Draw the temperature profile in counter and parallel flow heat exchanger, why counter flow is more efficient

Temperature profile in Heat Exchanger:

The plot of “flow temperature” Vs “length of the tube” is known as temperature profile in Heat exchanger.  From the temperature profile we can conclude, which flow pattern is best in heat exchanger and why it is so.

Parallel flow temperature profile in 1-1 Heat Exchanger:

Sketch of 1-1 Heat Exchanger:

1-1   Heat exchanger means, 1-tube side and 1- shell side pass heat exchanger. It is as shown in the below figure

Parallel flow:

Temperature profile of 1-1 Heat exchanger – Parallel flow:

Counter Flow:

In counter flow tube side flow and shell side flow are in opposite direction, and a typical flow scheme is as shown in the figure.

Temperature profile of 1-1 Heat exchanger – Counter flow:



If we observe, we can see that, in counter flow there is uniform temperature difference between hot and cold fluids and this difference decreases with the length of the tube in parallel flow. From the above two temperature profiles we can conclude that counter flow is more efficient than parallel flow.

What is the driving force for Heat Transfer?

Temperature gradient (Temperature difference) is the driving force for heat transfer.

According to second law of Thermodynamics heat will flow from high temperature region to the low temperature region under normal conditions. If we use external force, like heat engine, heat can be transported from low temperature region to high temperature region too.

In case of conduction, Fourier's Law gives that,

q α ΔT

So, we can say that heat flow is directly proportional to the driving force.

Rotameter, Variable area meter, advantages, disadvantages, applications, flow to height relation, Force balance in rotameter,diagram

A variable area meter is a meter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.

A rotameter is an example of a variable area meter.

Rotameter:

Some important features of Rotameters:

•  In area meters "pressure drop" is constant.
• The area through which the fluid flows varies with flow rate. The area is related through proper calibration to the flow rate.
• These rotameters can be used for liquids and gases.

Rotameter consists of a gradually tapered tube, it is arranged in vertical position. The tube contains a float, which is used to indicate the flow of the fluid. This float will be suspended in the fluid while fluid flows from bottom of the tube to top portion. The entire fluid will flow through the annular space between the tube and float. The float is the measuring element. The tube is marked with the divisions and the reading of the meter is obtained from the scale reading at the reading edge of the float. Here to convert the reading to the flow rate a calibration sheet is needed.

For higher temperatures and pressure, where glass is not going to withstand, we use metalic tapered tubes. In metalic tubes, the float is not visible so we use a rod, which is called extension, which will be used as a indicator.

floats may be constructed using different types of materials from lead to aluminium or glass or plastic. Stainless steel floats are common. According to the purpose of the meter float shape will be selected.

Advantages:

•  Pressure drop is constant
• No special fuel or external energy is required to pump
• Very easy to construct and we can use a wide variety of materials to construct.

Disadvantages:

• Due to its use of gravity, a rotameter must always be vertically oriented and right way up, with the fluid flowing upward.
•  Due to its reliance on the ability of the fluid or gas to displace the float, graduations on a given rotameter will only be accurate for a given substance at a given temperature. The main property of importance is the density of the fluid; however, viscosity may also be significant. Floats are ideally designed to be insensitive to viscosity; however, this is seldom verifiable from manufacturers' specifications. Either separate rotameters for different densities and viscosities may be used, or multiple scales on the same rotameter can be used
• Rotameters normally require the use of glass (or other transparent material), otherwise the user cannot see the float. This limits their use in many industries to benign fluids, such as water.
• Rotameters are not easily adapted for reading by machine; although magnetic floats that drive a follower outside the tube are available.

Relation between flow and meter reading: ( Force balance in rotameter)

There are three forces acting on the float.

1. Gravity force (Weight of the float)
2. Drag force ( Due to fluid flow, in the direction of flow)
3. Buoyant force ( Due to density difference beween float and water)

By balancing the above forces,

Where
F_D = Drag force
g = Acceleration due to gavity
Vf = volume of float
rho-f = Density of float
rho = Density of fluid

In the above equation the right hand side is constant, so the drag force is constant. If flow rate increases the float position must change to keep the drag force as constant.

