ME 259
Heat Transfer
Lecture Slides I
Dept. of Mechanical Engineering,
1/22/05
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Introduction
Reading: Incropera & DeWitt
Chapter 1
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Heat Transfer as a Course
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Has a “reputation” for being one of the
most challenging courses in ME
Why??
– Physically diverse: thermodynamics,
material science, diffusion theory, fluid
mechanics, radiation theory
– Higher-level math: vector calculus, ODEs,
PDEs, numerical methods
– Physically elusive: heat is invisible;
developing intuition takes time
– Appropriate assumptions: required to
simplify and solve most problems
However, Heat Transfer is interesting, fun,
and readily applicable to the real world
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Relevance of Heat Transfer
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Electric Power Generation
Alternate Energy Systems
Combustion/Propulsion Systems
Building Design
Heating & Cooling Systems
Domestic Appliances
Materials/Food Processing
Electronics Cooling & Packaging
Cryogenics
Environmental Processes
Space Vehicle Systems
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Definition of Heat Transfer
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Flow of energy due solely to a temperature
difference
– all other forms of energy transfer are
categorized as work
– from 2nd Law of Thermodynamics, heat
flows in direction of decreasing temperature
– heat energy can be transported through a
solid, liquid, gas, or vacuum
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Heat Quantities
Quantity
Text Notation
SI Unit
English Unit
heat
(heat transfer)
Q
Joule (J)
Btu
heat rate
(heat transfer rate)
(heat energy rate)
(rate of heat flow)
q
Watt (W)
Btu/hr
heat flux
(heat rate per unit area)
q”
W/m2
Btu/hr-ft2
heat rate per unit length
q’
W/m
Btu/hr-ft
volumetric heat generation q
(rate of heat production per
unit volume)
W/m3
Btu/hr-ft3
Conversions:
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1 Btu = 1054 J
1 kcal = 4184 J
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Relationship Between the Study of
Heat Transfer & Thermodynamics
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1st Law of Thermodynamics for Closed
System:
Q  W  Esys
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Thermodynamics - allows calculation of total
heat transferred (Q) during a process in which
system goes from one equilibrium state to
another (i.e., the “big picture”)
Heat Transfer - provides important physical
laws that allow calculation of instantaneous
heat rate, length of time required for process to
occur, and temperature distribution within
material at any time (i.e., the “details” required
for design)
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Heat Transfer Modes
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Conduction
– transfer of heat due to random molecular or
atomic motion within a material (aka
diffusion)
– most important in solids
Convection
– transfer of heat between a solid surface
and fluid due to combined mechanisms of
a) diffusion at surface; b) bulk fluid flow
within boundary layer
Radiation
– transfer of heat due to emission of
electromagnetic waves, usually between
surfaces separated by a gas or vacuum
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Heat Transfer Modes - Conduction
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Rate equation (Fourier & Biot, 1820) is known
as Fourier’s law; for 1-D conduction,
dT
qx  kA
dx
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or
dT
qx  k
dx
where qx = heat rate in x-direction (W)
q”x = heat flux in x-direction (W/m2)
T = temperature (°C or K)
A = area normal to heat flow (m2)
k = thermal conductivity of material
(W/m-K); see Tables A.1-A.7
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Heat Transfer Modes - Conduction
Steady-state heat conduction through a plane
wall:

T1
k
T2
L
q (T1>T2)
x
dT
qx  constant   k
dx
dT
if k  constant, then
 constant
dx
dT T2  T1
T1  T2


