affecting Thermal Conductivity The Optimum Thickness Of Insulation:



- 13 -

Lecture 12 / 13 Critical Thickness of Insulation:

“The thickness up to which heat flow increases and after which heat flow

decreases is termed as Critical thickness. In case of cylinders and spheres it is

called ‘critical radius’.

A. Critical Thickness Of Insulation For Cylinder: r2 ( = r0) = k/h0

The above relations represents the condition for minimum resistance and

consequently *maximum heat flow rate. The insulation radius at which resistance

to heat flow is minimum is called the ‘critical radius’ (rc). The critical radius rc is

dependent of the thermal quantities k and h0 and is independent of r1 (i.e cylinder

radius)

B: Critical Thickness Of Insulation For Sphere.

Refer fig. The equation of heat flow through a sphere with insulation is given

as

r2 (=rC) =2k/h0

Examples base on critical radius for cylinder/ sphere Summery of the equation for heat transfer by conduction through different Objects Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 14 -

Lecture 1 CONVECTION:

“It is the transfer of heat within a fluid by mixing or circulation of one portion of fluid with another.”

Convection is the transfer of heat from one point to another within or between fluids or between a fluid and a solid.

The effectiveness of heat transfer by convection depends largely upon the mixing motion of the fluid.

Convection is of two types. They are: - (1) Natural/Free Convection (2) Forced Convection

FREE OR NATURAL CONVECTION: - If the motion of fluid is caused by density difference produced by temperature gradient, then it is known as Free/Natural Convection.

FORCED CONVECTION: - If the motion of fluid is caused artificially by some external agency like pump, fan, blower, etc. then it is known as forced convection. In this case, fluid motion is independent of density gradients.

NEWTON’S LAW OF COOLING:- The law for convective heat transfer between a surface and an adjacent fluid is,

Q = hA (ts - tf)

Where Q=Convective heat flow rate A=Area exposed to heat transfer ts & tf = surface and fluid temperature

h= convective heat transfer coefficient or film coefficient

LAMINAR AND TURBULENT FLOW LAMINAR FLOW: When the flow is laminar, the molecules move in the streamlined fashion or in flat or curved un-mixing layers/streams. There is no lateral mixing and no eddies are present. TURBULENT FLOW: When the motion of fluid particles is highly irregular and has no specific direction it is known as turbulent flow. The flow is no more a streamlined flow and eddies of various sizes are formed in the flow.



- 15 -

Lecture 2 BOUNDARY LAYER:- It is that part of flowing fluid in which the motion is affected by the presence of a solid boundary. Two types of boundary layer are (1) Hydrodynamic boundary layer (2) Thermal boundary layer THE NUSSELT NUMBER:-

Methods available for the calculation of value of h or Nu may be (i) Dimensional Analysis (ii) Solution of Boundary layer equations (iii) Analogy between heat and momentum transport

DETERMINATION OF NUSSELT NUMBER:

Nu = hL/k From the above equation, greater convective coefficient is obtained at thinner boundary layer. Hence to promote heat transfer, the boundary layer thickness (δ) should be reduced.

SIGNIFICANCE OF DIMENSIONLESS NUMBERS:-

1. REYNOLDS NUMBER (Re): 2. PRANDTL NUMBER (Pr): 3. NUSSELT NUMBER (Nu) :- 4. STANTON NUMBER (St):- 5. GRASHOFF NUMBER (Gr):-

FORCED CONVECTION:-

1 FILM TEMPERATURE:

2 MEAN TEMPERATURE: (BULK TEMPERATURE OR CUP-MIXING

TEMPERATURE) Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 16 -

Lecture 3-5

CORRELATIONS FOR FORCED CONVECTION IN LAMINAR FLOW : (a) LAMINAR FLOW OVER A FLAT PLATE: (Re < 5 x 105)

(i) Local value of heat transfer coefficient (h)

Nux = h x x / k = 0 . 3 3 2 ( P r ) 1 / 3 (R e x ) 1 / 2 a n d

R e x = x V ρ / μ It is also known as Blasius equation

(ii) Average value of heat transfer coefficient is given by

Nu = hL/k = 0.664 (Pr)1/3 (ReL) ½ and ReL= L V ρ / μ

(b) LAMINAR FLOW INSIDE PIPE (TUBES) (Re < 2300)

