Heat Exchangers

A heat exchanger is an adiabatic steady flow device in which two or more flowing stream of fluids exchange heat between themselves due to temperature difference without loosing or gaining any heat from the surroundings.

Classification of heat Exchangers

Classification of Heat Exchangers

1. Direct transfer type heat exchanger : Both fluids could not come into contact with each other but exchnage heat through the pipe wall of separation. 

Examples:

• Economiser
• Air preheater
• Concentric type heat exchanger
• Pipe in pipe heat exchnager
• Super heaters

1. Parallel flow heat exchanger : Both fluids flow in same direction. 
   
2. Counter flow heat exchanger : Both fluids flow in opposite direction. 
   
3. Cross flow heat exchanger : both fluids flow in perpendicular direction with respect to each other. example : Automobile radiator  
   

2. Direct Contact type heat exchanger : Both hot and cold fluids mixed up with each other in order to exchange heat between themselves. These type of heat exchnagers are used when the mixing of fluids is harmless or desirable.

Examples:

• Cooling tower
• Jet Condonser

3. Regenerative type heat exchanger : Both hot and cold fluids alternatively pass through the heat exchanger i.e. high thermal capacity cellulose matraix, one heating it and other picking up from it.

Example : Ljungstorm air preheater use in gas turbine power plants.

Heat Exchanger Analysis

Let m =  Mass flow rate, kg/s

      Cp = Specific heat of fluid at constant pressure,  J/Kg-K

      Ti = inlet temperature 

      Te = exit temperature

      h in subscript represents hot fluid

      c in subscript represents cold fluid

Assuming that there is no heat loss to the surroundings and changes in potential and kinetic energy are negligible, from energy balance

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

   - (ΔH )hot fluid =(ΔH)cold fluid

\[\boxed{m_h C_{ph} (T_{hi} - T_{he}) = m_c C_{pc} (T_{ce} - T_{ci})} \]

Overall heat transfer coefficient (U)

\[\frac{1}{U} = \frac{1}{h_1} + \frac{1}{h_2} + F_1 + F_2 \]

Fouling factor (F) : It takes into account the thermal resistance offered by any scale or deposite formed on the either side of wall due to the chemical reaction between the flowing fluid and pipe material. Its unit is $m^2 K / watt$.

Temperature profile of fluids in heat exchanger

Variation of temperature when one of the fluids condense or boils:

Log Mean Temperature Difference (LMTD) Method

LMTD is defined as

\[ΔT_m = \frac{ΔT_i - ΔT_e}{ln(\frac{ΔT_i}{ΔT_e})}\]

• For Parallel flow HE

              \(ΔT_i = T_{hi} - T_{ci}\)

              \(ΔT_e = T_{he} - T_{ce}\)

• For Counter flow HE

              \(ΔT_i = T_{hi} - T_{ce}\)

              \(ΔT_e = T_{he} - T_{ci}\)

Heat transfer rate between hot and cold fluid $= Q = m_h C_{ph} (T_{hi} - T_{he}) = m_c C_{pc} (T_{ce} - T{ci})$

Area of the heat exchanger $ A = \frac{Q}{U ΔT_m}$

Note:

• For the same hot and cold fluids and for the same mass flow rate of both the fluids and for specified inlet and outlet temperatures, LMTD value for a counter-flow heat exchanger is always greater than that for a parallel-flow heat exchanger i.e. for the same heat transfer rate required the area of counter flow heat exchanger shall be lesser than parallel flow heat exchanger.
• When both the fluids have equal capacity rates (i.e. $m_h C_{ph} = m_c C_{pc}$) in counter flow heat exchanger then the temperature difference between the hot and the cold fluids will remain constant along the heat exchanger and that is equal to LMTD.

Effectiveness of heat exchanger ε

It is defined as the ratio of actual heat transfer rate between hot and cold fluid to the maximum possible heat transfer rate. 

\[ε = \frac{Q_{actual}}{Q_{max}}\]

where,

$Q_{actual} = m_h C_{ph} (T_{hi} - T_{he}) = m_c C_{pc} (T_{ce} - T{ci})$

$Q_{max} = (mC_p)_{small} * (T_{hi} - T_{ci})$

$(mC_p)_{small}$ is the smaller capacity rate between $m_h C_{ph}$ and $m_c C_{cp}$.

NTU Method

Number of Transfer Units (NTU) is defined as 

\[NTU = \frac{UA}{(mC_p)_{small}}\]

Since NTU is proportional to area of HE, it signifies the overall size of heat exchanger.

Capacity Rate Ratio (C)

It is defined as the ratio of smaller capacity rate to bigger capacity rate. 

\[C = \frac{(mC_p)_{small}}{(mC_p)_{Big}}\]

Note: C = 0 if one of fluid changes its phase.

ε = f(NTU, C)

• For parallel flow heat exchanger,

\[ε_{parallel} = \frac{1 - e^{- (1+C) NTU}}{1 + C}\]

• For Counter flow heat exchnager

\[ε_{counter} = \frac{1 - e^{-(1-C) NTU}}{1 - Ce^{-(1-C) NTU}}\]

If C = 0 then $ε_{parallel} = ε_{counter} = 1 - e^{-NTU}$

Note:

• When all the inlet and outlet temperatures are specified, the size of the heat exchanger can easily be determined using the LMTD method.
• NTU method is used when exit temperatures are not known.