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Heat transfer coefficient
From Wikipedia, the free encyclopedia
The heat transfer coefficient, inthermodynamicsand in mechanicaland chemical engineering,is used
in calculating the heat transfer,typically byconvectionor phase transitionbetween a fluid and a solid:
where
Q= heat flow in input or lost heat flow , J/s = W
h= heat transfer coefficient, W/(m2!
A= heat transfer surface area, m2
= difference in temperature between the solid surface and surrounding fluid area,
"rom the above e#uation, the heat transfer coefficient is
the proportionalitycoefficient between the heat flu$, that is heat flow per unit
area, q/A, and the thermodynamic driving force for the flow of heat (i%e%, the
temperature difference, T!%
The heat transfer coefficient has&'units in watts per s#uared meter )elvin: W/
(m2!%
*eat transfer coefficient is the inverse of thermal insulance%This is used for building
materials (+value! and for clothing insulation%
There are numerous methods for calculating the heat transfer coefficient in different
heat transfer modes, different fluids, flow regimes, and under
different thermohydraulicconditions% ften it can be estimated by dividing
the thermal conductivityof the convectionfluid by a length scale% The heat transfer
coefficient is often calculated from the -usselt number(adimensionless number!%
There are also online calculatorsavailable specifically for heat transfer fluid
applications%
.n understanding of convection boundary layers is necessary to understanding
convective heat transfer between a surface and a fluid flowing past it% . thermal
boundary layer develops if the fluid free stream temperature and the surface
temperatures differ% . temperature profile e$ists due to the energy e$change
resulting from this temperature difference%
http://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Mechanical_engineeringhttp://en.wikipedia.org/wiki/Mechanical_engineeringhttp://en.wikipedia.org/wiki/Chemical_engineeringhttp://en.wikipedia.org/wiki/Chemical_engineeringhttp://en.wikipedia.org/wiki/Heat_transferhttp://en.wikipedia.org/wiki/Heat_transferhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Phase_transitionhttp://en.wikipedia.org/wiki/Phase_transitionhttp://en.wikipedia.org/wiki/Proportional_(mathematics)http://en.wikipedia.org/wiki/Proportional_(mathematics)http://en.wikipedia.org/wiki/Heat_fluxhttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/Thermal_insulancehttp://en.wikipedia.org/wiki/Thermal_insulancehttp://en.wikipedia.org/wiki/R-value_(insulation)http://en.wikipedia.org/wiki/Clothing_insulationhttp://en.wikipedia.org/wiki/Thermal_hydraulicshttp://en.wikipedia.org/wiki/Thermal_conductivityhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Nusselt_numberhttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://www.heat-transfer-fluid.com/resources/heat-transfer-coefficient-calculator.phphttp://www.heat-transfer-fluid.com/resources/heat-transfer-coefficient-calculator.phphttp://en.wikipedia.org/wiki/File:Thermal_Boundary_Layer.jpghttp://en.wikipedia.org/wiki/File:Thermal_Boundary_Layer.jpghttp://en.wikipedia.org/wiki/Mechanical_engineeringhttp://en.wikipedia.org/wiki/Chemical_engineeringhttp://en.wikipedia.org/wiki/Heat_transferhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Phase_transitionhttp://en.wikipedia.org/wiki/Proportional_(mathematics)http://en.wikipedia.org/wiki/Heat_fluxhttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/Thermal_insulancehttp://en.wikipedia.org/wiki/R-value_(insulation)http://en.wikipedia.org/wiki/Clothing_insulationhttp://en.wikipedia.org/wiki/Thermal_hydraulicshttp://en.wikipedia.org/wiki/Thermal_conductivityhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Nusselt_numberhttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://www.heat-transfer-fluid.com/resources/heat-transfer-coefficient-calculator.phphttp://en.wikipedia.org/wiki/Thermodynamics -
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Thermal oundary 0ayer
The heat transfer rate can then be written as,
.nd because heat transfer at the surface is by conduction,
These two terms are e#ual1 thus
+earranging,
a)ing it dimensionless by multiplying by representative length 0,
The right hand side is now the ratio of the temperature
gradient at the surface to the reference temperature gradient%
While the left hand side is similar to the iot modulus% This
becomes the ratio of conductive thermal resistance to theconvective thermal resistance of the fluid, otherwise )nown as
the -usselt number, -u%
Alternative Method (A simple method for determining the overall heat transfer
coefficient)
. simple method for determining an overall heat transfer coefficient that is useful to find the heat transfer
between simple elements such as walls in buildings or across heat e$changers is shown below% -ote thatthis method only accounts for conduction within materials, it does not ta)e into account heat transfer
through methods such as radiation% The method is as follows:
Where:
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= the overall heat transfer coefficient (W/m2!