(i) SIEDER-TATE EQUATION: Nu = 1.86 (Re. Pr. D/L)1/3 14.0

w

b

CORRELATIONS FOR FORCED CONVECTION IN TURBULENT FLOW:

(a) TURBULENT FLOW OVER A FLAT PLATE: (Re > 5 X 105 )

(i) Local heat transfer coefficient: Nu x = h x*x/k = 0.0296 (Pr)1/ 3 (Re

x)0 .8

(ii) Average heat Transfer Coefficient Nu = hL/k = 0.037 (Pr)1/ 3

(Re)0 .8

(b) TURBULENT FLOW INSIDE TUBES: [0.5 < Pr < 120 and 2300 < Re <

107]

(i) Mc-Adams Equation:

hD / kb = 0.023 4.08.0

kCpVD

b

OR Nu = 0.023 (Re)0.8 (Pr)0.4

(ii) DITTUS-BOELTER EQUATION:

Nu = 0.023 (Re)0.8 (Pr)n

Here the fluid properties are calculated at mean bulk fluid temperature.

(iii) COLBURN EQUATION:

Nu = hL/k = 0.023 (Re)0. 8 (Pr)1/ 3

St = Nu/Re.Pr = 0.023 (Re) –0.2 (Pr) –2/3


- 17 -

(iv) SIEDER-TATE EQUATION:

Nu = 0.023 (Re)0.8 (Pr)1/3 14.0

b

w


- 18 -

Lecture 6-8

FREE/NATURAL CONVECTION:- The free convection heat transfer may be correlated by an equation,

Nu = Φ (Gr) Ψ (Pr)

Gr = 2

23

tgL

If 104 < Gr*Pr < 109 , Laminar flow If 109 < Gr*Pr < 1012 , Turbulent flow

CORRELATIONS FOR FREE CONVECTION:-

(a) VERTICAL PLATES AND CYLINDERS:

(i) LAMINAR FLOW: 104 < Gr*Pr < 109 NuL = 0.59 (Gr*Pr)1/4

(ii) TURBULENT FLOW: 109 < Gr*Pr < 1012 NuL = 0.10 (Gr*Pr)1/3

(b) HORIZONTAL PLATE:

(i) upper surface heated or lower surface cooled for laminar, 105 < Gr*Pr ≤ 2 X 107 NuL = 0.54 (Gr*Pr)1/4,

for turbulent, 2 X 107 < Gr*Pr ≤ 3 X 1010 NuL = 0.14 (Gr*Pr)1/3,

(ii) lower surface heated or upper surface cooled

for laminar, 3 X 105 < Gr*Pr ≤ 3 X 1010 NuL = 0.27 (Gr*Pr)1/4,

For turbulent, 7 X 106 < Gr*Pr ≤ 11 X 1010, NuL = 0.107 (Gr*Pr)1/3,

(c) HORIZONTAL CYLINDERS:-

(ii) Laminar flow, 104 < Gr*Pr < 109 NuL = 0.53 (Gr*Pr)1/4,

(iii) Turbulent flow, 109 < Gr*Pr < 1012 NuL = 0.13 (Gr*Pr)1/3,



- 19 -

Lecture 9 Chap.4 Thermal Radiation

Introduction:

The exact nature of radiation is still not fully understood. Two theories have been proposed to explain the phenomenon of radiation:

Wave theory, proposed by Maxwell. Quantum theory, proposed by Max Planck.

Thermal radiations exhibit characteristics similar to those of visible light,

and follow optical laws. These can reflected, refracted and are subject to scattering and absorption when they pass through a media. They get polarized and weakened in strength with inverse square of radial distance from the radiating surface.

