ChE 350ChE 350ChE 350ChE 350Process Heat TransferProcess Heat TransferProcess Heat TransferProcess Heat Transfer
1
Darrell VelegolPenn State [email protected] notes 06jan2009
01 Introduction01 Introduction01 Introduction01 Introduction• today. Conduction, convection, radiation. q = UA ∆TlmF
SyllabusStory CENTER. owNershipCost of heating a home in winter?
• HW / quiz HW 01. Coming on Thursday
2
quiz 01. Pre-test (due Thursday before class)
• announce.No class on inauguration day, 20jan2009.Next week. MLK Jr. week.
• pre-read. Ch 1 of Pitts & Sissom (P&S)Wikipedia “Heat Transfer”
Heat transfer and sweatHeat transfer and sweatHeat transfer and sweatHeat transfer and sweat
What factors go into how much you sweat during exercise?
3
Conduction … at the Marine Corps MarathonConduction … at the Marine Corps MarathonConduction … at the Marine Corps MarathonConduction … at the Marine Corps Marathon
Mechanism
insulators – phononsmetals – electrons
4
Convection … at the Marine Corps MarathonConvection … at the Marine Corps MarathonConvection … at the Marine Corps MarathonConvection … at the Marine Corps Marathon
5
Mechanism
fluid movement
Radiation … at the Marine Corps MarathonRadiation … at the Marine Corps MarathonRadiation … at the Marine Corps MarathonRadiation … at the Marine Corps Marathon
6
Mechanism
electromagnetic radiation
The most important equation in “heat transfer”The most important equation in “heat transfer”The most important equation in “heat transfer”The most important equation in “heat transfer”
TFUAq ∆=
q = heat transfer rate [=] W or BTU/h
7
q = heat transfer rate [=] W or BTU/hq = qconduction + qconvection + qradiation
U = overall heat transfer coefficient [=] W/m2-KA = area [=] m2
∆T = Tout – Tin
F = geometric factor, often near to 1.000
( )∫=ft
dttqQ0
Example: Body heat lost by heat transferExample: Body heat lost by heat transferExample: Body heat lost by heat transferExample: Body heat lost by heat transfer
How many Cal/day must you eat to keep a constant body T?
Typical value for U? (P&S p 271)
What is the surface area of a person?
8
… now what causes “sweat”?
Story CENTER: owNershipStory CENTER: owNershipStory CENTER: owNershipStory CENTER: owNership
• Where do you imagine yourself in 5 years? 20 years?• How many books do you read a year?• Think of your 5 best friends and list their names. Are you leading each other in excellence?
Character
Excellence
Ownership
10
each other in excellence?• Name a person who you look up to. A hero? President of the United States? Movie star? Teacher? Your dad or mom?
Ownership
Tenacity
Entrepreneurship
Relationship
Goal: Comfortable, competent talking with expertsGoal: Comfortable, competent talking with expertsGoal: Comfortable, competent talking with expertsGoal: Comfortable, competent talking with experts
1 solve the most essential “standard problems”.
11
2 apply standard problems to processes and devices.
Lean Pocket and …sleeve (susceptor)
Find me in my officeFind me in my officeFind me in my officeFind me in my office
Instructor: Dr. Darrell Velegol108 Fenske Lab, (814) [email protected], www.velegol.org
Location: 307 Hammond Building, overflow 327 Sackett
Time: Tuesday/Thursday 11:15-12:30
12
Time: Tuesday/Thursday 11:15-12:30
Pre-reqs: ChE 220, 330
Web: ANGEL, take notes!
Our TAsOur TAsOur TAsOur TAs
TAs: Neetu Chaturvedi (175 Fenske + virtual)Laura Ramirez (175 Fenske + virtual)
Office Hours: 3:30-4:30 Mon for Velegol.Survey?