= the contact area for each fluid side (m2! (with .34 and .32 e$pressing either surface!
= the thermal conductivity of the material (W/m!
= the individual convection heat transfer coefficient for each fluid (W/m2!
= the wall thic)ness (m!
.s the areas for each surface approach being e#ual the e#uation can be written as the transfer coefficient
per unit area as shown below:
or
-T5: ften the value for is referred to as the difference of two radii where the inner and outer radii
are used to define the thic)ness of a pipe carrying a fluid, however, this figure may also be considered as
a wall thic)ness in a flat plate transfer mechanism or other common flat surfaces such as a wall in a
building when the area difference between each edge of the transmission surface approaches 6ero%
7omponent Wt% 8
7 9%; < 9%
"e >?%@ < >>
n 9%@ < 9%>
A a$ 9%9
& a$ 9%9B
aterial -otes:
Typical uses include machine, plow, and carriage bolts, tie wire, cylinder head studs, and machined parts, Cbolts,
concrete reinforcing rods, forgings, and noncritical springs%
Ahysical Aroperties etric 5nglish 7omments
Density ;%?B g/cc 9%2? lb/in 7hemical composition of 9%B8 7, 9%@>8 n, 9%298 &i, annealed at ?@9E7
(4B?9E"!%
echanical Aroperties
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*ardness, rinell 4> 4>
*ardness, noop 4@> 4@> 7onverted from rinell hardness%
*ardness, +oc)well ?9 ?9 7onverted from rinell hardness%
*ardness, Fic)ers 4BB 4BB 7onverted from rinell hardness%
Tensile &trength, Cltimate B2B Aa ;@499 psi
Tensile &trength, Gield 2>9 Aa 2499 psi
5longation at rea) 4? 8 4? 8 in B9 mm
+eduction of .rea 9 8 9 8
odulus of 5lasticity 299 HAa 2>999 )si Typical for steel
ul) odulus 49 HAa 2999 )si Typical for steels
AoissonIs +atio 9%2> 9%2> Typical "or &teel
'6od 'mpact > J @%4 ftlb as rolled, B J ( ftlb! annealed at ;>9E7 (4B9E"!, @B J (? ftlb! normali6ed at >99E7
(4@B9E"!
&hear odulus ?9 HAa 44@99 )si Typical for steels
5lectrical Aroperties
5lectrical +esistivity 4%;4e99B ohmcm 4%;4e99B ohmcm 29E7 (@?E"!
5lectrical +esistivity at 5levated Temperature 9%9994444 ohmcm 9%9994444 ohmcm ?99E7 (4;9E"!
5lectrical +esistivity at 5levated Temperature 9%99944> ohmcm 9%99944> ohmcm >99E7 (4@B9E"!
5lectrical +esistivity at 5levated Temperature 9%99944;> ohmcm 9%99944;> ohmcm 4999E7
5lectrical +esistivity at 5levated Temperature 2%24e99B ohmcm 2%24e99B ohmcm 499E7 (242E"!
5lectrical +esistivity at 5levated Temperature 2%>@e99B ohmcm 2%>@e99B ohmcm 299E7 (>9E"!
5lectrical +esistivity at 5levated Temperature %>e99B ohmcm %>e99B ohmcm 99E7 (;B9E"!
5lectrical +esistivity at 5levated Temperature ;%@e99B ohmcm ;%@e99B ohmcm @99E7 (4449E"!
5lectrical +esistivity at 5levated Temperature >%2e99B ohmcm >%2e99B ohmcm ;99E7 (42>9E"!
Thermal Aroperties
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7T5, linear 29E7 44% m/mE7 @%2? in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u%1 29499E7 (@?242E"!
7T5, linear 29E7 42%4 m/mE7 @%;2 in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u%1 29299E7 (@?>9E"!
7T5, linear 2B9E7 42%2 m/mE7 @%;? in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u1 2999E7 (@?B;9E"!
7T5, linear 2B9E7 4% m/mE7 ;%> in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u1 2999E7 (@?;B9E"!
7T5, linear B99E7 4%> m/mE7 ;%;2 in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u1 29B99E7 (@?>9E"!
7T5, linear B99E7 4%2 m/mE7 ;%?> in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u1 29@99E7 (@?4449E"!
