Heat Exchangers

Heat exchangers are devices designed to transfer heat from one fluid to another without the fluids coming into contact. There are a wide variety of applications for heat exchangers, for example: radiators, air conditioning and power plants.

Mechanism of Heat Transfer by Conduction

The transfer of heat energy by conduction takes place within the boundaries of a system.

The rate equation which describes this mechanism is given by Fourier Law

Where    = rate of heat flow in X-direction by conduction in J/S or W,

k = thermal conductivity of the material. It quantitatively measures the heat conducting ability and is a physical property of t he material that depends upon the composition of the material, W/mK,

A = cross-sectional area normal to the direction of heat flow, m2,

dT/dx = temperature gradient at the section,

Thermal Conductivity of Materials

Thermal conductivity is a physical property of a substance and In general, It depends upon the temperature, pressure and nature of the substance. Thermal conductivity of materials are usually determined experimentally and a number of methods for this purpose are well known.

Thermal Conductivity of Gases:

According to the kinetic theory of gases, the heat transfer by conduction in gases at ordinary pressures and temperatures take place through the transport of the kinetic energy arising from the collision of the gas molecules.

Thermal conductivity of gases depends on pressure when very low «2660 Pal or very high (> 2 × 109 Pa). Since the specific heat of gases Increases with temperature, the thermal conductivity Increases with temperature and with decreasing molecular weight.

Thermal Conductivity of Liquids:

The molecules of a liquid are more closely spaced and molecular force fields exert a strong influence on the energy exchange In the collision process. The mechanism of heat propagation in liquids can be conceived as transport of energy by way of unstable elastic oscillations. Since the density of liquids decreases with increasing temperature, the thermal conductivity of non-metallic liquids generally decreases with increasing temperature, except for liquids like water and alcohol because their thermal conductivity first Increases with increasing temperature and then decreases.

Thermal Conductivity of Solids:

(i) Metals and Alloys:

The heat transfer in metals arises due to a drift of free electrons (electron gas). This motion of electrons brings about the equalization in temperature at all points of t he metals. Since electrons carry both heat and electrical energy. The thermal conductivity of metals is proportional to its electrical conductivity and both the thermal and electrical conductivity decrease with increasing temperature. In contrast to pure metals, the thermal conductivity of alloys increases with increasing temperature. Heat transfer In metals is also possible through vibration of lattice structure or by elastic sound waves but this mode of heat transfer mechanism is insignificant in comparison with the transport of energy by electron gas.

(ii) Nonmetals:

Materials having a high volumetric density have a high thermal conductivity but that will depend upon the structure of the material, its porosity and moisture content High volumetric density means less amount of air filling the pores of the materials. The thermal conductivity of damp materials considerably higher than the thermal conductivity of dry material because water has a higher thermal conductivity than air. The thermal conductivity of granular material increases with temperature.

Types of heat exchanger

Fixed Tube sheet, Floating head and U-tube condensers

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• Shell Side

• Tube Side

• Increase number of tubes

• Decrease tube outside diameter

• Increase LMTD correction factor and heat exchanger effectiveness

• Use counter flow configuration

• Use multiple shell configuration

• Increase surface area

• Increase tube length

• Increase shell diameter à increased number of tubes

• Employ multiple shells in series or parallel

There are two main types of heat exchangers.

The first type is regenerative type, in which hot and cold fluids are in the same space which contain a matrix of materials which work alternately as source for heat flow.

The second type of a heat exchanger is called the recuperative type, in which heat are exchanged on either side of a dividing wall by fluids

Types of Heat Exchangers by their flow arrangements

Heat exchangers are classified by their flow arrangements. There are two basic types of heat exchangers: in line flow and cross flow.

In line exchangers

In in line exchangers, the hot and cold fluids move parallel to each other. Heat exchangers where the fluids move in the same direction are referred to as parallel flow, exchangers where fluids move in the opposite direction are referred to as counter flow.

In Parallel flow heat exchangers, the outlet temperature of the "cold" fluid can never exceed the outlet temperature of the "hot" fluid. The exchanger is performing at its best when the outlet temperatures are equal.

Counter flow heat exchangers are inherently more efficient than parallel flow heat exchangers because they create a more uniform temperature difference between the fluids, over the entire length of the fluid path. Counter flow heat exchangers can allow the "cold" fluid to exit with a higher temperature than the exiting "hot" fluid.

The efficiency of a counter flow heat exchanger is sometimes characterized by the Log Mean Temperature Difference (LMTD) between the fluids. Lower values of LMTD indicate better heat exchanger performance.

Cross flow

In cross flow exchangers, the hot and cold fluids move perpendicular to each other. This is often a convenient way to physically locate the inlet and outlet ports in a small package, however, it is less thermally efficient than a purely counter flow design.

Many actual heat exchangers are a mixture of cross flow and counter flow due to space constraints that force the flow paths to wind back and forth.

Double-pipe Heat Exchanger:

It consists of two concentric tubes with one fluid flowing in the inner tube and the other fluid flowing in the annulus. There are two flow arrangements:

1)      Parallel-flow

2)      Counter flow

Cross flow Heat Exchanger:

The fluids move in cross flow (perpendicular to each other) with one fluid flowing in the tubes and the other fluid flowing over the tubes in the transverse direction. There are two configurations of cross flow exchangers:

 1)      Finned with both fluids unmixed

 2)      Unfinned with one fluid mixed and the other unmixed

Shell-and-tube Heat Exchanger

·      Consists of many tubes in one or more shells

·      Baffles are used to direct the flow of the shell-side fluid and to support the tubes.