From the definition of drag coefficient,

As the fluid is flowing through the annulus region flow is directly proportional to annular area between the float and tube.



Where D_f = Diameter of the float

                D_t = Diameter of the tube.

For linearly tapered tube with a diameter at the bottom equal to the float diameter, the area for flow is a quadratic function of the height of the float ‘h’.

By neglecting a²h² term we get a linear relationship between flow and ‘h’.

In rotameter the flow is directly proportional to the square root of the reading on the tube.
 

Thermal Conductivity

Thermal Conductivity:

Thermal Conductivity of a material is defined from the above definition.

Heat flux of a material for unit temperature gradient for unit length is known as its thermal conductivity. Thermal Conductivity has the units of watts per meter per Celsius degree when heat flow is expressed in watts. The numerical values of thermal conductivities indicate how fast heat will flow in a given material.

Content:

1.       Basic concept of Thermal conductivity

2.       ThermalConductivity of gases

3.       ThermalConductivity of liquids

4.       ThermalConductivity of solids

5.       Experimental Determination of thermal conductivity

1.Basic concept of Thermal conductivity:

In general,

Here Potential is driving force for the transfer (In case of heat transfer it is temperature difference).

Conductance is defined as,

Therefore, Flow α (conductance X Potential)

In general conductance is directly proportional to the Area and inversely proportional to the length.

This can be written as,

 where ‘k’ is thermal conductivity of material.

From the above equation thermal conductivity is defined as below.

Definition of thermal conductivity:

When the conductance is reported for a quantity of material 1 ft thick material with heat flow area 1 ft², in 1 hr time, and with a temperature difference of 1^oF, it is called thermal conductivity ‘k’.

Finally heat flow equation can written as,

2. Thermal Conductivity of gases:

      Thermal conductivity evaluated experimentally.

      In general, the thermal conductivity is a strong function of temperature.

      The faster the molecules move, the faster they will transport energy.

      The thermal conductivity of a gas varies square root of the temperature (It may be recalled that the velocity of sound in gas varies with the square root of the temperature; this velocity is approximately the mean speed of the moles).

      Over a wide range of pressures thermal conductivity of gases considered to be constant.

Table 1: Thermal conductivities of some gases

Gases	Thermal conductivity (W/m .K)
Hydrogen	0.175
Helium	0.141
Air	0.024
Water vapour (saturated)	0.0206
CO­2	0.0146

3. Thermal Conductivity of liquids:

The physics of mechanism of thermal-energy conduction in liquids is quantitavely the same as in gases; however, the situation is more complex because the molecules are more closely special and molecular force fields exert a strong influence on the energy exchange in the collision process.

Typical values of thermal conductivities are:

Table 2: Thermal conductivities of some liquids

Liquids	Thermal conductivity (W/m .K)
Mercury	8.21
Water	0.556
Ammonia	0.540
Lubricating oil, SAE 50	0.147
Freon 12, CCl2F2	0.073

4. Thermal Conductivity of solids:

Thermal energy may be conducted in solids by two modes: lattice vibration and transport by free electrons.

                In good electrical conductors a rather large number of free electrons move about in the lattice structure of the material. Just as these electrons may transport electric charge; they may also carry thermal energy from a high-temperature region to a low temperature, as in the cases of gases.

In fact these electrons are frequently referred to as the electron gas.

Energy may also be transmitted as vibrational energy in the lattice structure of the material. In general, however, this lattice mode of energy transport is not as large as the electron transport, and for this reason good electrical conductors are almost always good heat conductors. V.Z. Cu, Al, and Ag, and electrical insulators are usually good heat insulators. A notable exception is diamond which is an electrical insulator; but which can have a thermal conductivity five times as high as silver or copper. It is this fact enables a jeweller to distinguish between genuine diamonds and fake stones. A small instrument is available to a thermal heat pulse. A true diamond will exhibit a far more rapid response than the non-genuine stone.

Solids	Thermal conductivity (W/m .K)
Silver	410
Copper	385
Aluminium	202
Nickel	93
Iron	73
CS, 1% C	43
Lead	35

References:

1.       “Heat Transfer”, J.P. Holman, Pages: 6-10

2.       “unit operations of chemical engineering”, Warren.l. Mccabe and Julian C. Smith, Pages: 291-292.

