Difference between the Effectiveness Effectiveness NTU and LMTD Methods for Analyzing Heat Exchangers? y !eff "ines# "enior $rod%ct Engineer# Engineered "oftware# &nc' As with any engineering (roble)# there there are vario%s ways to a((roach a sol%tion when sizing and selecting a heat exchanger or analyzing its ther)al (erfor)ance' &f the selected heat exchanger is %ndersized# the design heat transfer conditions will n ot be achieved' *es%lting in less heat transfer and higher o%tlet fl%id te)(erat%res# which leads to off+,%ality (rod%ction# exceeding environ)ental li)its# or creating safety hazards that re,%ire )itigation' -orrective action wo%ld re,%ire the (%rchase and installation of a (ro(erly sized heat exchanger# ca%sing additional downti)e for installation' A (ro(erly (ro(erly sized heat exchanger )%st have so)e excess ca(acity to acco%nt for fo%ling that will occ%r d%ring o(eration b%t significant oversizing res%lts in higher ca(ital and %nnecessary installation costs for ther)al ca(acity' The ther)al ca(acity of a heat e xchanger is its ability to transfer heat between two fl%ids at different te)(erat%res' &t is a f%nction of the heat exchanger design and the fl%id (ro(erties on both sides' The ther)al ca(acity of the heat exchanger wil l )atch the ther)al ca(acity re,%ired by the (rocess conditions .te)(erat%res and flow rates/ if it has s%fficient heat transfer area to do so' The Effectiveness+NTU and Log Mean Te Te)(erat%re )(erat%re Difference .LMTD/ are two sol%tion )ethods that a((roach heat exchanger analysis fro) different angles' oth )ethods share co))on (ara)eters and conce(ts and will arrive at the sa)e sol%tion to heat exchanger ther)al ca(acity' To %nderstand the difference between these two )ethods# we need to %nderstand the 0ey ter)inology and the e,%ations %sed in each sol%tion )ethod'
"tarting in $&$E+1L2 3 $rofessional 45'6# all (ara)eters in both )ethods are calc%lated to hel( syste) design engineers# heat exchanger )an%fact%rers# and (lant engineers size# select# and eval%ate the (erfor)ance of heat exchangers in their (i(ing syste)s'
The LMTD Method The LMTD )ethod is (erha(s the )ost co))only 0nown )ethod %sed to analyze heat transfer in heat exchangers and is described in the T%b%lar Exchanger Man%fact%rers Association .TEMA/ "tandards and other well+0nown ind%stry references' The e,%ation to calc%late the heat transfer rate is given by7
Q˙ UA) CMTD) UA) CF) LMTD) =( ( =( ( (
8here7 •
Q˙9 Heat Transfer *ate .TU:hr or 8/
•
UA 9 Heat Exchanger Ther)al -a(acity .TU:hr;<1 or 8:<-/
•
U 9 Heat Transfer -oefficient .TU:hr;ft=;<1 or 8: )=;<-/
•
A 9 Heat Transfer Area .ft = or )=/
•
-MTD 9 -orrected .or Tr%e/ Mean Te)(erat%re Difference .<1 or <-/
•
LMTD 9 Logarith)ic Mean Te)(erat%re Difference .<1 or <-/
•
-1 9 -onfig%ration -orrection 1actor .di)ensionless/
Log Mean Temperature Difference (LMTD) The Log Mean Te)(erat%re Difference .LMTD/ is calc%lated %sing the e,%ation for the current flow (attern .%nless it is a co)(letely single (ath (arallel flow (attern/7
LMTD=(dT ) / ln(dT A – dT B A / dT B)
8here7 •
dT A 9 .T hot in > T cold o%t/
•
dT 9 .T hot o%t > T cold in/
counter
Configuration Correction Factor (CF) The -onfig%ration -orrection 1actor .-1/ acco%nts for the d eviation of the internal flow (attern of the act%al heat exchanger fro) that of a single (ass co%nter c%rrent flow (attern' "o)e )an%fact%rers (rovide a -1 data table for their heat exchanger while others deter)ine -1 %sing a standard gra(h fro) the T%b%lar Exchanger Man%fact%rers Association .TEMA/ for the act%al heat exchanger config%ration' To deter)ine the -1# two te)(erat%re difference ratios .$ and */ )%st first be calc%lated fro) the fo%r fl%id te)(erat%res entering and leaving the heat exchanger'
