Introduction to heat and mass transfer chapter 1

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Chapter 1: Introduction andBasic Concepts

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Thermodynamics and Heat Transfer • Thermodynamics: study the changes from one

equilibrium state to another that can be caused by theamount of heat transfer , and thermodynamics makesno reference to how long the process will take.

• Heat transfer: determine the rateso energy t at can e trans errefrom one system to another as aresult of temperature difference. Inother worlds, it answers how long

the process will take. It is anon-equilibrium phenomenon and can not bedetermined by thermodynamics laws .

Thermodynamics zeroth order law


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Heat Transfer • Temperature difference is a necessary condition for

heat transfer.• Heat transfer has the direction of

decreasing temperature .• Heat transfer is a vector and it has

oth magnitude and direction.• The rate (magnitude) of heat transfer in a certain

direction depends on the magnitude of the temperaturegradient in that direction.

• The larger the temperature gradient , the higher the rateof heat transfer .

Application Areas of Heat Transfer

Heat and other Forms of Energy• Energy can exist in numerous forms such as:

– thermal, – mechanical, – kinetic, – potential, – electrical, – magnetic, – chemical, and – nuclear.

• The total energy E (or e on a unit mass basis) of asystem includes all aforementioned energy forms.

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

• Internal energy : May be viewed as the sum of thekinetic and potential energies of the molecules.

• Sensible heat: The kinetic energy of the molecules.• Latent heat: The internal energy associated with

the phase of a system.• Chemical (bond ) energy : The internal energy

associated with the atomic bonds in a molecule.• Nuclear energy: The internal energy associated

with the bonds within the nucleus of the atom itself.


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Internal Energy and Enthalpy

• In the analysis of systemsthat involve fluid flow, wefrequently encounter thecombination of properties uand Pv .

• The combination is definedas enthalpy (h = u + Pv ).

• The term Pv represents theflow energy of the fluid(also called the flow work).

Specific Heats of Gases, Liquids, and Solids

• Specific heat: the energy required to raisethe temperature of a unit mass of a substance

by one degree.• Two kinds of specific heats:

– specific heat at constant volume cv – spec c eat at constant pressure c p

• The specific heats of a substance, in general,depend on two independent properties suchas temperature and pressure.

• At low pressures all real gases approachideal gas behavior, and therefore theirspecific heats depend on temperature only.

• Incompressible substance: A substance whose specificvolume (or density) does not change with temperature or

pressure (water, steel).• The constant-volume and constant-pressure specific heats

are identical for incompressible substances.• The specific heats of incompressible substances depend

on temperature only.

Energy TransferEnergy can be transferred to or from a given mass

by two mechanisms: heat transfer and work.

Heat transfer rate: The amount of heat transferred per unit time.

Heat flux: The rate of heat transfer per unit areanormal to the direction of heat transfer.

when is constant:

Power: The work isdone per unit time.


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THE FIRST LAW OF THERMODYNAMICS

The first law of thermodynamics ( conservation of energy principle ):

Heat generation : the conversion ofnuclear, chemical, mechanical, andelectrical energies into thermalenergy.

Energy Balance for Closed Systems (Fixed Mass)

A closed system consists of a fixed mass .

Energy Balance for Steady-Flow Systems

A large number of engineering devices such as waterheaters and car radiators involve mass flow in and outof a system, and are modeled as control volumes .The term steady means no change with time at aspecified location.Mass flow rate: The amount of mass flowing through across section of a flow device per unit time.Volume flow rate: The volume of a fluid flowingthrough a pipe or duct per unit time.


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Heat Transfer Mechanisms• Three basic modes:

– conduction , – convection , – radiation .

• All modes of heattransfer require theexistence of a temperature difference .

• All heat transfer modes are from the high-temperatureto a lower-temperature .

Conduction

Conduction: The transfer of energy from the moreenergetic particles of a substance to the adjacent lessenergetic ones as a result of interactions between the

particles.

In ases and li uids conductionis due to the ,collisions and diffusion of the molecules during theirrandom motion.

In solids , it is due to the combination of vibrationsof the molecules in a lattice and the energy transport

by free electrons .


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Conduction

Fourier’s law of heat conduction :

Thermal conductivity of the material.

(W)cond dT

Q kAdx

= −&

Thermal ConductivityThermal conductivity: The rate of heat transferthrough a unit thickness of the material per unit area

per unit temperature difference.

