HEAT TRANFER LECTURE NOTES

8/13/2019 HEAT TRANFER LECTURE NOTES

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HEAT AND MASS TRANSFER

Prabal Talukdar Associate Professor

De artment of Mechanical En ineerin

IIT Delhi

[email protected]

MECH/IITD


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Course Coordinator: Dr. Prabal Talukdar Room No: III, 368

E-mail: [email protected]

Lectures: Tue, Wed, Fri: 9-9.50 a.m.(Room No: IV LT1)

Tut: 1-1.50 p.m.Course webpage:http://web.iitd.ac.in/~prabal/courses.htmlPre-requisite: Fluid Mechanics (AML 160)

(Tentative Room no: III352

MEL 242: Heat and Mass Transfer (3-1-0)Syllabus (for total 42 lectures)Introduction and basics of to heat transfer : Modes of heat transfer, Fouriers law, conductivity, diffusivity.Heat conduction e uation : 1D Heat conduction General heat conduction e uation Boundar and initialconditions, Heat generation.Steady heat conduction : Heat conduction in plane wall, cylinder, sphere, network analysis, critical radius of insulation, heat transfer from fins.Transient heat conduction: Lumped system analysis, transient heat conduction in large plane walls, longcy n ers an sp eres w spa a e ec , e s er an ro er c ar sNumerical methods of heat conduction : Finite difference formulation, numerical methods for 1D and 2D steadystate heat conduction.( 10 lectures)Introduction to convection : Fundamentals, Velocity and thermal boundary layer, laminar, turbulent flows,

conservation equations for mass, momentum and energy, solution of boundary layer equations, Analogy betweenheat and momentum transfer, Non-dimensional numbersExternal heat transfer : Drag and heat transfer, parallel flow over flat plates, flow across cylinders and spheresInternal heat transfer : Mean velocity and mean temperature, entrance region, constant heat flux and temperature

, ,Natural/free convection : Equation of motion of Grashof number, natural convection over surfaces and inside

enclosures( 13 lectures)


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Boiling and condensation : Boiling heat transfer, pool boiling, flow boiling, condensation heat transfer, filmcondensation, heat transfer correlations.

Heat Exchangers : Types of heat exchangers, overall heat transfer coefficient, analysis of heat exchangers, thelog mean temperature method, -NTU method.( 4 lectures)Introduction to radiation : Fundamentals, radiative properties of opaque surfaces, Intensity, emissive power,ra os ty, anc s aw, en s sp acement aw, ac an ray sur aces, m ss v ty, a sorpt v ty, pectra an

directional variations, Stephan Boltzmann law, Kirchhoffs lawView factors : Definitions and relations, radiation heat transfer between two black surfaces, between diffuse graysurfaces, network method above two surfaces, re-radiating surface, radiation shield, radiation effects ontem erature measurements.( 7 lectures)Mass Transfer : Introduction, analogy between heat and mass transfer, mass diffusion, Ficks Law, boundaryconditions, steady mass diffusion through a wall, cylinder and sphere, water vapour migration in buildings,transient mass diffusion, mass transfer in a moving medium, diffusion of vapor through a stationary gas: Stefan

( 4 lectures)

Quiz Quiz 1 Quiz 2Tentative Date Au ust 27 ovember 5

Evaluation:Tuts and Quiz (2 nos): 20% (Closed note, book)

,Minor Test II: 25% (Open note, closed book)Major Test: 35% (Open note, closed book)Total: 100%Textbook: Fundamental of Heat and Mass Transfer: F. P.

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Incropera and D. P. DewittHeat Transfer: Yunus A. Cengel

Heat Transfer: J.P. Holmann


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Heat Transfer as a Course Has a reputation for being one of the most challenging,fundamental, conceptual courses in ME. It is the heart oft erma eng neer ng

Why?? , ,

theory, fluid mechanics, radiation theory

Higher-level math: vector calculus, ODEs, PDEs, numerical

Physically elusive: heat is invisible; developing intuition takestime

Appropriate assumptions: required to simplify and solve most problems

However, Heat Transfer is interesting, fun, and readily

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applicable to the real world


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Heat Transfer Applications

Heat transfer is commonly encountered in engineering systems andother aspects of life, and one does not need to go very far to see some

.