Temperature Effectiveness (P) The Te)(erat%re Effectiveness .$/ is the ratio of the t%be side te)(erat%re change to the )axi)%) te)(erat%re difference across the heat exchanger'
P=d Ttube/d Tmax
8here7 •
dT)ax 9 .T
hot in
> T cold in/
Temperature Difference Ratio (R) The Te)(erat%re Difference *atio .*/ is the ratio of the te)(erat%re change across the shell side to the te)(erat%re difference across the t%be side'
R=d Tshell/ d Ttube
$ is li)ited to val%es between 6 and 4'6# b%t the *+val%e can be greater than 4'6 beca%se the t%be side is %sed as the reference side'
Corrected Mean Temperature Difference (CMTD) After calc%lating $ and *# -1 is then deter)ined gra(hically %sing the location of the $ val%e on the a((ro(riate * c%rve' &n other words# the heat exchanger o(erates at a (oint on a n * -%rve based on
the Te)(erat%re Effectiveness established by the o(erating conditions' The location of the o(erating (oint establishes the -onfig%ration -orrection 1actor that is %sed to calc%late the -orrected .or tr%e/ Mean Te)(erat%re Difference across the heat exchanger'
CMTD=( CF) LMTD) (
&t is desirable to o(erate a heat exchanger within a reasonable range aro%nd the 0nee@ of the * c%rves'
Required Thermal Capacit (!") # LMTD Method The re,%ired ther)al ca(acity .UA/ needed to achieve the heat transfer rate established by the te)(erat%res and flow rates is calc%lated fro) the Heat Transfer *ate and the -orrected Mean Te)(erat%re Difference'
UArequired=Q˙/( CMTD)
The heat exchanger will o(erate at this ther)al ca(acity as long as it has s%fficient heat transfer area at these o(erating conditions# incl%ding a factor for fo%ling'
Effectiveness+NTU Method The Effectiveness+NTU )ethod ta0es a different a((roach to solving heat exchange analysis by %sing three di)ensionless (ara)eters7 Heat -a(acity *ate *atio .H-**/# Effectiveness ./# and N%)ber of Transfer Units .NTU/' The relationshi( between these three (ara)eters de(ends on the ty(e of heat exchanger and the i nternal flow (attern'
$eat Capacit Rate Ratio ($CRR) The first di)ensionless (ara)eter is the Heat -a(acity *ate *atio .H-**/# the ratio of the )ini)%) to the )axi)%) val%e of Heat -a(acity *ate .H-*/ for the hot and cold fl%ids' The H-* of a fl%id is a )eas%re of its ability to release or absorb heat' The H-* is calc%lated for both fl%ids as the (rod%ct of the )ass flow rate ti)es the s(ecific heat ca(acity of the fl%id' p HCR=w c
8here7 •
H-* 9 Heat -a(acity *ate of the hot or cold fl%id .TU:hr;<1 or 8:<-/
•
w 9 )ass flow rate of the fl%id .lb:hr or 0g:sec/
•
c( 9 s(ecific heat ca(acity of the fl%id .TU:lb;<1 or !:0g <-/
n/HCRma x HCRR=HCRmi
8here7 •
H-*)in 9 )ini)%) val%e of Heat -a(acity *ate of the hot or cold fl%id
•
H-*)ax 9 )axi)%) val%e of Heat -a(acity *ate of the hot or cold fl%id The H-** is li)ited to val%es between 6 and 4'6 and is si)ilar to the * ratio in the LMTD )ethod' 8hen * B 4'6 H-** 9 *' 1or val%es of * C 4'6# H-** 9 4:*'
Effectiveness (%) The second (ara)eter# Effectiveness ./# is defined as the ratio of the act%al heat transfer rate to the )axi)%) (ossible heat transfer rate for the given flow and te)(erat%re conditions'
ϵ=Q˙ /Q˙max
8here7 •
Q˙9 act%al heat transfer rate
•
ma x9 )axi)%) (ossible heat transfer rate Q˙
The )axi)%) (ossible heat transfer rate is achieved if the fl%id with the )ini)%) val%e of H-* ex(eriences the )axi)%) dT across the heat exchanger'