Surface Emission Properties

( I ) Total emissive power (E): ( II ) Monochromatic (spectral ) emissive power ( E ): (III) Emission from real surface – emissivity: Emissivity ( ) : Normal Total Emissivity, n, Absorptivity, Reflectivity and Transmissivity: By the conservation of energy principle, Ga + Gr + Gt = G Dividing both sides by G, we get Ga/G + Gr/G + Gt/G = G/G + + = 1 ----- ( I ) Black body: Opaque body: A transparent body White body: Reflections are of two types: Regular reflection diffused reflection, Gray body: Colored body Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 20 -

Lecture 10 Black body: A black body has the following properties: ( I ) It absorbs all the incident radiation falling on it and does not transmit or reflect regardless of wavelength and direction. ( II ) It emits maximum amount of thermal radiations at all wavelengths at any specified temperature. (III) It is a diffuse emitter ( i.e., the radiation emitted by a black body is independent of direction). The Stefan- Boltzmann Law:

i.e. Eb = σ T4 ------ (I ) Equation (I ) can be written as Eb = 5.67 ( T/100)4 Kirchhoff’s Law: The law states that at any temperature the ratio of total emissive power E to the total absorptivity α is a constant for all substances, which are in thermal equilibrium with their environment.

A1 E1 = α1 A1 Eb ε = α

(α is always smaller than 1. Therefore, the emissive power E is always smaller than the emissive power of a black body at equal temperature). Thus, kirchhoff’s law also states that the emissivity of a body is equal to its absorptivity when the body remains in thermal equilibrium with its surroundings. Plank’s Law: In 1990 Max Plank showed by quantum arguments that the spectrum distribution of the radiation intensity of a black body is given by

1exp

2)(

52

kTchhc

bE

---- (Planck’s law)

A plot of (Eλ)b as a function of temperature and wavelength is given in fig. It should be carefully noted that Plank’s distribution law holds for a hypothetical black body. Real surfaces show marked deviation from Plank’s law. Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 21 -

Lecture 11 Wien’s Displacement Law: In 1893 Wien established a relationship between the temperature of a black body and the wavelength at which the maximum value of monochromatic emissive power occurs. A peak monochromatic emissive power occurs at a particular wavelength. Wien’s displacement law state that the product of λmax and T is constant i.e λmax T = Constant i.e. λmax T = 2898 µ m K = 0.0029 m k This law holds true for more substances; there is however some daviation in the case of a metallic conductor where the product λmax T is found to be vary with absolute temperature. It is used in predicting very high temperature through measurement of wavelength. A combination of Planck’s law and Wien’s displacement law yields the condition for the maximum monochromatic emissive power for black body.

110*898.210*4388.1exp

10*898.210*374.0

1exp

)(max)(

3

2

5315

max

2

5max1

T

TC

CE b

or (Eλb )max = 1.285 * 0.10-5 T5 W/m2 per meter wavelength Key points :

1. To find Emissive power or Total Emissive power, use Stefan Boltzmann Law

2. To find Monochromatic Emissive power, use Planck’s Law 3. To find wavelength or Temperature at which radiation is maximum, use

Wien’s law. 4. To find maximum Monochromatic Emissive power of body, use

combination of Planck’s Law & Wien’s law. Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 22 -

Lecture 12 Radiation Shields: In certain situations it is required to reduce the overall heat transfer between two radiating surfaces. This is done by either using materials which are highly reflective or by using radiation shields between the heat exchanging surfaces. The radiation shields reduce the radiation heat transfer by effectively increasing the surface resistances without actually removing any heat from the overall system. This sheets of plastic coated with highly reflecting metallic films on both sides serve as very effective radiation shields. These are used for the insulation of cryogenic storage tanks. A familiar application of radiation shields is in the measurement of the temperature of a fluid by a thermometer or a thermocouple which is shielded to reduce the effects of radiation.

The bulb of a thermometer or a thermocouple junction, used for measurement of fluid temperature, should be shielded in order to reduce radiation effects to minimum. Otherwise the temperature indicated may involve some error.

Refer blow fig. Let us consider two parallel planes, 1 and 2, each of area A ( A1 = A2 = A) at temperatures T1 & T2 respectively with a radiation shield placed between them as shown in below fig.

111111

111

])[(])[(

2231

21

12

12

shieldwithoutnet

shieldwithnet

QQ

- (VII)

21211)(

)(

321

42

41

12

TTAQ net



- 23 -

Lecture 13 Heat transfer with change of Phase

The most important processes which are associated with change of phase

(I) Boiling

(II) Condensation

(III) Melting or Solidification

(IV) Sublimation

Nu and Pr are familiar for single phase convection, here some new dimention

less parameters are Jakob number Ja and Bond nuimber Bo are used.