Compact Heat Exchangers

·      They have dense arrays of finned tubes or plates.

·      They are used when at least one of the fluids is a gas

heat exchanger heat transfer rate formula

By considering overall energy balances for the hot and cold fluids, the total heat transfer rate is obtained as

Q = Mh x Cph (Thi-Tho) = C _h (Thi-Tho)  and

Q = Mc x Cpc (Tci-Tco) = C _c (Tci-Tco)
                                                

Where C_h and C_c are the hot and cold fluid heat capacity rates.

Also, energy balance across the exchanger wall gives

Heat transfer rate Q = U x As x Delta T lmtd

Where ΔT_lmtd is the log mean temperature difference (LMTD).

Delta T lmtd = Delta T2 – Delta T1/ln (Delta T2/Delta T1)

For parallel-flow heat exchanger,

Delta T1 = Delta Thi – Delta Tci

Delta T2 = Delta Tho – Delta Tco

 For counter flow heat exchanger,

Delta T1 = Delta Thi – Delta Tco

Delta T2 = Delta Tho – Delta Tci

Heat Exchanger Effectiveness-NTU Method

Ø The LMTD method of heat exchanger analysis is not convenient when only the inlet temperatures are known. In this case it is preferable to use an alternative approach termed the effectiveness-NTU method.

Ø The effectiveness of a heat exchanger is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate, i.e.

E = q /q max

Where,

qmax = Cmin (Thi - Tci)                                      

C_min = C_c or C_h, whichever is smaller.

E = Ch (Thi – Tho)/ Cmin (Thi – Tci)

   = Cc (Tco – Tci) / Cmin (Thi – Tci)

                                                         

Ø The effectiveness must be in the range 0 £ E £ 1. When it is known, the actual heat transfer rate may be determined from

      q = E Cmin (Thi – Tci)

For any heat exchanger, E is a function of two parameters, which are NTU and C_r, i.e.

       E =  f (NTU, C_r)                                                                      

    where,

       NTU is the number of transfer units, defined as

       NTU = U x A / Cmin                                                                                                       

      C_r is the heat capacity ratio, defined as

      Cr = Cmin/Cmax                                                                                           

Ø In heat exchanger design calculations, it is more convenient to work with E-NTU relations of the form

                   NTU = f (E, C_r)                                                                           

    

Comparison of parallel flow and counter flow operations

1) For the same inlet and outlet temperatures, ΔTlmtd, counter flow > ΔTlmtd, parallel flow. Hence, counter flow operation performs better than parallel flow operation.

2) Tc,o can exceed Th,o for counter flow but not for parallel flow.

General design consideration for tube side fluid

-High flow rate

-More corrosive fluid

-Fluids with high fouling and scaling

-High temperature

-Less viscous fluid

-Fluids with low pressure drop

General design consideration for shell side fluid

- Low temperature

 -Less corrosive fluids

- Low fouling and scaling

- Low flow rate

- Fluids with high pressure drop

- More viscous fluid

• Put dirty stream on the tube side - easier to clean inside the tubes

• Put high pressure stream in the tubes to avoid thick, expensive shell

• When special materials required for one stream, put that one in the tubes to avoid expensive shell

• Cross flow gives higher coefficients than in plane tubes, hence put fluid with lowest coefficient on the shell side

• If no obvious benefit, try streams both ways and see which gives best design

How to find out Shell thickness of condenser?

T = PD/2S

Where,

T = shell wall thickness

P = gauge pressure in the shell

D = diameter of shell

S = stress in the shell

Fouling in Condenser

Shell and tubes can handle fouling but it can be reduced by

·keeping velocities sufficiently high to avoid deposits

·avoiding stagnant regions where dirt will collect

·avoiding hot spots where coking or scaling might occur

·Avoiding cold spots where liquids might freeze or where corrosive products may condense for gases.

Baffles purposes in condenser

·Baffles serve two purposes:

1) Support the tubes for structural rigidity, preventing tube vibration and sagging.

2) Divert (direct) the flow across the bundle to Wet the the maximum tube surface area.

-When the tube bundle employs baffles,

-This leads to developing flow forever.

-For a baffled heat exchanger the higher heat transfer coefficients result from the increased turbulence.

-The heat transfer coefficient is higher than the coefficient for undisturbed flow around tubes without baffles.

-The velocity of fluid fluctuates because of the constricted area between adjacent tubes across the bundle.

Method to Increase heat transfer coefficient in condenser

o   Decrease the baffle spacing

o   Decrease baffle cut

Method to reduce Pressure Drop in condenser

•    Shell side

o   Increase the baffle cut

o   Increase tube pitch

o   Increase the baffle spacing

o   Use double or triple segmental baffles

•    Tube side

o   Increase tube diameter

o   Decrease number of tube passes

o   Decrease tube length and increase shell diameter and number of tubes

What are the allowable pressure drops and velocities in the exchanger?

Pressure drops are very important in exchanger design (especially for gases).  As the pressure drops, so does viscosity and the fluids ability to transfer heat.  Therefore, the pressure drop and velocities must be limited.  The velocity is directly proportional to the heat transfer coefficient which is motivation to keep it high, while erosion and material limits are motivation to keep the velocity low.  Typical liquid velocities are 1-3 m/s.  Typical gas velocities are 15-30 m/s.  Typical pressure drops are (5-8 psi) on the tube side and (3-5 psi) on the shell side.