lecture01 c

7/27/2019 Lecture01 c

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MECH 301 HEAT TRANSFER

Thursday 11:00 – 12:30 Walker LT Friday 10:00 – 11:30 Chadwik ROTB Dr. Volfango Bertola Harrison Hughes/Walker, Room UG43 [email protected]

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1. Introduction (1 lecture) 2. Heat conduction (5 lectures) 3. Convection (3 lectures) 4.

Radiation (3 lectures)

5. Heat Exchangers (3 lectures)

Course outline

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Text Books • Fundamentals of Heat and Mass Transfer, F.M. Incropera & D.P. De

Witt (Wiley) Reference • Heat Transfer: A Basic Approach, N. Özisik (McGraw Hill) • Heat Transfer, J.P. Holman (McGraw Hill) • Thermal-Fluid Sciences: An Integrated Approach, S.R. Turns (CUP) Advanced • Conduction of Heat in Solids, H.S. Carslaw & J.A. Jaeger (OUP) • Convective Heat and Mass Transfer, W.M. Kays & M.E. Crawford

(McGraw Hill) • Convective Heat Transfer, A. Bejan (Wiley) • Radiative Transfer, H.C. Hotell & A. Sarofim (McGraw Hill)

Books

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Assessment Assessment Duration Timing

(Semester) % of finalmark Resit

opportunity Examination

(May) 3 hours 2 80 BEng. : Yes –Next session

4 continuousassessments Take home Throughout

the semester 20 N / A

Exam Answer 4 questions of 6 – questions cover: conduction,

convection, radiation, heat exchangers AssignmentsIn Weeks 4-6-8-10 (Problem sheet - submit one week later)

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Assignments • 4 Problem sheets with 3/4 questions – 5 marks each (total:

20% of the final mark) • Purposes: (1) encourage study / revision throughout the

semester; (2) self-assessment (feedback!) • Submissions ONLY through VITAL •

Group working OK but submissions MUST be independent

• Assignments may require more than the lecture notes (e.g.,material properties) – you MUST find the relevantinformation on your own (books, web, etc.)

• Submission deadlines are strict. DO NOT ask for extensions,etc. – Submit Mitigating Circumstance if necessary

• Feedback: (1) individual comments on VITAL; (2) workedsolutions available ~1 week after submission deadline

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Email reply policy Case 1 Important, individual queries – Reply ASA(Reasonably)P ! Case 2 • Repeated queries (i.e., more students asking the same or

similar questions)

• Queries of general interest

Reply to all class via VITAL and/or discussion in classroom !

Case 3 Any queries about exam or assignment questions (e.g.“should I focus more on this topic or on that topic?” or“which equation shall I use to answer this question?”)

NO REPLY "

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Some (important) things • No cheating, no plagiarism, etc. • Attend lectures (boring lecture more useful than

no lecture) – ATTENDANCE IS RECORDED(PollEverywhere)

• Don’t be late (attendance poll closes ~30 min afterscheduled beginning of lecture)

• Do not wait until one week before the exam tostart studying!

To answer polls on PollEverywhere SMS to: 020 3322 5822 http://www.polleverywhere.com/mech301

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Lecture 1 Introduction to heat transfer

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Heat transfer If T1 = T2 the systems are atequilibrium (and vice-versa)

h is the so-called heat transfer coefficient (indeed, a coefficient of ignorance!) In general, heat transfer occurs according three different modes: Conduction: Energy exchange atmolecular scale. Solids, fluids at rest

T

T2

Q If T1 ≠ T2 the systems areNOT at equilibrium: there is aheat transfer from the hotsystem to the cold system

T1 T2

.

Convection: Conduction + macroscopicmass transport. Typical of fluids

Radiation: Energy exchangeamong bodies invacuum

Simplest idea: the heat transfer rate per unit area (or the heat flux) isproportional to the temperature difference

q’’ = Q/A= h(T1 – T2) .

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Heat transfer examples Conduction T1 T1 > T2 T2 No movement of

medium

Forced Convection T3

T3

T1 T2 T3 > T1 & T2 > T1 Heat transfer principally dueto background fluid flow

Free Convection

T1 Tamb

T1 > Tamb Temperature difference initiates fluidflow and subsequently heat transfer

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Radiation

Earth

Sun No medium requiredfor heat transfer

Phase Change Heat Transfer LatentHeat Energy transfer occurs by

virtue of the latent heatof the phase change

Water Ice

Heat transfer examples

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Conduction: a molecular mechanism Consider two particles with differentenergies:

The energy of particles is proportional to temperature: E = KBT

If they collide, the high-energy particlegives some of its energy to the low-energy particle

High-energy hot

cold Low-energy

This mechanism is called DIFFUSION, and occurs equally in solids, liquidsand gases (not in vacuum!!!)

T

x

q .

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Fourier’s law To calculate the heat transfer rate, we need a phenomenological relationship(no way to get it using equilibrium thermodynamics!):

q = -k dT/dx Heat flux: heat transfer rate per unit area, perpendicular to the direction oftransfer

Fourier’s law

• The heat flux is proportional to the temperature GRADIENT (dT/dx) • The minus sign indicates that heat flows from higher temperatures to

lower temperatures (i.e., takes into account the 2nd Principle) • k is a property of the material called “thermal conductivity” (another

coefficient of ignorance!) Its metric units are W/(mK)

T

x

q . dx

dT

.