Jakob number Ja = CpΔt/λ is the ratio of the maximum sensible energy

absorbed to the latent heat.

Bond number Bo = g(ρl - ρv)L2/ σ, is the ratio of the gravitational body force to

the surface tension force

Phenomena of Boiling: The boiling heat transfer process may occur in the following forms or different

regimes of boiling are as follows:

(A) According to applied forces:

( I ) Pool boiling

( II ) Forced Convection boiling

(B) According to Temperature:

( I ) Sub cooled or local boiling

( II ) Saturated or boiling with net evaporation

The first two forms of boiling depends upon the presence of bulk fluid motion

while the last two forms depends on the bulk liquid temperature.

Pool Boiling (Free Convection Boiling)

Forced Convection Boiling

Sub cooled or Local Boiling

Saturation boiling or boiling with net evaporation:



- 24 -

Lecture 14 Regimes of pool boiling: - The phenomena of pool boiling is characterized by different regimes

- Nukiyama, in 1934 actually distinguished the existence of various regimes of

boiling. Brew and Miller extended the theory further in 1937.

- Consider the case of pool boiling of water, Over a heated flat plate or hot wire

submerged in a pool or water, at tsat. After getting the datas, the heat flux (q/A) is

plotted against the excess temperature Δte = (tW – tsat).

The boiling phenomena is divided in three types of boiling which takes place in

six regimes as shown in the table

Sr. No.

Type of Boiling Regime No.

Type of Regime

1 Interface

Evaporation

1 Free convection boiling

2 Nucleate boiling 2

3

Bubbles form but condense as they rise.

Bubbles rise to interface causing rapid

evaporation

3 Film Boiling 4

5

6

Partial nucleate boiling with unstable film

Stable film boiling

Radiation Predominant

( I ) Interface Evaporation: (II) Nucleate Boiling (III ) Film Boiling

Critical heat flux point/ Burnout point/Boiling crisis point Leiden frost point: Point D on the boiling curve, where the heat flux

becomes minimum due to the film resistance, is called Leiden frost point.

Here heat is a minimum qD = qmin., and the surface is completely covered by a

vapour blanket. Heat Transfer from the surface to the liquid occurs by

conduction through the stable vapour film.


- 25 -



- 26 -

Lecture 15 Nucleate boiling The nucleate boiling is of maximum engineering importance. It involves two processes. ( a ) The nucleation or formation of bubbles

( b ) The subsequent growth and motion of these bubbles

Factors affecting nucleate boiling:

The nucleate boiling is affected by the following factors: 1. Material, Shape and condition of heating surface.

2. Liquid properties

3. Pressure

4. Mechanical agitation

( a ) Nucleation - Three typical shapes of vapor bubbles may be observed as shown in the figure

below

( I ) Unwetted Surface ( II ) Partially wetted surface (III ) Totally wetted surface Bubble growth and collapse

Bubble Growth and Motion: Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 27 -

Lecture 16 Condensation Phenomena: - Condensation is reverse of boiling

There are two types of condensation.

( I ) Filmwise Condensation

( II )Dropwise condensation

( I ) Film Condensation:

( II ) Dropwise condensation: Difference between Drop- wise Condensation and Film- wise Condensation



- 28 -

Lecture 16 Chap.6 HEAT EXCHANGERS

Heat exchange devices are indispensable parts of systems that exchange energy between hot and cold materials. Heat exchange devices are widely used in everyday life, industrial processes, and all situations that employ hot and cold materials to transmit and exchange energy.

Classification of Heat Exchangers

Heat exchanger is an apparatus or an equipment in which effective transfer of heat takes place between a hot fluid & cold fluid.

The purpose of this exchanger is to remove heat from a fluid or to add heat to a fluid.

Examples: Boilers & Condensers in steam plant, heaters & coolers, oil coolers of heat engine, automobile radiators, evaporators & condensers in refrigeration unit, etc.