Q˙ HCRmi d Tmax) n) =( (
8here7 •
H-* )in 9 )ini)%) val%e of heat ca(acity rate between the hot and cold fl%ids
•
dT )ax 9 .T hot in > T cold in/ This definition of Effectiveness ./ is si)ilar to the definition of Te)(erat%re Effectiveness .$/ in the LMTD )ethod b%t %ses the side with the )ini)%) val%e of the Heat -a(acity *ate as the reference instead of the t%be side' 8hen * B 4'6# 9 $' 1or val%es of * C 4'6# 9 $*'
&um#er of Transfer !nits (&T!) The last di)ensionless (ara)eter# the N%)ber of Transfer Units .NTU/# is the ratio of the heat exchangers ability to transfer heat .UA/ to the fl%ids )ini)%) ability to absorb heat .H-* )in/'
n NTU=UA/HCRmi
The NTU is a f%nction of the Effectiveness and H-** established by the (rocess te)(erat%res and flow rates and is indicative of the size of the heat exchanger needed' The greater the val%e of NTU# the larger the heat transfer s%rface area .A/ re,%ired to )eet the (rocess conditions' NTU is nor)ally not calc%lated fro) the e,%ation above# b%t instead solved gra(hically or %sing e,%ations for NTU as a f%nction of the Effectiveness and H-**'
Required Thermal Capacit (!") # %'&T! Method The ther)al ca(acity .UA/ re,%ired to achieve the heat transfer rate is deter)ined by re+arranging the NTU e,%ation after deter)ining the val%e of NTU for the (artic%lar heat exchanger config%ration'
UArequi NTU) HCRmi r e d=( n) (
"i)ilar to the LMTD )ethod# the heat exchanger will o(erate at this ther)al ca(acity as long as it has s%fficient heat transfer area at these o(erating conditions# ta0ing into acco%nt the fo%ling factor'
Mathematical &T! olution E,%ations exist for calc%lating NTU fro) Effectiveness and H-** for so)e# b%t not all# heat exchanger config%rations' 1or exa)(le# for a (%re single (ass co%nter c%rrent flow heat exchanger7
(
)(
)
NTU= 1/HCRR−1 l nϵ ϵ −1/HCRR∙ −1
E,%ations for NTU vary by heat exchanger config%ration# b%t the )athe)atical relationshi( for so)e ty(es of heat exchangers is not readily available or easily derived'
raphical &T! olution As with the LMTD )ethod# a sol%tion can be fo%nd gra(hically %sing an +NTU c%rve for the act%al heat exchanger config%ration' NTU is deter)ined %sing the location of the Effectiveness on the a((ro(riate H-** c%rve' The +NTU c%rves for (%re single (ass (arallel flow .worst config%ration/ and (%re single (ass co%nter c%rrent flow .best config%ration/ are shown' The co%nter c%rrent config%ration shows all H-** lines a((roaching an Effectiveness of 4'6 as NTU increases# indicating that this config%ration can achieve any val%e of Effectiveness for all ranges of H-**# as long as the heat transfer area is s%fficiently large eno%gh' However# the (arallel flow config%ration shows an achievable Maxi)%) Effectiveness for each H-** c%rve' "ince the heat exchanger )%st o(erate on an H-** c%rve within the region defined by the H-** 9 6 and H-** 9 4'6 c%rves# val%es of Effectiveness above the Maxi)%)
Effectiveness cannot be achieved regardless of how )%ch heat transfer s%rface area is available .i'e' how large the NTU val%e beco)es/'
