Chapter 1 Introduction to Heat Transfer

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Introduction

Heat is the form of energy that can be transferred from one system to another as a

result of temperature difference.

The science that deals with the determination of the rates of such energy

transfers is heat transfer.

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Cont

The science of thermodynamics deals with the amount of heat transfer as a system undergoes a process from one equilibrium state to another.

The science of heat transfer deals with the rate of heat transfer, which is the main quantity of interest in design and evaluation of heat transfer equipment.

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Application Areas of Heat Transfer

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Energy Transfer

The amount of heat transferred per unit during the process is denoted by Q. Unit : Joule (J)

The rate of heat transferred per unit time is is denoted by Unit: Joule per second (J/s) or Watt (W)

Q!

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Cont

The total amount of heat transfer Q during a time interval t can be determined from

The rate of heat transfer per unit area normal

to the direction of heat transfer is called heat flux.

=t

dtQQ0

!

)/(, 2mWAQq!

! =

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The First Law of Thermodynamics

Conservation of energy principle states that energy can neither be created nor destroyed; it can only change forms.

Total energy entering

the system

Total energy leaving

the system

Change in the total energy of

the system

_ =

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Energy balance for closed systems (fixed mass) Stationary closed system: Ein Eout = U = mCvT (J)

when the system involves heat transfer only and no work interactions across the boundary.

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Energy Balance for steady flow systems Mass flow rate and the volume flow rate of a fluid flowing in a pipe can be expressed as

When the changes in kinetic and potential energies are negligible, the energy balance for the system reduces to:

cVAm =! mVAV c!! ==

!Q = !mh = !mCpT(kJ / s)

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Heat Transfer Mechanisms

Heat can be transferred by: Conduction Convection Radiation All modes of heat transfer require the existence of a temperature difference. Heat transfer are from high temperature medium to a lower one.

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Basic theory of heat conduction

Transfer of energy from energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.

Take place in solids, liquids, gases. In gases and liquids: due to collisions and

diffusions of the molecules during random motion.

In solids: due to combination of vibrations of the molecules and the energy transported by free electrons.

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Cont

The rate at which heat is conducted through a material is proportional to the area normal to the heat flow and to the temperature gradient along the heat flow path.

It depends on the geometry of the medium,

its thickness, and the material of the medium, as well as the temperature different across the medium.

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For a one dimensional, steady state heat flow the rate is expressed by Fouriers equation:

where: k = thermal conductivity, W/m-K = rate of heat flow, W A = contact area L = plane layer of thickness T = T2 - T1 = temperature difference

)(

)(

WLTkAQ

WdxdTkAQ

cond

cond

=

=

!

!

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Thermal conductivity, k Material ability to conduct heat. Unit: W/m-K or W/moC Definition: The rate of heat transfer through a

unit of thickness of the material per unit area per unit temperature difference.

It is a measure of how fast heat will flow in that material.

A large value of thermal conductivity indicates that the material is a good conductor, and a low value indicates the material is a poor heat conductor or insulator.

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Basic theory of heat convection

Made of energy transfer between a solid surface and the adjacent liquid or gas that is in motion.

There are two types of convection: 1. forced convection - fluid is forced to flow over the surface by

external mean, such as fan. 2. natural convection - caused by buoyancy forces that are

induced by density difference due to variation of temperature in the fluid.

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Example

Hot metal

Hot metal

Forced Convection Natural Convection

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The rate of convection heat transfer is expressed by Newtons Law of Cooling as

= hAs (Ts-T) (W)

h = heat transfer coefficient (W/m2.oC)

A = surface area thro which convection HT takes place

Ts = surface temperature

T = temperature of the fluid

convQ!

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Basic theory of heat radiation

Energy emitted by matter in the form of electromagnetic waves as a result of the changes in the electronic configurations of the atoms/molecules.

Does not require any medium. Energy transfer by radiation is the fastest (at

the speed of light) and it suffers no attenuation in a vacuum.

This is exactly how the energy from the sun reaches the earth.

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The maximum rate of radiation that can be emitted from a surface at an absolute temperature Ts is given by Stefan Boltzmann Law : = As Ts4 (W) = 5.67 x 10-8 W/m2.K4 = 0.1714 x 10-8 Btu/h.ft2.R4 = Stefan Boltzmann constant

max,emitQ!

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When a surface of emissivity and a surface A at an absolute temperature Ts is completely enclosed by a much larger (or black) surface at absolute temperature Tsurr separated by a gas (such as air), the rate of radiation HT: = As (Ts4 Tsurr4) (W)

= emissivity = 0 1 blackbody, = 1

radQ!

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