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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?