7T5, linear B99E7 4%? m/mE7 ?%22 in/inE" 7omposition of 9%98 7, 9%448 n, 9%948 A, 9%98 &, 9%98 &i,
9%98 7u1 29;99E7 (@?42>9E"!
7T5, linear 4999E7 4%; m/mE7 ?%4; in/inE" Typical steel
&pecific *eat 7apacity 9%?@ J/gE7 9%44@ TC/lbE" B9499E7 (422242E"!
&pecific *eat 7apacity at 5levated Temperature 9%B4B J/gE7 9%42 TC/lbE" 4B9299E7 (99>9E"!
&pecific *eat 7apacity at 5levated Temperature 9%B2? J/gE7 9%42@ TC/lbE" 2992B9E7 (>9?9E"!
&pecific *eat 7apacity at 5levated Temperature 9%B? J/gE7 9%44 TC/lbE" 2B999E7 (?9B;9E"!
&pecific *eat 7apacity at 5levated Temperature 9%B@> J/gE7 9%4@ TC/lbE" 99B9E7 (B;9@@9E"!
&pecific *eat 7apacity at 5levated Temperature 9%B?@ J/gE7 9%4 TC/lbE" B999E7 (@@9;B9E"!
&pecific *eat 7apacity at 5levated Temperature 9%@2 J/gE7 9%4> TC/lbE" ;B9?99E7 (4?94;9E"!
&pecific *eat 7apacity at 5levated Temperature 9%@> J/gE7 9%4BB TC/lbE" B9B99E7 (;B9>9E"!
&pecific *eat 7apacity at 5levated Temperature 9%;9? J/gE7 9%4@> TC/lbE" BB9@99E7 (49294449E"!
&pecific *eat 7apacity at 5levated Temperature 9%;; J/gE7 9%4? TC/lbE" @B9;99E7 (429942>9E"!
&pecific *eat 7apacity at 5levated Temperature 4%B? J/gE7 9%;? TC/lbE" ;99;B9E7 (42>94?9E"!
Thermal 7onductivity B9%; W/m B2 TCin/hrft2E" 499E7 (242E"!
Thermal 7onductivity B4%> W/m @9 TCin/hrft2E" 9E7
Thermal 7onductivity at 5levated Temperature 2%; W/m 4;4 TCin/hrft2E" ?99E7
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Thermal 7onductivity at 5levated Temperature 2>%? W/m 29; TCin/hrft2E" 4299E7 (24>9E"!
Thermal 7onductivity at 5levated Temperature 9%4 W/m 29> TCin/hrft2E" ;99E7 (42>9E"!
Thermal 7onductivity at 5levated Temperature 2%> W/m 22? TCin/hrft2E" 4999E7 (4?9E"!
Thermal 7onductivity at 5levated Temperature %> W/m 2B TCin/hrft2E" @99E7 (4449E"!
Thermal 7onductivity at 5levated Temperature ?%2 W/m 2@B TCin/hrft2E" B99E7 (>9E"!
Thermal 7onductivity at 5levated Temperature 4%; W/m 2?> TCin/hrft2E" 99E7 (;B9E"!
Thermal 7onductivity at 5levated Temperature B%; W/m 4; TCin/hrft2E" 99E7 (B;9E"!
Thermal 7onductivity at 5levated Temperature ?%4 W/m TCin/hrft2E" 299E
Disclaimer: The information on this page has not been chec)ed by an independent person% Cse thisinformation at your own ris)%
+G57*
HomeThermos Index
Heat Transfer
Introduction..... Symbols.....Heat transfer by conduction..... Heat transfer by
radiation.....Heat transfer by Convection..... Heat Exchangers.....
Introduction
This page provides notes on heat transfer that may be useful to mechanical engineers. Thesubject is very complicated and any user who reuires accurate heat transfer values isadvised to refer to uality reference documents or use specialised software.
!hen a hot surface us surrounded by an area which is colder energy in the form of heat willbe transferred from the hot surface to the cooler area. The rate of this transfer is dependedon the temperature di"erence and the process will continue until both the surface and thesurroundings are at the same temperature. This process in called heat transfer and ta#esplace by one or more of the following methods
ConductionConvection$adiation
Conduction ta#es place in solids% liuids% and gases. Solids o"er the least resistance totransfer of heat by conduction. Conduction reuires physical contact between materialthrough which the heat is transferred. & materials temperature is related to the motion ofthe constituent molecules. The conduction process involves the molecule moving at highervelocities transferring their #inetic energy to the adjacent molecures which have lower#inetic energy.