TYPES OF HEAT EXCHANGERS The various types of heat exchangers are:

I. Nature of heat exchanger process. II. Relative direction of fluid motion. III. Design and constructional features. IV. No. of Passes V. Physical state of fluids.

NNAATTUURREE OOFF HHEEAATT EEXXCCHHAANNGGEERR PPRROOCCEESSSS..

Heat exchangers are further classified as: 1) DIRECT CONTACT (OR OPEN) HEAT EXCHANGER. 2) INDIRECT CONTACT HEAT EXCHANGERS. 1) DIRECT CONTACT (OR OPEN) HEAT EXCHANGERS.

2) INDIRECT CONTACT HEAT EXCHANGERS.

i. REGENERATORS ii. RECUPERATERS



- 29 -

Lecture 17

RELATIVE DIRECTION OF FLUID MOTION According to the relative direction of two fluids, the exchangers are further classified as 1) PARALLEL / COCURRENT/ UNIDIRECTIONAL FLOW HEAT EXCHANGER. 2) COUNTER FLOW HEAT EXCHANGER. 3) CROSS FLOW HEAT EXCHANGER. 1) PARALLEL / UNIDIRECTIONAL FLOW HEAT EXCHANGERS. 2) COUNTER FLOW HEAT EXCHANGERS. 3) CROSS FLOW EXCHANGERS.

In these exchangers, the two fluids flow at right angles to each other. Two different arrangements are commonly used. In one case, each of the fluids is unmixed as it flows through the heat

exchanger. Due to this, temperatures of the fluids leaving the exchanger are not uniform.

PHYSICAL STATE OF FLUIDS

They are further divided in to 1) CONDENSERS 2) EVAPORATERS

1) CONDENSERS

In condensers, the condensing fluid remains at constant temperature throughout the exchanger while cold fluid temperature gradually increases from inlet to exit.

The hot fluid looses latent heat which is taken up by cold fluid. The temperature distribution is shown in the FIGURE below.

2) EVAPORATERS

In evaporators, the boiling fluid (cold fluid) remains at constant temperature while the hot fluid temperature gradually decreases.

The temperature distribution is shown in the FIGURE above. In both exchangers, since the temperature of one of the fluid remains

constant, it is immaterial whether the fluids flow in same direction or opposite.



- 30 -

Lecture 18 DESIGN & CONSTURUCTIONAL FEATURES On the basis of design & constructional features, the heat exchangers are classified as: DOUBLE PIPE HEAT EXCHANGER SHELL AND TUBE HEAT EXCHANGER MULTIPLE SHELL AND TUBE HEAT EXCHANGER COMPACT HEAT EXCHANGERS

a) FINNED HEAT EXCHANGER / EXTENDED HEAT EXCHANGERS b) PLATE TYPE HEAT EXCHANGER c) SPIRAL HEAT EXCHANGER

ADVANTAGES

DISADVANTAGES OTHER TYPES OF SHELL AND TUBE HEAT EXCHANGER

They are classified as: A. Fixed tube heat exchanger B. Floating head heat exchanger C. U-tube heat exchanger D. Reboiler / Kettle type heat exchanger

a) With internal floating head b) With U tube (hair pin)



- 31 -

Lecture 19 -20 Heat Exchanger Performance: For designing or predicting the performance of a heat exchanger it is necessary that the total heat transfer may be related with its governing parameters: (i) U (overall heat transfer coefficient) due to various modes of heat transfer, (ii) A total surface area of the heat transfer, and (iii) t1, t2 (the inlet and outlet fluid temperatures). OVERALL HEAT TRANSFER COEFFICIENT (U):

UA= oow

io

ii hAkLrr

hA1

2ln1

1

U i =

oo

i

w

ioi

i hAA

kLrrA

h1

2ln1

1

…………………..…. (iii)

U o =

ow

ioo

ii

o

hkLrrA

hAA 1

2ln1

1

…………………………. (iv)

U i =

oo

iio

w

i

i hrrrr

kr

h1ln1

1

…………………………. (v)

U o =

oio

w

o

ii

o

hrr

kr

hrr 1ln1

1

……………………… (vi)

SCALE FORMATION / FOULING ON SURFACES OF TUBES FOULING FACTOR (R s ):

U o =

osoio

w

o

sii

o

ii

o

hhrr

kr

hrr

hrr 11ln11

1



- 32 -

Lecture 21-22 LOGARITHMIC MEAN TEMPERATURE DIFFERENCE (LMTD):

In a heat exchanger the temperatures of the hot and cold fluids keep on changing from point to point along the length of exchanger. In such cases mean temperature difference when multiplied by U and appropriate A will give the correct heat flow rate.