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Thermal conductivity Thermal conductivity is aproperty of the material Gases have very low k Metals have high k Thermal conductivity maydepend on temperature: k = k(T) Thermal conductivity maydepend on the position k = k(x,y,z)

It could be even worse: thermal conductivity may depend even on thedirection we are looking at (in general, k is a TENSOR!!!) e.g. composite materials are often strongly anisotropic K = k ij(x, y, z, T(x, y, z))

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Example problem #1.1 The wall of an industrial furnace isconstructed from 0.15 m thick fireclay

brick having a thermal conductivity of 1.7W/mK. Measurements made duringsteady-state operation revealtemperatures of 1400 K and 1150 K atthe inner and outer surfaces, respectively.What is the rate of heat loss through a

wall which is 0.5 m by 3 m on a side?

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Convective heat transfer Convection is the heat transfer mode characteristic of fluids

Molecular diffusion (microscopic) Most important example: heat transfer between a surface and a fluid flow:

Bulk motion (macroscopic)

T∞ u∞

U(y)

Velocity decreases from u∞ (free stream) tozero (wall): velocity boundary layer

T(y)

Tw Temperature varies between T

∞ (free stream)

and Tw (wall): thermal boundary layer Tw > T

∞ or Tw < T

∞

The thickness of the two boundary layers is not the same in general!!! Forced convection: fluid motion is imposed by external means (e.g. a fan) Free convection: fluid motion is induced by buoyancy

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Convective Heat Transfer

Forced Convection Free Convection Mixed Convection • Forced Convection

In forced convection, the heat transfer takes place principally due to thebackground fluid flow.

• Free Convection In free convection, the temperature distribution initiates the flow whichsubsequently transfers heat.

• Mixed Convection There are contributions of both forced and free convection.

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The heat transfer coefficient Q = h A (Tw – T

∞) Its metric units are W/(m2K)

Typical values of the heat transfer coefficient:

.

Heat transfer with phase change is the best option to increase the heatflux when we have limited temperature differences

…Not so many choices to increase the heat transfer rate: • Increase the area of the heat transfer surface (technical and economicconstraints)

• Increase the temperature difference between the fluid and the surface(technical and environmental constraints)

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Local and average heat transfer coefficients

If the boundary layers change with the position, h will change too

Development ofboundary layers

In general: h (or hx) = h(!, µ, k, cP, w, g, a, D, "T, etc…)

Other reasons for non-uniformity: change of the fluid temperature (e.g. fluidheated in a pipe), of the fluid velocity (convergent/divergent tube), etc. Thus, h is a LOCAL heat transfer coefficient (= depends on the position) h = hx dA 1

A # A h = hx dX 1

L # L One can also define AVERAGEheat transfer coefficients

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Radiative heat transfer Vacuum: No conduction No convection T1 T1 T2

Radiation (e.m. waves $ photons)

Q .

Every object having a finite temperature emits energy by radiation

E = hP%

% = c/&

(frequency) hP = 6.62 x 10-34 (Planck’s const.) c = 3 x 10

8

m/s

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Ideal and real surfaces

T1

Ideal surfaces: q’’ = (T4 ( = 5.67 x 10-8 W/m2K4 Stefan-Boltzmann constant

q’’1)2 = (T14

T2 q’’2)1 = (T2

4

q’’1-2 = ( (T14 – T2

4) . The NET heat flux from thehot surface to the cold oneis:

We assume that radiation occurs only among surfaces, and that any fluidthat may be there is transparent to radiation (non-participating)

Real surfaces: q’’ = *(T4 0 < * < 1 Emissivity

Irradiation (G) Reflected (GR) Emitted (E)

G = GReflected + GAbsorbed Net heat flux = E + GR – G

E + GR – GR – GA E – GA

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Identifying heat transfer modes

q5: net radiation exchange between the outer surface of the flask and the innersurface of the cover

q6: conduction through the cover q7: free convection from the cover to the room air q8: net radiation exchange between the outer surface of the cover and the

surroundings

q1: free convectionfrom the coffee tothe flask

q2: conductionthrough the flask

q3: free convectionfrom the flask tothe air space

q4: free convectionfrom the air spaceto the cover

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Relationship to Thermodynamics First Law: conservation of energy E

in

, Eout

: rates of internal energy transfer in

and out, respectively, across thesurface of the system due to heattransfer

Eg: rate of internal energy generationwithin the system

Est

: rate of internal energy storage

within the system

. .

.

. Ein + Eg – Eout = "Est Ein + Eg = Est + Eout

. . . . Second Law: heat cannot flow spontaneously from a lower temperature toa higher temperature Heat transfer phenomena occur in different modes but are alwaysspontaneous (= they follow the 2nd Law) Heat transfer is non-reversible

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Example problem #1.2

An uninsulated steam pipe passes through a room in which the air and wallsare at 25°C. The outside diameter of the pipe is 70 mm, and its surfacetemperature and emissivity are 200°C and 0.8, respectively. If the coefficientassociated with free convection heat transfer from the surface to the air is 15W/m2, what is the rate of heat loss from the surface per unit length of pipe?

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