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Convection results in a gas or liuid. The 'uid adjacent to a hot surface heats up as a resultof conduction. The density of this 'uid is reduced and it therefore rises to be replaced by acolder 'uid of higher density. This process continues resulting in convective 'ow producingan enhanced transfer of heat throughout the 'uid.
The transfer of heat energy by radiation can occur in a vacuum % unli#e conduction andconvection. Heat radiation is the same form of wave energy transfer as light% radio% and x(ray wave energy. The rate of emmission of heat energy is related to the temperaturedi"erence% the distance between the surfaces% and the emissivity of the surfaces. )rightre'ective surfaces have the lowest emissivity values.
*otes on thermal insulation systems are found on webpage.Thermal Insulation
Symbols
K = *eat "low +ate (W !t 4= inside(hot!temperature,( !t &4= inside surface (hot!temperature,( !t 2= outside(cooler!temperature,( !t &4= outside surface(cooler!temperature,( !
. = .rea,( m 2!C = verall *eat Transfer 7oefficient,( W m 2 4!+ = Thermal +esistance, ( W 4% !
Kr= +adiated transferred energy (W!Kco= 7onducted transferred energy (W!Kcv= 7onvective transferred energy(W!T4= Temperature or radiating body (!T2Temperature or &uroundings (!
.4= .rea of +adiating surface (m2!.2=.rea of +eceiving surface (m2!
e4= 5missivity of+adiating surfacee2= 5missivity of
&urroundings= &tefan olt6manconstant = B,@; $ 49?Wm2
= fluid density ()g / m!= fluid viscosity ()g /m%s!= coeff% of vol e$pansion(4 /!= Temperature difference()!
c = specific heat (J/)g% !a = velocity of &ound(m/s!h = heat transfercoefficient (W /m2!) = Thermal conductivity(W/m!v = "luid velocity (m/s!0 = characteristicdimensiong = accelaration due to
gravity (m/s2
!
Heat Transfer by Conduction
dKco= ).(dt/d$!
Kco= ()%. /$!% (t 4t 2!
C = )/$
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Therefore K = C%.(t 4t 2!
Thermal resistance + = 4 / C%.
The heat has to pass through the surface layers on both sides of the wall+b+ p,--
+/b+
# = .%h s4(t s4 t 4! = )%.(t 4t 2! / $ = .h s2(t 2t s2!
C = 4 / (4/h s4L $/ ) L 4/ h s2!
+ = 4/ .%h s4L 4/ .%h s2L $/ .%) = + s4L + s2L +
Table Showing Various values for k at 20 oC
0etal#,!
m(12(1
.luminium 2;
.ntimony 4?%B
eryllium 24?
rass 449
7admium >2
7obalt @>7onstantan 22
7opper >?
Hold 4B
'ridium 4;
7ast 'ron BB
Aure 'ron ?9%
WrMt 'ron B>
0ead B%2
agnesium 4B@
olybdenum 4?
onel 2@
0isc.solids # ,!m(12(1
.sphalt 4%2@
itumen 9%4;
rM6e loc) 9%4B
ric)wor) 9%@
ric)Dense 4%@
7arbon 4%;
7onc0D 9%2
7oncD 9%B
7onc*D 4%B
"irebric) 4%9>
Hlass 4%9B
Hlass oro% 4%
'ce 2%4?
0imestone 4%4ica 9%;B
7ement 4%94
Aarafin Wa$ 9%2B
Aorcelain 4%9B
3iuids#,
!m(12(1
en6ene 9%4@
7arb TetMide 9%44
.cetone 9%4@
5ther 9%4
Hlycerol 9%2?
erosene 9%4Bercury ?
ethanol 9%24
achine il 9%4B
Water 9%B?
&odium ?
4ases#,
!m (12 (1
.ir 9%92
.mmonia 9%922
.rgon 9%94@
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-ic)el >9%B
Alatinum ;
&ilver 2;
7%&teel B9
&t%&teel 2B
Tin @;
Ninc 44
5lastics
.crylic 9%2
-ylon @ 9%2B1
Aolythene*igh Den
9%B
AT"5 9%2B
AF7 9%4>
&and 9%9@
Insulation#,!m(
12(1
alsa 9%9?
&traw7omp 9%9>
7otton Wool 9%92>
Aolystyrene5$pMd
9%9
"elt 9%9
Hlass Wool 9%9(29o
7apo) 9%9
agnesia 9%9;
Alywood 9%4
+oc) Wool 9%9B
&awdust 9%9@
&lag Wool 9%92
Wood 9%4
&heeps Wool 9%9?
