Chapter 1 heat trasfer

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Chapter 1: Introduction and

Basic Concepts


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ObjectivesWhen you finish studying this chapter, you should be able to:

Understand how thermodynamics and heat transfer are related toeach other,

Distinguish thermal energy from other forms of energy, and heattransfer from other forms of energy transfer,

Perform general energy balances as well as surface energy

balances, Understand the basic mechanisms of heat transfer, which are

conduction, convection, and radiation, and Fourier's law of heatconduction, Newton's law of cooling, and the StefanBoltzmannlaw of radiation,

Identify the mechanisms of heat transfer that occur simultaneouslyin practice,

Develop an awareness of the cost associated with heat losses, and

Solve various heat transfer problems encountered in practice.


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Thermodynamics and Heat Transfer

The science ofthermodynamics deals with theamount of heat transferas a system undergoes aprocess from one equilibrium state to another,

and makes no reference to how long the processwill take.

The science ofheat transfer deals

with the determination of the rates

of energy that can be transferred

from one system to another as a

result of temperature difference.


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Thermodynamics deals with equilibrium statesand changes from one equilibrium state toanother. Heat transfer, on the other hand, deals

with systems that lack thermal equilibrium, andthus it is a nonequilibrium phenomenon.

Therefore, the study of heat transfer cannot bebased on the principles of thermodynamics alone.

However, the laws of thermodynamics lay theframework for the science of heat transfer.

Thermodynamics and Heat Transfer


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Heat Transfer

The basic requirement for heat transferis the presence

of a temperature difference.

The second law requires that heat

be transferred in the direction of

decreasing temperature. The temperature difference is the driving force for heat

transfer.

The rate ofheat transferin a certain direction depends

on the magnitude of the temperature gradient in thatdirection.

The largerthe temperaturegradient, the higherthe rateofheat transfer.


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Application Areas of Heat Transfer


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Heat and Other Forms of Energy

Energy can exist in numerous forms such as: thermal,

mechanical,

kinetic,

potential,

electrical,

magnetic,

chemical, and

nuclear.

Their sum constitutes the total energyE(oreon aunit mass basis) of a system.

The sum of all microscopic forms of energy is calledthe internal energyof a system.


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Internal energy may be viewed as the sum ofthe kinetic and potential energies of themolecules.

The kinetic energy of the molecules is calledsensible heat.

The internal energy associated with thephase of

a system is called latent heat.

The internal energy associated with the atomicbonds in a molecule is called chemical(or

bond) energy. The internal energy associated with thebonds

within the nucleus of the atom itself is callednuclear energy.


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Internal Energy and Enthalpy

In the analysis of systemsthat involve fluid flow,we frequently encounterthe combination of

properties u andPv.

The combination isdefined as enthalpy(h=u+Pv).

The termPv representsthe flow energy of thefluid (also called the flowwork).


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Specific Heats of Gases, Liquids, and

Solids Specific heatis defined as the energy required to

raise the temperature of a unit mass of a substance byone degree.

Two kinds of specific heats: specific heat at constant volumecv, and specific heat at constant pressurecp.

The specific heats of a substance, in general, dependon two independent properties such as temperature

and pressure. For an ideal gas, however, they depend on

temperature only.


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Specific Heats

At low pressures all real gases approach ideal gasbehavior, and therefore their specific heats depend ontemperature only.

A substance whose specific volume (or density) does

not change with pressure is called an incompressiblesubstance.

The constant-volume and constant-pressure specificheats are identical for incompressible

substances. The specific heats of incompressible

substances depend on temperature

only.


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Energy Transfer

Energy can be transferred to or from a given mass by two

mechanisms: heat transfer, and

work.

The amount of heat transferred during a process is denoted by Q.

The amount of heat transferred per unit time is called heattransfer rate, and is denoted by Q.

The total amount of heat transferQduring a time interval Dtcanbe determined from

The rate of heat transfer per unit area normal to the direction ofheat transfer is called heat flux, and the average heat flux isexpressed as

0

(J)

t

Q Qdt

D

2

(W/m )

Q

q A

(1-6)

(1-8)


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The First Law of Thermodynamics

The first law of thermodynamics states that energycan neither be created nor destroyed during a process;

it can only change forms.

The energy balancefor any system undergoing any

process can be expressed as (in the rate form)

Total energy

entering the

system

Total energy

leaving the

system

Change in the

total energy of

the system

- =

(W)in out systemE E dE dt

Rate of net energy transfer

by heat, work, and mass

Rate of change in internal

kinetic, potential, etc., energies

(1-9)

(1-11)


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In heat transfer problems it is convenient to write

a heat balanceand to treat the conversion ofnuclear, chemical, mechanical, and electrical

energies into thermal energy as heat generation.