13
Course gradingCourse gradingCourse gradingCourse grading
A = 90%, B = 80%, C = 70%, D = 60%.
homework 10%weekly quiz 30%midterm exam 30%final exam (date to be determined) 30%
14
Tentative schedule of topicsTentative schedule of topicsTentative schedule of topicsTentative schedule of topics
Conduction. 1-D, 2-D, 3-D, fins.Convection. Boundary layers, Sieder-Tate.Radiation. Blackbodies, gray bodies.Heat exchangers. F factor, design equation.
Questions.• Size of HX? Cost? Increase capacity enough with flow?
15
• Size of HX? Cost? Increase capacity enough with flow?• Will applying radio waves to metal nanoparticles increase T?• Is adding insulation cost effective?• Can a microcomputer be cooled enough?
References. Most are on reserve in Engr Library.References. Most are on reserve in Engr Library.References. Most are on reserve in Engr Library.References. Most are on reserve in Engr Library.
P&SBSL
16
01 Introduction01 Introduction01 Introduction01 Introduction• today. Conduction, convection, radiation. q = UA ∆TlmF
SyllabusStory CENTER. owNershipCost of heating a home in winter?
• HW / quiz HW 01. Coming on Thursday
17
quiz 01. Pre-test (due Thursday before class)
• announce.No class on inauguration day, 20jan2009.Next week. MLK Jr. week.
• pre-read. Ch 1 of Pitts & Sissom (P&S)Wikipedia “Heat Transfer”
Example: Home heating cost Example: Home heating cost Example: Home heating cost Example: Home heating cost –––– what do you need?what do you need?what do you need?what do you need?
For Velegol’s home – a typical home – estimate the yearly heating bill ($200, $2k, $20k)? What do you need to know?
18
Summary Summary Summary Summary
TFUAq ∆=
Character
21
Character
Excellence
Ownership
Tenacity
Entrepreneurship
Relationship
List of symbols for Lecture 01List of symbols for Lecture 01List of symbols for Lecture 01List of symbols for Lecture 01
q = heat transfer rate [=] W or BTU/hq = qconduction + qconvection + qradiation
U = overall heat transfer coefficient [=] W/m2-KA = area [=] m2
∆T = Tout – Tin
F = geometric factor, often near to 1.000
22
F = geometric factor, often near to 1.000
( )∫=ft
dttqQ0
Opinion Box Opinion Box Opinion Box Opinion Box
• Take out a sheet of paper.• Keep your paper anonymous, without your name.
Let me know …• What made sense?• What was confusing?
23
• What was confusing?• Questions? Technical? Center? Personal? Fun?• Suggestions?• Comments?
02 The Conduction Equation02 The Conduction Equation02 The Conduction Equation02 The Conduction Equation
• today. demo: the magic conducting spoon!four important conservation lawsgeneral conduction equation
• HW / quiz. HW 01. Would you hire yourself? Ch 01 Problems.quiz 02. Chs 01 and part of 02
24
quiz 02. Chs 01 and part of 02
• announce.No class on 20jan2009.Next week. MLK Jr. week.
• pre-read. P&S chs 01 and 02
Opinion Box Opinion Box Opinion Box Opinion Box
• What made sense?• What was confusing?• Questions? Technical? Center? Personal? Fun?• Suggestions?• Comments?
25
A demonstration of conductionA demonstration of conductionA demonstration of conductionA demonstration of conduction
What factors go into how quickly a spoon gets hot or cold by conduction?
26
Quantifying conductionQuantifying conductionQuantifying conductionQuantifying conduction
dx
dTkAq −=
Fourier’s Law
27
qcond = conductive heat flow [=] W or BTU/hk = thermal conductivity [=] W/m-K or BTU/h-ft-FA = area of transfer [=] m2
dT/dx = temperature gradient [=] K/m or F/ft
Fourier’s Law
Example: P&S 1.1 about conductionExample: P&S 1.1 about conductionExample: P&S 1.1 about conductionExample: P&S 1.1 about conduction
Find heat per area through 4.0 cm slab, with T1 = 38 C, T2 = 21 C, k = 0.19 W/m-K.