7ellulose 9%9>
7arbon Dio 9%94B
7arbon on 9%92
*elium 9%42
*ydrogen 9%4@?
ethane 9%99
-itrogen 9%92
$ygen 9%92
Water Fap% 9%94@
Heat Transfer by Radiation
6 r, radiated energy 7!8T 1, Temperature or radiating body 728T 9Temperature or Suroundings 728& 1, &rea of $adiating surface 7m
98
& 9,&rea of $eceiving surface 7m98e 1, Emissivity of $adiating surfacee 9, Emissivity of Surroundings, Stefan )olt:man constant , ;% x 1? (@! m(92(A
hr, heat Transfer coeBcient for radiation 7!m(92(18
Heat radiation from a body to the surroundings
6 r, e17T1A( T9A8 &1
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Heat radiation including the e"ect of the surroundings
6 r, 7 e1T1A( e9T9A8 &1
*ow the heat transfer using the heat transfer coeBcient ,
6 r, h r& 17 T 1( T 98 therefore h r, e 17T 1 T 987 T 19 T 998
missivity Values
$efer to lin#Emissivity Daluesfor better table
&urfaceaterial
5mmissity &urface aterial 5mmissity
.luminium$idised
9%44 Tile 9%>;
.luminiumAolished
9%9B Water 9%>B
.luminiumanodised
9%;; Wooda) 9%>
.luminiumrough
9%9; Aaint 9%>@
.sbestosoard
9%> Aaper 9%>
lac) odyatt 4%99 Alastics 9%>4 .v
rass Dull 9%22 +ubber-at3*ard 9%>4
rassAolished
9%9 +ubber 3-at3&oft 9%?@
ric) Dar) 9%> &teel3$idised 9%;>
7oncrete 9%?B &teel Aolished 9%9;
7opper$idised
9%?;&t%&teelWeathered
9%?B
7opperAolished
9%9 &t%&teelAolished 9%4B
Hlass 9%>2 &teel Halv% ld 9%??
Alaster 9%>? &teel Halv new 9%2
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!atural convection
*u , C74r.5r8 nC and n are tabled below
*ote Convection heat transfer values are very speciJc to the geometry of the surface andthe heat transfer conditions ( These example euations are very general in nature and should
not be used for serious calcs. The lin#s below provide much safer euations..
Surface (Hr%Ar! 7 n
Dertical5lates/Cylinders
49 to 49 > 9%B> 9%2B
49 >to 49 42 9%4 9%
Hori:ontal 5ipes 49 to 49 > 9%B 9%2B
Hori:ontal 5latesHeated Gace up orCooled Gace own
49 Bto 2 $49 ;
9%B 9%2B
2 $49 ;to
$49 49 9%4 9%
Hori:ontal 5latesHeated Gace up orCooled Gace own
$49 Bto $49 49
9%2; 9%2B
"orced Convection
3aminar 'ow over 5late *u , ?%
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Grom this euation we can see that the O value is directly proportional to 6% the heattransfer rate. &ssuming the heat transfer surface and temperature di"erence remainunchanged% the greater the O value% the greater the heat transfer rate. In other words%this means that for a same #ettle and product% a higher O value could lead to shorterbatch times.
Several euations can be used to determine the O value% one of which is
whereh , convective heat transfer coeBcient% !/7m9C8 K)tu/7hr(ft9G8L3 , thic#ness of the wall% m KftLV , thermal conductivity% !/7mC8 K)tu/7hr(ftG8L
Heat transfer through a metal wall
The convective heat transfer coeBcient 7h8% sometimes referred to as the JlmcoeBcient% is often used when calculating heat transfer between a 'uid and a solid. Inthe case of a heat exchanger% heat transfer basically occurs from 'uid 1 7source of heat8to solid 7metal wall8 to 'uid 9 7product being heated8. In the event that heat transferoccurs through several solids% the above euation can be adapted by supplementing thesolidWs thic#ness 738 divided by its thermal conductivity 7V8.
To simplify the calculation% the following values may be used as a reference for theconvective heat transfer coeBcientsGluid Convective heat transfer coeBcient 7h8
!ater about 1??? !/7m9
C8 K1=< )tu/7hr(ft9
G8L
Hot !ater1??? X
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reactivity with the product. If such is the case and the heat transfer rate needs to beimproved% changing the heat source from hot water to steam may provide the neededsolution.