The energy balance in that case can be expressedas

, (J)in out gen thermal systemQ Q E E D

Net heat

transfer

Change in

thermal energy

of the system

Heat

generation

(1-13)


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Energy Balance

Closed systems

Stationary closed

system, no work:

Steady-Flow Systems

For system with one inlet and

one exit:

When kinetic and potentialenergies are negligible, and

there is no work interaction

(J)vQ mc T D (kg/s)in out m m m

(kJ/s)pQ m h mc T D D

(1-15)

(1-18)


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Heat Transfer Mechanisms

Heat can be transferred in three basic modes: conduction,

convection,

radiation.

All modes of heat

transfer require the

existence of a temperature difference.

All modes are from the high-temperature

medium to a lower-temperature one.


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Conduction Conduction is the transfer of energy from the more

energetic particles of a substance to the adjacent lessenergetic ones as a result of interactions between the

particles.

Conduction can take place in solids,

liquids, or gases

In gases and liquids conduction is due to

the collisions and diffusion of the

molecules during their random motion.

In solids conduction is due to the

combination ofvibrations of the

molecules in a lattice and the energy

transport by free electrons.


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Conduction

1 2 (W)condT T T

Q kA kAx x

D

D D

Area Temperature differenceRate of heat conductionThickness

where the constant of proportionality kis the

thermal conductivityof the material.

In differential form

which is called Fouriers law of heat conduction.

(1-21)

(1-22)(W)conddT

Q kAdx


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Thermal Conductivity

The thermal conductivity of a material is a

measure of the ability of the material to conduct

heat.

High value for thermal conductivity

good heat conductor

Low valuepoor heat conductororinsulator.


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Thermal Conductivities of Materials

The thermal conductivities

ofgases such as air vary by

a factor of104 from those

ofpure metals such ascopper.

Pure crystals and metals

have the highest thermal

conductivities, and gasesand insulating materials the

lowest.


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Thermal Conductivities and

Temperature

The thermal conductivities

of materials vary with

temperature.

The temperaturedependence of thermal

conductivity causes

considerable complexity in

conduction analysis.

A material is normally

assumed to be isotropic

(i.e., uniform in alldirections .


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Thermal diffusivity

The thermal diffusivity represents how fast heat

diffuses through a material.

Appears in the transient heat conduction analysis.

A material that has a high thermal conductivity or a

low heat capacity will have a large thermal diffusivity. The larger the thermal diffusivity, the fasterthe

propagation ofheat into the medium.

2Heat conducted ( m s)Heat stored p

k

c

(1-23)


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Convection

Convection is the mode of energy transfer between a

solid surface and the adjacent liquid or gas that is in

motion. Convection is commonly classified into three sub-

modes:

Forced convection,

Natural (or free) convection,

Change of phase (liquid/vapor,

solid/liquid, etc.)

Convection =Conduction+Advection

(fluid motion)


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Convection

The rate ofconvection heat transferis expressed byNewtons law of coolingas

his the convection heat transfer coefficientinW/m2C.

h depends on variables such as the

surface geometry, the nature of fluid

motion, the properties of the fluid,

and the bulk fluid velocity.

( ) (W)conv s sQ hA T T (1-24)


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Radiation

Radiation is the energy emitted by matter in the form ofelectromagnetic waves(orphotons) as a result of thechanges in the electronic configurations of the atoms ormolecules.

Heat transfer by radiation does not require the presence ofan intervening medium.

In heat transfer studies we are interested in thermalradiation (radiation emitted by bodies because of their

temperature). Radiation is a volumetric phenomenon. However, radiation

is usually considered to be asurface phenomenon forsolids that are opaque to thermal radiation.


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The maximum rate of radiation that can be emitted from a

surface at a thermodynamic temperature Ts(in K or R) is givenby the StefanBoltzmann lawas

s=5.670X108 W/m2K4 is the StefanBoltzmann constant.

The idealized surface that emits radiation at this maximum rate

is called a blackbody.

The radiation emitted by all real surfaces is less than the

radiation emitted by a blackbody at the same temperature, and

is expressed as

eis the emissivityof the surface.

4

,max (W)emit s sQ A Ts

4

,max (W)

0 1

emit s sQ A Tes

e

Radiation - Emission

(1-25)

(1-26)


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Radiation - Absorption

The fraction of the

radiation energy incident

on a surface that is

absorbed by the surface istermed the absorptivity .

Both eand of a surface depend on the temperatureand the wavelength of the radiation.

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Chapter 1 heat trasfer

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