28
For more complex problems, need conduction eqFor more complex problems, need conduction eqFor more complex problems, need conduction eqFor more complex problems, need conduction eq
P&S p 18-19
30
The mass balanceThe mass balanceThe mass balanceThe mass balance
moutin rmmdt
dm+−=
reactions, ChE 430
e.g., rm
=− kCAC
Bflow (ChE 330)
macroscopic mass balance (ChE 210)
31
e.g., rm
=− kCAC
Bflow (ChE 330)diffusion (ChE 410)
Antoine Lavoisier
( )
0
0
≈⋅∇
=⋅∇+∂
∂
v
vρρ
t
microscopic mass balance (various forms)
The momentum balance (Newton’s law)The momentum balance (Newton’s law)The momentum balance (Newton’s law)The momentum balance (Newton’s law)
bvvvv
+∇−∇=
∇⋅+
∂
∂
=
pt
Fma
2ηρ
32
Fluid flow, ChE 330
Isaac Newton George Gabriel Stokes1643-1727 1819-1903
The energy balance (1The energy balance (1The energy balance (1The energy balance (1stststst law of thermo)law of thermo)law of thermo)law of thermo)
wqhmhmgxv
umdt
doutoutinin &&& ++−=
++
2
2
Heat Transfer, ChE 350
33
Thermo, ChE 220, 320
FTUAq lm∆=
James Joule1818-1889
The entropy balance (2The entropy balance (2The entropy balance (2The entropy balance (2ndndndnd law of thermo)law of thermo)law of thermo)law of thermo)
Thermo, ChE 320
( )
T
qsmsm
dt
msdoutoutinin +−= &&
34
Rudolph Clausius1822-1888
How does entropy matter? $ / MM BTUshigher pressure steam costs more …than lower pressure steam …for the same energy content.
The “conduction equation” from a control volumeThe “conduction equation” from a control volumeThe “conduction equation” from a control volumeThe “conduction equation” from a control volume
P&S p 16
35
Conduction equation from a control volumeConduction equation from a control volumeConduction equation from a control volumeConduction equation from a control volume
( ) ( ) ( )
( ) ( ) ( )Tzcyx
TzcyxTVcTmcU
Vqqqqqqqt
U
genoutinacc
vvv
zzzyyyxxx
===
′′′+−+−+−=
+−=
+++
∆∆∆∆ρ
∆∆∆∆ρ∆∆ρ∆∆
∆∆
∆∆∆∆
rate of heat generated per volume(e.g., reaction, electrical, nuclear)
36
( ) ( ) ( )
W][dx
dTzyk
dx
dTkAq
zyxqqqqqqqt
Tzcyx
x
zzzyyyxxxv
=−=−=
′′′+−+−+−= +++
∆∆
∆∆∆∆
∆∆∆∆ρ∆∆∆
Complete form of the conduction equationComplete form of the conduction equationComplete form of the conduction equationComplete form of the conduction equation
v
qz
Tk
zy
Tk
yx
Tk
xt
T
c
k
.V
ρ
ρα
∆
′′′+
∂
∂
∂
∂+
∂
∂
∂
∂+
∂
∂
∂
∂=
∂
∂
≡
→
vc
0 as limit take and Substitute
38
vv c
q
z
T
y
T
x
T
c
k
t
T
ρρ
′′′+
∂
∂+
∂
∂+
∂
∂=
∂
∂2
2
2
2
2
2
... k uniform constant, Assume
vv c
qT
c
q
z
T
y
T
x
T
t
T
ρα
ρα
′′′+∇=
′′′+
∂
∂+
∂
∂+
∂
∂=
∂
∂ 2
2
2
2
2
2
2
P&S p 16, eq 2.2
Story CENTER: EntrepreneurshipStory CENTER: EntrepreneurshipStory CENTER: EntrepreneurshipStory CENTER: Entrepreneurship
Character
Excellence
Ownership
Tenacity
40
Tenacity
Entrepreneurship
Relationship
http://www.mlk.psu.edu
The conduction equation for several casesThe conduction equation for several casesThe conduction equation for several casesThe conduction equation for several cases
0 .conversion energy withstate, Steady .