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Human bod

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Heat Transfer - Thermod namics Thermodynamics is concerned with the amount of heat transfer as a

system undergoes a process from one equilibrium state to another,

and it gives no indication about how long the process will take. A thermodynamic analysis simply tells us how much heat must be

conservation of energy principle.

We are normally interested in how long it takes for thehot coffee in a thermos to cool to a certaintemperature, which cannot be determined from a

. Determining the rates of heat transfer to or from a

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,variation of the temperature, is the subject of heat transfer


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Definition Heat transfer is energy transfer due to a temperature difference in a

medium or between two or more media

Different types of heat transfer processes are called different modesof heat transfer

Conduction heat transfer is due to a temperature gradient in astationary medium or media

Convection heat transfer occurs between a surface and a movin fluid at different temperatures

Radiation heat transfer occurs due to emission of energy in the

orm o e ec romagne c waves y a o es a ove a so u e zerotemperature Net radiation heat transfer occurs when there exists a temperature

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difference between two or more surfaces emitting radiation energy


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Conduction Conduction heat transfer is due to random molecular and atomic

vibrational, rotational and translational motions High temperature and more energetic molecules vibrate more and

transfer energy to less energetic particles as a result of molecularcollisions or interactions

& is characterized by a transport property know as the Thermal Conductivity, k (W / m K)

x

W = watts m = Meters K = temperature in Kelvin

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particles of a substance to the adjacent less energetic ones as aresult of interactions between the particles.

Conduction can take place in solids, liquids, or gases. In gases andliquids, conduction is due to the collisions and diffusion of themolecules during their random motion. In solids, it is due to thecombination of vibrations of the molecules in a lattice and theenergy transport by free electrons

geometry of the medium, its thickness, and the material of themedium, as well as the temperature difference across the medium

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Fouriers Law(W)

TkA

TTkAQ 12cond

=

=&

In the limiting case of x 0, the equation above reduces to thedifferential form Fouriers law of heat

conduction after J. Fourier,who expressed it first in his

heat transfer text in 1822

(W)

dx

dTkAQ cond =

&

transfer in the positive x direction is a

positive quantity

T1=T2 =

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Thermal Conductivit Specific heat C p is a measure of a materials ability to store thermal

ener . For exam le C = 4.18 kJ/k C for water and C = 0.45

kJ/kgC for iron at room temperature, which indicates that watercan store almost 10 times the energy that iron can per unit mass.

,ability to conduct heat . For example, k = 0.608 W/mC for water

and k = 80.2 W/mC for iron at room temperature, which indicatesa ron con uc s ea more an mes as er an wa er can.

Thus water is a poor heat conductor relative to iron, althoughwater is an excellent medium to store thermal energy

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Ran e of Thermal Conductivit The thermal conductivities of gases

such as air vary by a factor of 10 4

from those of pure metals such ascopper.

Note that pure crystals and metals

have the highest thermal,insulating materials the lowest.

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A simple experimental setup to

determine the thermal conductivity .

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The range of

of various materialsat room temperature

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The thermal conductivity of a substance is

in the gas phase.

Unlike gases, the thermal conductivities ofmost qu s ecrease w t ncreas ngtemperature, with water being a notableexception.

In solids, heat conduction is due to twoeffects: the lattice vibrational waves induced

b the vibrational motions of the molecules positioned at relatively fixed positions in a periodic manner called a lattice , and the

electrons in the solid .The thermal conductivity of a solid is obtained by adding the lattice

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.of pure metals are primarily due to the electronic component .


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the way the molecules are arranged

Unlike metals, which are good electrical and heat conductors,crysta ne so s suc as amon an sem con uctors suc assilicon are good heat conductors but poor electrical conductors. As aresult, such materials find widespread use in the electronics industry.For example, diamond, which is a highly ordered crystalline solid,has the highest known thermal conductivity at room temperature.

