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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 Volfango.Bertola@liverpool.ac.uk  

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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?