-o)(aring LMTD and +NTU -%rves The +NTU c%rves for two ty(es of shell and t%be heat exchangers is shown' The left c%rve shows a one shell : two t%be (ass heat exchanger and the right c%rve shows a two shell : fo%r t%be (ass heat exchanger' These heat exchangers have corres(onding -1+$+* c%rves shown in the disc%ssion of the LMTD )ethod' The one shell : two t%be (ass heat exchanger has so)e ( ortion of flow that is co%nter flow# so)e is (arallel flow# and so)e is cross flow' Each H-** c%rve flattens to a )axi)%) val%e of Effectiveness as was the case for the (%re single (ass (arallel flow heat exchanger' 1or this config%ration# the Maxi)%) Effectiveness for a given H-** c%rve is greater than that for a (%re single (ass (arallel flow config%ration' The two shell : fo%r t%be (ass heat exchanger +NTU c%rve shows that the )ore shells and t%be (asses in the heat exchanger# the )ore the (erfor)ance a((roaches that of a single (ass co%nter c%rrent heat exchanger'
Engineering Analogies Analogies are often )ade between conce(ts in )any engineering disci(lines' oltage dro(# c%rrent# and electrical resistance are analogo%s to (ress%re dro(# fl%id flow# and hydra%lic resistance# which are analogo%s to the te)(erat%re difference# heat transfer rate# and ther)al resistance' "i)ilarly# a direct co)(arison can be )ade between the ther)al ca(acity of a heat exchanger and the flow ca(acity of a control valve' A control valve is sized and selected to )eet the hydra%lic re,%ire)ents of the (i(ing syste)# which incl%des the design flow rate and (ress%re dro( across the valve' The control valve is slightly over+ sized to ens%re s%fficient ca(acity to deliver the re,%ired flow' The 1low -oefficient .-v/ re(resents the flow ca(acity of a valve# which varies with valve (osition fro) zero at f%lly closed to a )axi)%) val%e at 466F o(en' etween 6F and 466F the valve (osition is throttled s%ch that the flow coefficient of the valve )eets the flow coefficient re,%ired by the (rocess conditions .flow rate and (ress%re dro(/' "i)ilarly# a heat exchanger is sized and selected to )eet the ther)al re,%ire)ents of the syste)# which incl%des the design heat transfer rate at a tr%e )ean te)(erat%re difference across the heat exchanger' The Ther)al -a(acity .UA/ re(resents the heat exchangers ability to transfer heat and has a )axi)%) val%e based on the heat transfer s%rface area .A/ and the )axi)%) (ossible val%e of the heat transfer coefficient .U/G which de(ends on both fl%ids convection heat transfer coefficients# t%be wall thic0ness# )aterial cond%ction heat transfer coefficient# and fo%ling factors' The heat exchanger is not always o(erating at this )axi)%) Ther)al -a(acity b%t instead can be throttled@ to )eet the Ther)al -a(acity re,%ired by the (rocess conditions' This throttling of Ther)al -a(acity is acco)(lished by changing both fl%ids convection heat transfer coefficients by reg%lating the flow rates .and# therefore# the o%tlet te)(erat%res/ with control valves'
"%))ary
$i(ing syste)s are b%ilt to trans(ort fl%id to do wor0# transfer heat# and )a0e a (rod%ct' 8 hen designing (i(ing syste)s to s%((ort heat transfer between fl%ids# both the hydra%lic and ther)al conditions )%st be eval%ated to ens%re the (ro(er e,%i()ent is selected and installed' Eval%ating both the hydra%lic and ther)al conditions of a syste) can be a da%nting tas0 for any engineer and is often divided into different gro%(s who s(ecialize in a s(ecific field' The division often res%lts in )is%nderstanding# )isco))%nication# and )ista0es when integrating the wor0 of the vario%s gro%(s' &)(ro(erly sized e,%i()ent# whether the e,%i()ent is a (%)(# control valve or heat exchanger# res%lts in additional ca(ital and )aintenance costs# off+,%ality (rod%ction# environ)ental exc%rsions# and (otentially increase safety ris0s' Using co)(rehensive software tools li0e $&$E+1L23 $rofessional hel(s the design engineer# (rocess engineer# and owner:o(erator have a clear view of the syste) o(eration' • • • •
heatexchanger nt% l)td effectiveness