Even small amounts in a pure metal of foreignmolecules that are good conductors themselvesser ous y srup e ow o ea n a me a .

For example, the thermal conductivity of steelcontaining just 1 percent of chrome is 62 W/mC,while the thermal conductivities of iron

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and chromium are 83 and 95 W/mC,


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The variation of

conductivity ofvarious solids,

,

with temperature(from White)

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Thermal Diffusivit The product C p, which is frequently encountered in heat transfer

analysis, is called the heat capacity of a material. Both thespecific heat C

pand the heat capacity C

prepresent the heat

storage capability of a material.

p p volume, as can be noticed from their units J/kgC and J/m 3C,

respectively. Another material property that appears in the transient heat

conduction analysis is the thermal diffusivity, which representshow fast heat diffuses through a material and

is defined as The larger the thermal diffusivitythe faster the propagation of heatinto the medium. A small value ofthermal diffusivity means that heat

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t e a d us v ty ea s t at eatis mostly absorbed by the materialand a small amount of heat will beconducted further


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Note that the thermal diffusivityranges from 0.14 x 10 -6 m2/s forwater to 174 x 10 -6 m2/s for silver,which is a difference of more than athousand times.

Also note that the thermal

same. This is not surprising, sincemeat as well as fresh vegetables and

, possess the thermal properties ofwater.

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Forced Convection Natural Convection

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o ng on ensat on


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Convection

Convection heat transfer involves both energy transfer due to random

Convection heat transfer includes both forced convection and naturalconvection

In convect on eat trans er, t e trans er o eat s etween a sur aceand a moving fluid (liquid or gas), when they are at different

temperatures. The rate of transfer is given by Newtons Law ofCooling .

)TT(hq s''

=

Moving fluid

T

Ts

q

Ts > T

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Typical values of convectionea rans er coe c en

2

Free ConvectionGases 2-25

Liquids 50 -1000

Forced Convection-

Liquids 50 -20,000

with Phase Change

Boiling orCondensation 2500 -100,000

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Radiation All surfaces of finite temperature emit energy in the form of electromagnetic

waves In the absence of an intervening medium, there is a heat transfer by radiation

between two surfaces at different temperatures

The maximum flux, E (W / m 2), at which radiation may be emitted from a

ac o y sur ace s g ven y:

Stefan Boltzmann Law

where

4s b TE =

b

Ts

E b or E = Surface emissive power (W / m 2)

T = absolute temperature (K)

= Stefan-Boltzmann constant = 5.67 x 10 -8 (W / m 2 K 4)

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For a real surface:

For a surface with absor tivit , the incident radiation G, W/m 2

sTE =

that is absorbed by the surface is given by:

= G

whereG abs

G = incident radiation (W / m 2)

T = absolute temperature (K)

= surface emissivity (0 1)

=

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For a gray surface =

When radiant energy is incident on a transparent surface, it can beabsorbed, reflected, or transmitted through the material. Hence,

( )GGGGG reflecteddtransmitteabsorbed ++=++=

=where

= materials surface reflectivity

= materials transmissivity

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Consider a small gray surface at temperature T s that is completelyenclosed by the surroundings at temperature T sur .

The net rate of radiation heat transfer from the surface is:

44'' qq sur

sur 4

sur

4

ssur s

''

rad TTGEq ==

sur sr sur srad A===q s

Ts

Where h r is the radiation heat transfer coefficient, W / m 2 K

22 TTTTh ++=

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Conduction example

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Convection example from your hand when it is

exposed to moving airand water, assuming thesurface temperature of

your hand is 30C.

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Radiation ex. An instrumentation packagehas a spherical outer surfaceof diameter D = 100 mm and

= . .package is placed in a largespace simulation chamberwhose walls are maintainedat 77 K. If the operation ofthe electronic components isrestricted to the temperatureran e of 40 T 85C what is the range of acceptablepower dissipation for thepackage?

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HEAT TRANFER LECTURE NOTES

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