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ChE 350 ChE 350 ChE 350 ChE 350 Process Heat Transfer Process Heat Transfer Process Heat Transfer Process Heat Transfer 1 Darrell Velegol Penn State University www.velegol.org [email protected] notes 06jan2009

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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?

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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

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Convection … at the Marine Corps MarathonConvection … at the Marine Corps MarathonConvection … at the Marine Corps MarathonConvection … at the Marine Corps Marathon

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Mechanism

fluid movement

Radiation … at the Marine Corps MarathonRadiation … at the Marine Corps MarathonRadiation … at the Marine Corps MarathonRadiation … at the Marine Corps Marathon

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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

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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?

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… now what causes “sweat”?

Blank for writing Blank for writing Blank for writing Blank for writing

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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

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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”.

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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

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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?

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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%

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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?

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• 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

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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?

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Blank for writing Blank for writing Blank for writing Blank for writing

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Blank for writing Blank for writing Blank for writing Blank for writing

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Summary Summary Summary Summary

TFUAq ∆=

Character

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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

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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

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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?

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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?

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Quantifying conductionQuantifying conductionQuantifying conductionQuantifying conduction

dx

dTkAq −=

Fourier’s Law

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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.

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blankblankblankblank

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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

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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)

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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

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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

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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 +−= &&

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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

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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)

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( ) ( ) ( )

W][dx

dTzyk

dx

dTkAq

zyxqqqqqqqt

Tzcyx

x

zzzyyyxxxv

=−=−=

′′′+−+−+−= +++

∆∆

∆∆∆∆

∆∆∆∆ρ∆∆∆

blankblankblankblank

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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

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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

blankblankblankblank

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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

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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

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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

blankblankblankblank

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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

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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

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∇2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2

titletitletitletitle

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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.

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• 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

titletitletitletitle

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Blank for writing Blank for writing Blank for writing Blank for writing

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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”

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EnB. entropy balance, also “2 law of thermodynamics”

Blank for writing Blank for writing Blank for writing Blank for writing

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titletitletitletitle

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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)

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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

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∇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

Thank you!Thank you!Thank you!Thank you!

65

titletitletitletitle

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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

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Ts = surface temperature [=] KT ∞ = ambient temperature [=] K

Example: Cost to heat Empire State BuildingExample: Cost to heat Empire State BuildingExample: Cost to heat Empire State BuildingExample: Cost to heat Empire State Building

How much does it cost to heat the Empire State Building?

$380,000$3,800,000

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$3,800,000$38,000,000?