Logarithmic Mean Temperature Difference (LMTD) is the temp – difference, which if constant, gives the same rate of heat transfer as actually occurs under different temperature differences.

CASE I: PARALLEL FLOW ARRANGEMENT

mt =

11

22

1122

lnch

ch

chch

tt

tttttt

OR mt =

1

2

12

lntt

tt

Where 2t & 1t denote the difference between the temperatures of hot and cold fluids at A = A and A = 0 respectively. Lecture 31 CASE (2) ( COUNTER FLOW ARRANGEMENT)

mt =

11

22

1122

lnch

ch

chch

tt

tttttt

OR mt =

1

2

12

lntt

tt

Where 2t & 1t denote the difference between the temperatures of hot and cold fluids at A = A and A = 0 respectively.

Examples based on LMTD Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 33 -

Lecture 23-24

LMTD CORRECTION FACTORS The mean temperature difference is strictly applicable only to parallel flow

and counter flow exchangers in which the two fluids flow only once across the exchanger i.e. single pass heat exchangers.

For multipass parallel and counter flow exchangers or with cross flow exchangers, first of all LMTD is to be calculated for single pass exchanger and then this LMTD is multiplied with correction factor F. This LMTD correction factor F, which takes into account the actual flow arrangement of the exchanger Thus Q = U A mT ; (for single pass exchanger)

Q = U A F wcounterflomt (for multipass or cross flow exchanger)

The correction factor F is calculated from charts. The factor F is a function of two dimensionless variables.

1. Capacity ratio R 2. Temperature ratio

The capacity ratio, R is defined as follows: Heat capacity of the fluid passing through tube R = ______________________________________ Heat capacity of the fluid passing through shell

= ss

tt

cmcm

Where suffices t and s denotes the fluid flowing through the tube or shell resp. Since

2112 sssstttt ttcmttcm

R = ss

tt

cmcm =

12

21

tt

ss

tttt

=

tube

shell

tt

The temperature ratio, is defined as;

= 11

12

ts

tt

tttt

=

inlet

tube

tt

Examples based on LMTD and Heat Exchanger Design



- 34 -

Lecture 25

HEAT EXCHANGER EFFECTIVENESS The effectiveness of a heat exchanger or temperature effectiveness is denoted by ε. It is defined as: The actual heat transfer rate ε = ----------------------------------------------------- The maximum possible heat transfer rate Theoretically, maximum heat transfer rate will occur with a counter flow heat exchanger if very large area when either of the following conditions is attained :

(a.) The exit temp. of the cold fluid equals the entry temp. of the hot fluid i.e. 12 hc tt

(b.) The exit temp. of hot fluid equals the entry temp. of the cold fluid i.e.

12 ch tt

ε =

11

12

min ch

ccc

ttCttC

……………………………….. (vii)

OR

ε =

11

21

min ch

hhh

ttCttC

Calculation Steps:

1. Draw Temperature Profile 2. Tabulate all given data 3. Calculate Q by Q = mCpΔt (either for cold or hot fluid) 4. Find missing temperature of any one fluid 5. Find Δtm 6. Find U. 7. Find A by Q = UAΔtm 8. Find diameter or no. of tubes etc.



- 35 -

Lecture 26 Shell and Tube Heat Exchanger: Construction Details of Heat Exchangers: SHELL TUBES TUBE PITCH CLEARANCE TUBE ARRANGEMENT The tubes are commonly laid on either 1) SQUARE PITCH 2) TRIANGULAR PITCH TUBE SHEET BAFFLES Classification of Transverse Baffles: BAFFLE SPACERS

ALLOCATION OF FLUIDS: SHELL OR TUBES DIFFERENT TYPES OF SHELL AND TUBE HEAT EXCHANGER

FIXED TUBE HEAT EXCHANGER This is the simplest type of heat exchanger. In fixed tube sheet heat exchanger, the tube sheets are welded to the

shell at both ends so that the shell & tube sheet material must be weld able to each other.