.0 ),conversion energy internal No .
222
2
2
2
2
2
2
′′′∂∂∂
=∂∂
∂
∂+
∂
∂+
∂
∂=
∂
∂
=′′′
qTTT
.t/
z
T
y
T
x
T
t
T
q
equation Poisson
equationFourier
α
41
0
.0 0 .
0
2
2
2
2
2
2
2
2
2
2
2
2
=∂
∂+
∂
∂+
∂
∂
=∂∂=′′′
=′′′
+∂
∂+
∂
∂+
∂
∂
z
T
y
T
x
T
t/,q
k
q
z
T
y
T
x
T
equation Laplace
The conduction equation in various coordinatesThe conduction equation in various coordinatesThe conduction equation in various coordinatesThe conduction equation in various coordinates
v
v
c
q
z
T
y
T
x
T
t
T
c
qT
t
T
ρα
ρα
′′′+
∂
∂+
∂
∂+
∂
∂=
∂
∂
′′′+∇=
∂
∂
2
2
2
2
2
2
2
:Cartesian
42
vc
q
z
TT
rr
T
rr
T
t
T
ρθα
′′′+
∂
∂+
∂
∂+
∂
∂+
∂
∂=
∂
∂2
2
2
2
22
2 11 :lCylindrica
The conduction equation in various coordinatesThe conduction equation in various coordinatesThe conduction equation in various coordinatesThe conduction equation in various coordinates
( )
vc
q
T
sinr
Tsin
sinrrT
rr
t
T
ρ
φθ
θθ
θθα
′′′+
∂
∂+
∂
∂
∂
∂+
∂
∂
=∂
∂
2
2
22
22
2
1
11
:Spherical
43
In P&S they use ψ for θ.
Example: P&S 1.1 for T profileExample: P&S 1.1 for T profileExample: P&S 1.1 for T profileExample: P&S 1.1 for T profile
Find the temperature profile for a 4.0 cm slab, with T1 = 38 C, T2
= 21 C, k = 0.19 W/m-K.
44
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
A = area for heat transfer [=] m2
b = body force [=] N/m3
cv = constant volume heat capacity [=] J/kg-K; c = cv ≈ cp for solidg = gravitational acceleration [=] 9.8 m/s2
h = enthalpy per mass [=] J/kg; later used as “heat transfer coef”k = thermal conductivity [=] W/m-K or BTU / h-ft-Fm = mass [=] kg or lbm (note to use gc conversion with lbm)
46
m = mass [=] kg or lbm (note to use gc conversion with lbm)m = mass flowrate [=] kg/s when m has an overdotp = pressure [=] Pa
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
q = heat transfer rate [=] W or BTU/hq’’’ = heat generation rate per volume [=] W/m3
s = entropy per mass [=] J/kg-KT = temperature [=] C or K or F or Ru = internal energy per mass [=] J/kgU = internal energy [=] J; usually used in HT for “overall HT coef”v = velocity, v = speed [=] m/s
47
v = velocity, v = speed [=] m/sV = volume [=] m3
w = rate of work [=] Wx, y, z, r = distances in various coordinates [=] m
( )∫=ft
dttqQ0
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
α = k/ρc = thermal diffusivity [=] m2/s∆ = change in, as in ∆x.θ (ψ in P&S), φ = angles in various coordinates [=] noneη = viscosity [=] kg/m-s or Pa-s; 1 cP = 0.001 Pa-s.ρ = mass density [=] kg/m3
∇ = ix ∂/∂x + iy ∂/∂y + iz ∂/∂z ∇2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2
48
∇2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2
03 103 103 103 1----D Conduction ProblemsD Conduction ProblemsD Conduction ProblemsD Conduction Problems
• today. resistances in series (like Ohm’s law)heat generationstory CENTER. Entrepreneurshipconvective boundary condition
• HW / quiz. HW 01. Would you hire yourself? Ch 01 Problems.