3.       “Process Heat Transfer”, D.Q. Kern, Pages:6-15

4.       “Heat Transfer a basic approach”, Necati Ozisik.

Thermal Conductivity of solids, silver, copper, aluminium, Nickel, iron, CS, Lead

Thermal Conductivity:

Thermal Conductivity of a material is defined from the above definition.

Heat flux of a material for unit temperature gradient for unit length is known as its thermal conductivity. Thermal Conductivity has the units of watts per meter per Celsius degree when heat flow is expressed in watts. The numerical values of thermal conductivities indicate how fast heat will flow in a given material.

Content:

1. Basic concept of Thermal conductivity

2. ThermalConductivity of gases

3. ThermalConductivity of liquids

4. Thermal Conductivity of solids

5. Experimental Determination of thermal conductivity

1.Basic concept of Thermal conductivity:

In general,

Here Potential is driving force for the transfer (In case of heat transfer it is temperature difference).

Conductance is defined as,

Therefore, Flow α (conductance X Potential)

In general conductance is directly proportional to the Area and inversely proportional to the length.

This can be written as,

where ‘k’ is thermal conductivity of material.

From the above equation thermal conductivity is defined as below.

Definition of thermal conductivity:

When the conductance is reported for a quantity of material 1 ft thick material with heat flow area 1 ft², in 1 hr time, and with a temperature difference of 1^oF, it is called thermal conductivity ‘k’.

Finally heat flow equation can written as,

2. Thermal Conductivity of gases:

Thermal conductivity evaluated experimentally.

In general, the thermal conductivity is a strong function of temperature.

The faster the molecules move, the faster they will transport energy.

The thermal conductivity of a gas varies square root of the temperature (It may be recalled that the velocity of sound in gas varies with the square root of the temperature; this velocity is approximately the mean speed of the moles).

Over a wide range of pressures thermal conductivity of gases considered to be constant.

Table 1: Thermal conductivities of some gases

Gases	Thermal conductivity (W/m .K)
Hydrogen	0.175
Helium	0.141
Air	0.024
Water vapour (saturated)	0.0206
CO­2	0.0146

3. Thermal Conductivity of liquids:

The physics of mechanism of thermal-energy conduction in liquids is quantitavely the same as in gases; however, the situation is more complex because the molecules are more closely special and molecular force fields exert a strong influence on the energy exchange in the collision process.

Typical values of thermal conductivities are:

Table 2: Thermal conductivities of some liquids

Liquids	Thermal conductivity (W/m .K)
Mercury	8.21
Water	0.556
Ammonia	0.540
Lubricating oil, SAE 50	0.147
Freon 12, CCl2F2	0.073

4. Thermal Conductivity of solids:

Thermal energy may be conducted in solids by two modes: lattice vibration and transport by free electrons.

In good electrical conductors a rather large number of free electrons move about in the lattice structure of the material. Just as these electrons may transport electric charge; they may also carry thermal energy from a high-temperature region to a low temperature, as in the cases of gases.

In fact these electrons are frequently referred to as the electron gas.

Energy may also be transmitted as vibrational energy in the lattice structure of the material. In general, however, this lattice mode of energy transport is not as large as the electron transport, and for this reason good electrical conductors are almost always good heat conductors. V.Z. Cu, Al, and Ag, and electrical insulators are usually good heat insulators. A notable exception is diamond which is an electrical insulator; but which can have a thermal conductivity five times as high as silver or copper. It is this fact enables a jeweller to distinguish between genuine diamonds and fake stones. A small instrument is available to a thermal heat pulse. A true diamond will exhibit a far more rapid response than the non-genuine stone.

Solids	Thermal conductivity (W/m .K)
Silver	410
Copper	385
Aluminium	202
Nickel	93
Iron	73
CS, 1% C	43
Lead	35

References:

1. “Heat Transfer”,J.P. Holman, Pages: 6-10

2. “unit operations of chemical engineering”, Warren.l. Mccabe and Julian C. Smith, Pages: 291-292.

3. “Process Heat Transfer”, D.Q. Kern, Pages:6-15

4. “Heat Transfer a basic approach”, Necati Ozisik.