, qx  k
dx
L
L
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Heat Transfer Modes - Conduction
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Example: What thickness of plate glass would
yield the same heat flux as 3.5 of glass-fiber
insulation with the same S-S temperature
difference (T1-T2) ?
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Heat Transfer Modes - Conduction
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Insulation “R-value”:
L ft 
" R - value" 
 Btu 
k
 hr - ft - F 
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where 1 W/m-K = 0.578 Btu/hr-ft-°F
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Heat Transfer Modes - Convection
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Rate equation (Newton, 1700) is known as
Newton’s law of “cooling”:
q  h(Ts  T )
Fluid flow, T
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or
q  hAs (Ts  T )
q
Ts (>T)
As
where q” = heat flux normal to surface
q = heat rate from or to surface As
Ts = surface temperature
T = freestream fluid temperature
As = surface area exposed to fluid
h = convection heat transfer coefficient
(W/m2-K)
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Heat Transfer Modes - Convection
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The convection heat transfer coefficient (h)
– is not a material property
– is a complicated function of the many
parameters that influence convection such
as fluid velocity, fluid properties, and
surface geometry
– is often determined by experiment rather
than theory
– will be given in most HW problems until we
reach Chapter 6
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Heat Transfer Modes - Convection
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Types of Convection
– Forced convection: flow caused by an
external source such as a fan, pump, or
atmospheric wind
– Free (or natural) convection: flow induced
by buoyancy forces such as that from a
heated plate
– Phase change convection: flow and latent
heat exchange associated with boiling or
condensation
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Heat Transfer Modes - Radiation
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Rate equation is the Stefan-Boltzmann law which gives
the energy flux due to thermal radiation that is emitted
from a surface; for a black body:
Eb  Ts4
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For non-black bodies,
E  Ts4
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where E = emissive power (W/m2)
 = Stefan-Boltzmann constant
= 5.67x10-8 W/m2-K4
 = emissivity (0< <1) of surface
Ts = surface temperature in absolute
units (K)
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Heat Transfer Modes - Radiation
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Radiation incident upon an object may be
reflected, transmitted, or absorbed:
G
G
G
G
where
G = irradiation (incident radiation)
 = reflectivity (fraction of G that is reflected)
 = transmissivity (fraction of G that is transmitted
 = absorptivity (fraction of G that is absorbed)
 = emissivity (fraction of black body emission)
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E and the interaction of G with each
participating object determines the net heat
transfer between objects
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Heat Transfer Modes - Radiation
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Heat transfer between a small object and
larger surroundings (As<<Asur):
4
q"   (Ts4  Tsur
) or
4
q  As (Ts4  Tsur
)
Tsur
q
 , As
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Ts
where  = emissivity of small object
As = surface area of small object
Ts = surface temperature of small
object (K)
Tsur = temperature of surroundings (K)
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Conservation of Energy – Control
Volume
Control volume energy balance:
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Q
mass out
mass in
W
– from thermodynamics:
 i ui  Pi vi  Vi2 / 2  gzi  
Q  W   m
i
2


m
u

P
v

V
 e e e e e / 2  gze  
e
dEcv
dt
– Incropera & DeWitt text notation:
Ein  Eout  E g  E st
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Conservation of Energy – Control
Volume
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Energy rates:
E in  all heat and work rates entering CV
E out  all heat and work rates exiting CV
E  rate of energy generation within CV
g
E st  rate of energy storage within CV
– where:
dT

Est  cvV
for ideal gases and
dt
incompressible substances
E st  0 if steady - state conditions exist
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Conservation of Energy – Control
Surface
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Surface energy balance:
Eout
Ein
– since a control surface is a special control
volume that contains no volume, energy
generation and storage terms are zero; this
leaves:
E in  E out  0
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Summary: The Laws Governing
Heat Transfer
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Fundamental Laws
– Conservation of mass
– Conservation of momentum
– Conservation of energy
Heat Rate Laws
– Fourier’s law of heat conduction
– Newton’s law of convection
– Stefan-Boltzmann law for radiation
Supplementary Laws
– Second law of thermodynamics
– Equations of state:
» ideal gas law
» tabulated thermodynamic properties
» caloric equation (definition of specific heat)
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Objectives of a Heat Transfer
Calculation
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ANALYSIS
– Calculate T(x,y,z,t) or q for a system
undergoing a specified process
» e.g., calculate daily heat loss from a house
» e.g., calculate operating temperature of a
semiconductor chip with heat sink/fan
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DESIGN
– Determine a configuration and operating
conditions that yield a specified T(x,y,z,t) or q
» e.g., determine insulation needed to meet a
specified daily heat loss from a house
» e.g., determine heat sink and/or fan needed to keep
operating temperature of a semiconductor chip
below a specified value
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Classes of Heat Transfer Problems
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Thermal Barriers
– insulation
– radiation shields
Heat Transfer Enhancement (heat
exchangers)
– boilers, evaporators, condensers, etc.
– solar collectors
– finned surfaces
Temperature Control
– cooling of electronic components
– heat treating & quenching of metals
– minimizing thermal stress
– heating appliances (toaster, oven, etc.)
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