The thermal conductivity of a material is a measureof the ability of the material to conduct heat.

A high value for thermal conductivity indicates thatthe material is a good heat conductor, and a low valueindicates that the material is a poor heat conductor orinsulator .

Thermal Conductivity

A simple experimental setup todetermine the thermalconductivity of a material.


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The range ofthermalconductivity of various materialsat roomtemperature.

The variation of thethermal conductivityof various solids,liquids, and gaseswith temperature.

Thermal Diffusivity

c p Specific heat, J/kg · °C: Heat capacity per unitmass

ρ c p Heat capacity, J/m 3·°C: Heat capacity per unitvolume

α Thermal diffusivity, m 2/s: Represents how fastheat diffuses through a material

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A material that has a high thermal conductivityor a low heat capacity will obviously have alarge thermal diffusivity.

The larger the thermal diffusivity, the faster the propagation of heat into the medium.

A small value of thermal diffusivity means thatheat is mostly absorbed by the material and asmall amount of heat is conducted further.

Convection

• Convection is the mode of energy transfer between asolid surface and the adjacent liquid or gas that is inmotion.

Convection = Conduction + Advection(fluid motion)

• Convection is commonly classified into three sub-modes: – Forced convection , – Natural (or free ) convection ,

– Change of phase (liquid/vapor,solid/liquid, etc.)


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Newton’s law of cooling

h convection heat transfer coefficient, W/m 2 · °C As the surface area through which convection heat transfer takes placeT s the surface temperatureT ∞ the temperature of the fluid sufficiently far from the surface.

The convection heat transfercoefficient h is not a property ofthe fluid.

It is an experimentallydetermined parameter whosevalue depends on all the variablesinfluencing convection such as- the surface geometry- the nature of fluid motion- the properties of the fluid- the bulk fluid velocity

Radiation• Radiation: The energy emitted by matter in the form of electromagnetic

waves (or photons ) as a result of the changes in the electronicconfigurations of the atoms or molecules.

• Unlike conduction and convection, the transfer of heat by radiation doesnot require the presence of an intervening medium .

• In fact, heat transfer by radiation is fastest (at the speed of light) and itsuffers no attenuation in a vacuum. This is how the energy of the sunreaches the earth.

• In heat transfer studies we are interested in thermal radiation , which isthe form of radiation emitted by bodies because of their temperature.

• All bodies at a temperature above absolute zero emit thermal radiation.

• Radiation is a volumetric phenomenon , and all solids, liquids, and gasesemit, absorb, or transmit radiation to varying degrees.

• However, radiation is usually considered to be a surface phenomenonfor solids.


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Stefan–Boltzmann law

σ = 5.670 × 10− 8 W/m 2 · K 4 Stefan–Boltzmann constant

Blackbody: The idealized surface that emits radiation at the maximum rate.

Emissivity ε : A measure of how closely asurface approximates a blackbody for whichε = 1 of the surface. 0≤ ε ≤ 1.

Radiation emitted by real surfaces

Blackbody radiation represents the maximumamount of radiation that can be emitted from asurface at a specified temperature.

Absorptivity α : The fraction of the radiation energy incident on a surfacethat is absorbed by the surface. 0≤ α ≤ 1

A blackbody absorbs the entire radiation incident on it ( α = 1 ).

Kirchhoff’s law: The emissivity and the absorptivity of a surface at agiven temperature and wavelength are equal.

The absorption of radiation incident on an

opaque surface of absorptivity .

Net radiation heat transfer: Thedifference between the rates ofradiation emitted by the surfaceand the radiation absorbed.

The determination of the net rateof heat transfer by radiation

between two surfaces is acomplicated matter since itdepends on

• the properties of the surfaces• their orientation relative to each

When a surface is completely enclosed by a muchlarger (or black) surface at temperature T surr separated by a gas (such as air) that does notintervene with radiation, the net rate of radiationheat transfer between thesetwo surfaces is given by

Radiation heat transfer between a surface andthe surfaces surrounding it.

other• the interaction of the medium

between the surfaces with radiation

Radiation is usuallysignificant relative toconduction or naturalconvection, butnegligible relative toforced convection.

Combined heat transfer coefficient hcombined Includesthe effects of both convection and radiation

When radiation and convection occursimultaneously between a surface and a gas:

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Introduction to heat and mass transfer chapter 1