TT

TC,in dAH,in C,out

H,out C,in H C

1 1ln T T

U AT T mCp mCp

TH TC

TH,inTH,out

TC

H H,in H,out C C,out C,in

H,in H,out C,out C,in

H C

1 1 and

mCp T T Q mCp T T

T T T TmCp Q mCp Q

TC,outQx

H H H C C C dH mCp dT Q mCp dT dH

H,in C,outH,in H

H,out C,in

ln T T A U T TT T Q

,out C,out C,inT T

H CH C

H C

and

QdA Q U T T dAU T T

Q QdT dTmCp mCp

LM

H,in C,out H,out C,in

Q QAU T

T T T TU

H C

H C H CH C

H C

1 1

mCp mCp

U T T dA U T T dAdT dT

mCp mCp

dT dT

H,in C,out

H,out C,in

lnT TT T

H C

H C H C

H C

1 1

1

dT dT U dAT T mCp mCp

d T TU

T T

H,in C,out 1T T A

dAmCp mCp

H,in C,out H,out C,in 1 2LM

H,in C,out 1

2H,out C,in

lnln

T T T T T TTT T T

TT T

H CT TH,out C,in H C0

H CSolved analytically if , , are constant

T T mCp mCp

mCp mCp U

TLM is also referred to as LMTD