Theory of Heat Exchanging

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Understanding of Qualities of An Ideal Heat Exchangers…..

Theoretical Base for Working of Heat Exchangers

• A Simple adiabatic Heat Exchanger model.

phihhot cTm ,, ,

pciccold cTm ,, ,

phehhot cTm ,, ,

pceccold cTm ,, ,

Hot fluid Cold fluid

hT

cT

Electrical Analogy of A Finite Heat Exchanger

Hot fluid Cold fluid

hT

cT

Basic Information for Overall Resistance/Conductance

Heat Transfer between two fluids separated by finite thick surface wall

First Level Engineering Compromise: Area

chgainiceccpcold TTLUDQTTcm 11,,,

Energy Balance:

2211 DUDU

chlossehihhphot TTLUDQTTcm 22,,,

1

2

2

1

D

U

D

U

Second Level Engineering Compromise: Teffective

Mean Temperature Difference

• A Simple adiabatic Heat Exchanger model.

phihhot cTm ,, ,

pciccold cTm ,, ,

phehhot cTm ,, ,

pceccold cTm ,, ,

Second Level Engineering Compromise: T

Simple Counter Flow Heat Exchangers

cpcold

hphot

cm

cmC

,

,

1C

Simple Counter Flow Heat Exchangers: C < 1

Simple Parallel Flow Heat Exchangers

Theoretical Base for Working of Heat Exchangers

• For an Infinitesimal Heat communication between cold and hot.

• A Simple adiabatic Heat Exchanger model.

phihhot cTm ,, ,

pciccold cTm ,, ,

phehhot cTm ,, ,

pceccold cTm ,, ,

Third Level Engineering Compromise: variation of U

U

How many "zones" are involved in A HX?

Various Simple Zones (HX)

How many "zones" are involved in A HX?

• "Zones" can best be defined as regimes of phase changes where the overall heat transfer coefficient (U) will vary. 

• Using T-Q (Temperature-Heat) diagrams are the best way to pinpoint zones. 

• The system is defined as co-current or countercurrent and the diagram is constructed. 

• The diagram on the left illustrates the use of T-Q diagrams. • These diagrams should accompany your basic (input-

output) diagram of the heat exchanger.   • Defining zones is one of the most important aspects of heat

exchanger design. 

Role of SG in Rankine Cycle

Gas to Phase Changing Fluid Heat Exchange

Liquid Heating

DPNL

Platen SHT

R

RHTR

LTSH

Economiser

APH ESP ID Fan

drum

Furnace

BCWpump

Bottom ash

stack

screentubes

Thermal Structure of A Boiler Furnace

dido Di

TubularFlow

Annular Flow

Overall heat transfer coefficient of a used HX, based on outside area:

ofowallfi

i

out

ii

outoutsideOverall

hRRR

AA

hAA

U11

1,

A Simple Heat Exchanger

owall

ii

outoutsideOverall

hR

hAA

U11

1,

i

owall d

d

kR ln

2

1

Overall heat transfer coefficient of a new/cleaned HX, based on outside area:

Thermal resistance of any annular solid structure:

MeanoutDPHX TUAQ