The shell is equipped with two nozzles for entry and exit of shell side fluid. FLOATING HEAD HEAT EXCHANGER U – TUBE HEAT EXCHANGER KETTLE REBOILERS / REBOILER EXCHANGER Kettle reboilers are of two types: 1) Internal floating head arrangement 2) U-tube arrangement. FINNED TUBE HEAT EXCHANGER / EXTENDED SURFACE EXCHANGER TYPES OF FINS i. LONGITUDINAL FINS ii. TRANSVERSE FINS Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 36 -

Lecture 27 PLATE TYPE HEAT EXCHANGER Plate type heat exchanger consists of series of rectangular parallel plates

held firmly together between substantial head frames. The plates have corner ports which permit the entry & exit of hot & cold fluid. The corner ports are sealed by gaskets & the plate edges are also sealed. The plates serve as heat transfer surfaces.

SPIRAL-PLATE HEAT EXCHANGER The plates are frequently of stainless steel & have corrugated faces which in

turn gives a high degree of turbulence even at low flow rates. The gap between the plates is 1.3 to 1.5mm & is provided with inlet & outlet

nozzles for fluids at ends. The hot fluid passes through alternate gaps i.e. between alternate pairs of

plates, transferring heat to cold fluid in the adjacent spaces. These exchangers are successfully used in dairy & brewery industries. Moreover they are relatively effective with viscous fluids with viscosities up to

about 300 poise. ADVANTAGES 1. They are very compact and requires very small floor space & provides large

heat transfer area in small volume. 2. It gives low pressure drop. 3. There is an absence of inter leakage of fluids. 4. Easy in dismantling for inspection & cleaning. 5. High heat transfer coefficient than shell & tube heat exchanger. 6. It is mostly used when close control of temperature is required & in case of

heat sensitive materials. 7. Heat transfer area can be increased by adding more plates. DISADVANTAGES 1. The maximum operating pressure is limited to 30 bar. 2. The operating temperature of any fluid used is limited to 250 C due to gasket

material.



- 37 -

Lecture 27 Evaporators

INTRODUCTION:

1. Classification of Evaporators: Accordingly, most evaporators are broadly classified as: (1) natural circulation, and (2) forced circulation. There are a few other types of widely used evaporators which will be discussed here.

Evaporation can be divided into three categories on the basis of boiling phenomena. i) Pool boiling: In this phenomena bulk or pool of liquid boils. Examples are

kettle boiling, natural circulation boiling units, thermo siphon reboilers in distillation.

ii) Convection heating and boiling: Example is forced circulation-boiling units.

iii) Film evaporation: In film evaporation, a thin liquid film is maintained on the heating surface.

Evaporators can be classified as : 1 Solar evaporator 2 Batch pan evaporator 3 Natural circulation evaporator 4 Short tube vertical evaporator 5 Horizontal tube evaporator 6 Basket type evaporator 7 Long tube vertical evaporator 8 Forced circulation evaporator 9 Rising film evaporator 10 Falling film evaporator 11 Agitated thin film evaporator 12 Horizontal spray film evaporator 13 Plate type evaporator 14 Vapour compression evaporator 1.1 Solar evaporator: 1.2 Batch pan evaporator: 1.3 Natural circulation evaporator: 1.4 Short tube vertical (STV)/horizontal evaporator: Lecture 28 1.5 Horizontal tube evaporator: 1.6 Basket evaporator: 1.7 Long tube vertical (LTV) evaporator: 1.8 Forced circulation evaporation: 1.9 Rising film evaporator 1.10 Falling film evaporator: 1.11 Agitated thin film evaporator:


- 38 -



- 39 -

Lecture 29

1.12 Horizontal spray film evaporator:

1.13 Plate Type Evaporator Characteristics of different types of evaporators Evaporator Typical products handled Comments Calandria Forced circulation

Falling film Natural circulation (Thermosyphon)

