Heat-Transfer : Heat Exchangers

(1) Economizer [Flue gases – Feed water]

(2) Air Preheater [Hot gases – Combustion air]

(3) Superheater [Flue gases – dry saturated Steam]

(4) Cooling Tower [Hot water –Atmosphere air]

(5) Jet Condenser [Steam – cold water]

(6) Oil cooler

(7) Steam Condenser (Vapour – Liquid): Steam condenser is a shell & tube Heat Exchanger.

From thermodynamics, we know that heat transferred in a constant pressure process is equal to change in enthalpy of fluid and as we commonly assume in any heat exchanger that both hot & cold fluids are flowing through the heat exchanger at constant pressure.

Rate of decrease of enthalpy of hot fluid = Rate of increase of enthalpy of cold fluid

CLASSIFICATION OF HEAT EXCHANGERS ON BASIS OF CONTACT:

(i) Indirect contact transfer type heat exchangers:

In this type of heat exchanger, both hot & cold fluids do not come into direct contact with each other but the transfer of heat occurs between them through a pipe wall of separation.

Examples:

(1) Surface condenser 

(2) Economizer 

(3) Superheater

(ii) Direct contact transfer type heat exchangers:

In this type of heat exchanger, both hot & cold fluids physically mix up with each other & exchange heat.

Example:

 (1) Cooling Tower 

 (2) Jet condenser

CLASSIFICATION OF  HEAT EXCHANGER ON BASIS OF RELATIVE DIRECTION:

(i) Parallel flow heat exchanger:  

In this heat exchanger, both Hot & Cold Fluid travel in the same direction parallel to each other.

(ii) Counterflow heat exchanger: 

In this heat exchanger, Hot & Cold Fluid travel in the opposite direction parallel to each other.

(iii) Cross flow heat exchanger: 

In this heat exchanger, Hot & Cold fluids travel in the perpendicular direction with respect to each other.

TEMPERATURE PROFILES OF HOT AND COLD FLUIDS:

(i) Parallel flow heat exchanger: 

(ii) Counterflow heat exchanger: 

The variation of ΔT with respect to x is much more pronounced in parallel-flow heat exchanger as compared to that in counter-flow heat exchanger.

 LOGARITHMIC MEAN TEMPERATURE DIFFERENCE (LMTD) OF HEAT EXCHANGER:

Logarithmic mean temperature difference is that constant temperature difference (maintained throughout heat exchanger) which would give same amount of heat transfer.

Q = U A ΔT_m

Where,

Q = total Heat Transfer Rate between hot & cold fluid

U = Overall Heat Transfer coefficient

ΔT_m = Logarithmic Mean Temperature Difference between hot and cold fluid

A = Total Heat Transfer Area of Heat Exchanger

(i) LMTD for Parallel flow heat exchanger: 

At x = 0, ΔT = ΔT_i = T_hi – T_ci

At x = L, ΔT = ΔT_e = T_he - T_ce

(ii) LMTD for Counterflow heat exchanger: 

At x = 0, ΔT = ΔT_i = T_hi – T_ce

At x = L, ΔT = ΔT_e = T_he – T_ci

For the same inlet & exit temperature of hot & cold fluids, The value of LMTD for counter-flow heat exchanger is more than that for parallel flow heat exchanger.

(iii) LMTD for Cross flow heat exchanger: 

LMTD for cross-flow heat exchanger can be obtained as

Where, F = correction factor,

 SPECIAL CASE REGARDING LMTD:

 When one of the fluids is undergoing change of phase like in steam condenser or evaporator or steam generator then,

Steam condenser:

(ΔT_m)_{parallel flow} = (ΔT_m)_{counter flow}

Effectiveness of heat exchanger:

It is defined as the ratio between actual heat transfer rate that is taking place between hot & cold fluids to the maximum possible heat transfer rate that can occur between them,

q_actual = Rate of enthalpy change of either fluid

q_actual = m_h C_ph (T_hi – T_he) = m_c C_pc (T_ce – T_ci)

q_max = maximum possible heat transfer rate= (m C_p)_small × (T_hi – T_ci)

Where (m C_p)_small  is the smaller capacity rate between hot & cold fluids.

Number of Transfer Units (NTU):

It is defined as the ratio between product of UA & small capacity rate between hot & cold fluids.

NTU being directly proportional to the area of the heat exchanger indicates overall size of the heat exchanger.

Capacity Rate Ratio (C):

C will become zero when one of the fluids is undergoing change of phase like steam condenser.

For any Heat Exchanger, ϵ = f (NTU, C)

 Effectiveness for the parallel flow heat exchanger:

Effectiveness for the counterflow heat exchanger:

 SPECIAL CASES:

CASE 1: when one of the fluids is undergoing change of phase, then C is equal to zero.

Hence,

CASE 2: The other extreme value of C=1, when both hot & cold fluids have equal capacity rates (m_h Cp_h = m_c C_pc)

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