50
• HW / quiz. HW 01. Would you hire yourself? Ch 01 Problems.quiz 02. Chs 01 and 02
• announce.Mid-term Exam.
• pre-read. P&S ch 02
Heat transfer in context: the 4 conservation lawsHeat transfer in context: the 4 conservation lawsHeat transfer in context: the 4 conservation lawsHeat transfer in context: the 4 conservation laws
general idea: acc = in – out + gen
MB. mass balanceMoB. momentum balance, also “Newton’s law”EB. energy balance, also “1st law of thermodynamics”EnB. entropy balance, also “2nd law of thermodynamics”
56
EnB. entropy balance, also “2 law of thermodynamics”
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
A = area for heat transfer [=] m2
b = body force [=] N/m3
cv = constant volume heat capacity [=] J/kg-K; c = cv ≈ cp for solidg = gravitational acceleration [=] 9.8 m/s2
h = enthalpy per mass [=] J/kg; later used as “heat transfer coef”k = thermal conductivity [=] W/m-K or BTU / h-ft-Fm = mass [=] kg or lbm (note to use gc conversion with lbm)
59
m = mass [=] kg or lbm (note to use gc conversion with lbm)m = mass flowrate [=] kg/s when m has an overdotp = pressure [=] Pa
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
q = heat transfer rate [=] W or BTU/hq’’’ = heat generation rate per volume [=] W/m3
s = entropy per mass [=] J/kg-KT = temperature [=] C or K or F or Ru = internal energy per mass [=] J/kgU = internal energy [=] J; usually used in HT for “overall HT coef”v = velocity, v = speed [=] m/s
60
v = velocity, v = speed [=] m/sV = volume [=] m3
w = rate of work [=] Wx, y, z, r = distances in various coordinates [=] m
( )∫=ft
dttqQ0
List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02List of symbols for Lecture 02
α = k/ρc = thermal diffusivity [=] m2/s∆ = change in, as in ∆x.θ (ψ in P&S), φ = angles in various coordinates [=] noneη = viscosity [=] kg/m-s or Pa-s; 1 cP = 0.001 Pa-s.ρ = mass density [=] kg/m3
∇ = ix ∂/∂x + iy ∂/∂y + iz ∂/∂z ∇2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2
61
∇2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2
Opinion Box Opinion Box Opinion Box Opinion Box
• Take out a sheet of paper.• Keep your paper anonymous, without your name.
Let me know …• What made sense?• What was confusing?
62
• What was confusing?• Questions? Technical? Center? Personal? Fun?• Suggestions?• Comments?
04 Fins04 Fins04 Fins04 Fins
• today. rectangular finsannular finsstory CENTER. Entrepreneurshipfin efficiency
• HW / quiz. HW 01. Would you hire yourself? Ch 01 Problems.
63
• HW / quiz. HW 01. Would you hire yourself? Ch 01 Problems.quiz 02. Chs 01 and 02
• announce.Mid-term Exam.
• pre-read. P&S ch 02
Opinion Box Opinion Box Opinion Box Opinion Box
• What made sense?• What was confusing?• Questions? Technical? Center? Personal? Fun?• Suggestions?• Comments?
64
Quantifying ConvectionQuantifying ConvectionQuantifying ConvectionQuantifying Convection
qconv = convective heat flow [=] WA = area of transfer [=] m2
h = heat transfer coefficient [=] W/m2-KTs = surface temperature [=] K
( )∞−= TThAq sconv
67
Ts = surface temperature [=] KT ∞ = ambient temperature [=] K
Top Related