Agitated film Rising film Plate type

There is wide variation in characteristics of liquor to be concentrated that requires judgment and experience in designing and operating evaporators. Some of the properties of evaporating liquids that influence the process of evaporation are:

i) Concentration: (ii) Foaming: (iii) Scale: (iv) Temperature sensitivity: (v) Materials of construction: Performance of tubular evaporators: The performance of a steam heated tubular evaporator is evaluated in terms of (i) capacity and (ii) economy Capacity: Capacity of an evaporator is defined as the number of kilogram of water vaporized or evaporated per hour. Evaporator economy: Economy of an evaporator is defined as the number of

kilogram of water evaporated per kilogram of steam fed to the evaporator. It is also called as steam economy. In single-effect evaporator the amount of water evaporated per kg of steam

fed is always less than one and hence economy is less than one. The fact that the latent heat of evaporation of water decreases as the pressure increases tends to make the ratio of water vapour produced per kg of steam condensed less than unity, Increase in economy of an evaporator is achieved by reusing the vapour produced. Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta


- 40 -

Lecture 30 The methods of increasing the economy are: (i) use of multiple effect evaporation system (ii) vapour recompression,

Boiling point elevation:

Material and enthalpy balances for single-effect evaporator: Overall material balance: Single- and Multiple-effect Evaporators The simplest method of evaporation is to feed the solution to the evaporator which is provided with sufficient heat transfer area. The vapour generated is condensed using a 'surface condenser' or a 'direct contact condenser'. The concentrated product is drawn from the bottom. This is called a single-effect evaporator.

Although simple in operation, a single-effect evaporator does not utilize steam efficiently. More than a kilogram of steam (1.1 to 1.3 kg is common) is needed in order to vaporize 1 kg of water from the solution. The reasons are the following:

(i) Very often, the feed temperature remains below its boiling point. A part of the steam is utilized to supply the sensible heat required to raise the feed to its boiling point. (ii) The latent heat of vaporization of water decreases with increasing

temperature. Steam condensing in the steam chest is at a higher temperature than that of the solution. So the latent heat released by condensation of 1 kg steam is less than that required for vaporization of 1 kg of water from the boiling solution.

(iii) Some amount of heat loss from the evaporator to the ambient always occurs. Now let us consider an arrangement in which two evaporators are put in series

such that the vapour generated in one is fed to the steam chest of the second for heating. Partly concentrated solution flows from the first to the second where it attains the desired final concentration. The vapour generated in the second evaporator is sent to a condenser. The arrangement is called the double-effect evaporator.

One important point is to be noted in this connection. The vapour leaving evaporator-1 is at the boiling temperature of the liquid leaving the first effect. In order that transfer of heat occurs from the condensing vapour (from evaporator-1) to the boiling liquid in evaporator-2 (i.e. the second effect), the liquid in evaporator-2 must boil at a temperature considerably less than the condensation temperature of the vapour in order to ensure reasonable driving force for the transfer of heat. A method of achieving this is to maintain a suitable lower pressure in the second effect (evaporator-2) so that the liquid boils in it at a lower temperature. If the first evaporator operates at atmospheric pressure, the second one must do so under vacuum.


- 41 -



- 42 -

Lecture 31-32 2. Multiple Effect Evaporators: A multiple-effect evaporator has been shown in Fig., and its operating principles have been briefly described. The type of the multiple-effect evaporator shown in Fig. is called the backward feed because the steam and the liquor flow in opposite directions. There are other types of feeding arrangements too. Evaporators up to fifteen effects are known to be in use. Multiple-effect evaporators allow high steam economy.

Multiple effect evaporators are classified as: i) Forward feed arrangement. ii) Backward feed arrangement. iii) Parallel feed arrangement. iv) Mixed feed arrangement.

Comparison between the Forward and Backward Feed Modes Table : Advantages and limitations of different modes of feed supply to multiple-effect evaporators Mode of feed supply

Advantages Limitations

Forward feed Backward feed Mixed feed Parallel feed Criteria for Selection of Evaporator:

The selection of evaporator is done on the basis of: 1. Factor related to process 2. Factor related to mechanical design


chap.1. fundamentals of heat transfer heat transfer by conduction conduction of heat means transport...

Documents