R. Shanthini 10 May 2010_modified 1 PM3125 Content of Lectures 1 to 6: Heat transfer: Source of heat...

R. Shanthini 10 May 2010_modified

1

PM3125

Content of Lectures 1 to 6:

Heat transfer: • Source of heat • Heat transfer • Steam and electricity as heating media• Determination of requirement of amount of

steam/electrical energy • Steam pressure• Mathematical problems on heat transfer

uploaded at http://www.rshanthini.com/PM3125.htm


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What is Heat?


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What is Heat?

Heat is energy in transit.


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Units of Heat• The SI unit is the joule (J),

which is equal to Newton-metre (Nm).

• Historically, heat was measured in terms of the ability to raise the temperature of water.

• The calorie (cal): amount of heat needed to raise the temperature of 1 gramme of water by 1 C0 (from 14.50C to 15.50C)

• In industry, the British thermal unit (Btu) is still used: amount of heat needed to raise the temperature of 1 lb of water by 1 F0 (from 630F to 640F)


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Conversion between different

units of heat:

1 J = 0.2388 cal = 0.239x10-3 kcal = 60.189 Btu

1 cal = 4.186 J = 3.969 x 10-3 Btu


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Sensible Heat

• What is 'sensible heat‘?

Sensible heat is associated with a temperature change


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Specific Heat Capacity

• To raise the temperature by 1 K, different substances need different amount of energy because substances have different molecular configurations and bonding (eg: copper, water, wood)

• The amount of energy needed to raise the temperature of 1 kg of a substance by 1 K is known as the specific heat capacity

• Specific heat capacity is denoted by c


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Calculation of Sensible Heat

where ΔT is the temperature change in the substance

Q = m c dT ∫ Q is the heat lost or gained by a substance

m is the mass of substance

c is the specific heat of substance which changes with temperature

T is the temperature

When temperature changes causes negligible changes in c,

Q = m c dT ∫ = m c ∆T


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When temperature changes causes significant changes in c,

Q = m c ∆T cannot be used.

Q = ∆H = m ∆h Instead, we use the following equation:

where ΔH is the enthalpy change in the substance

and ∆h is the specific enthalpy change in the substance.

To apply the above equation, the system should remain at constant pressure and the associated

volume change must be negligibly small.


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Q = m c ΔT (since c is taken as a constant)

= (300 g) (0.896 J/g oC)(70 - 25)oC

= 12,096 J

= 13.1 kJ

Calculate the amount of heat required to raise the temperature of 300 g Al from 25oC to 70oC.

Data: c = 0.896 J/g oC for Al


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Exchange of Heat

Heat lost by iron = Heat gained by water

(m c ΔT)iron = (m c ΔT)water

(100 g) (0.452 J/g oC)(80 - tf)oC

= (53.5 g) (4.186 J/g oC)(tf - 25)oC

80 - tf = 4.955 (tf -25)

tf = 34.2oC

Calculate the final temperature (tf), when 100 g iron at 80oC is tossed into 53.5g of water at 25oC.

Data: c = 0.452 J/g oC for iron and 4.186 J/g oC for water


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Latent Heat

• What is ‘latent heat‘?

Latent heat is associated with phase change of matter


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Phases of Matter


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Phase Change• Heat required for phase changes:

» Melting: solid liquid

» Vaporization: liquid vapour

» Sublimation: solid vapour

• Heat released by phase changes:» Condensation: vapour liquid

» Fusion: liquid solid

» Deposition: vapour solid


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Phase Diagram: Water


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Phase Diagram: Water

Saturated steam

Superheated steam

Saturated liquidCompressed liquid


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Phase Diagram: WaterExplain why water is at liquid

state at atm pressure


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Phase Diagram: Carbon DioxideExplain why CO2 is at gas state

at atm pressure

Explain why CO2 cannot be made a

liquid at atm pressure


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Latent Heat

Latent heat is the amount of heat added per unit mass of substance during a phase change

Latent heat of fusion is the amount of heat added to melt a unit mass of ice OR it is the amount of heat removed to freeze a unit mass of water.

Latent heat of vapourization is the amount of heat added to vaporize a unit mass of water OR it is the amount of heat removed to condense a unit mass of steam.


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Water: Specific Heat Capacities and Latent Heats

Specific heat of ice ≈ 2.06 J/g K (assumed constant)

Heat of fusion for ice/water ≈ 334 J/g (assumed constant)

Specific heat of water ≈ 4.18 J/g K (assumed constant)

Latent heat of vaporization cannot be assumed a constant since it changes significantly with the pressure,

and could be found from the Steam Table

How to evaluate the sensible heat gained (or lost) by superheated steam?


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Water: Specific Heat Capacities and Latent Heats

How to evaluate the sensible heat gained (or lost) by superheated steam?

Q = m c ∆T cannot be used since changes in c with changing

temperature is NOT negligible.

Q = ∆H = m ∆h Instead, we use the following equation:

provided the system is at constant pressure and the associated volume change is negligible.

Enthalpies could be referred from the Steam Table


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Properties of SteamLearnt to refer to Steam Table to find properties of steam such as saturated (or boiling point) temperature and latent heat of vapourization at give pressures, and enthalpies of superheated steam at various pressures and temperatures.

Reference:

Chapter 6 of “Thermodynamics for Beginners with worked examples” by R. Shanthini

(published by Science Education Unit, Faculty of Science, University of Peradeniya)

(also uploaded at http://www.rshanthini.com/PM3125.htm)


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Warming curve for waterWhat is the amount of heat required to change 2 kg of ice

at -20oC to steam at 150oC at 2 bar pressure?

-20oC ice


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-20oC ice

0oC melting point of ice


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-20oC ice


120.2oC boiling point of water at 2 bar

Boiling point of water at 1 atm pressure is 100oC. Boiling point of water at 2 bar is 120.2oC. [Refer the Steam Table.]


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-20oC ice


120.2oC boiling point of water at 2 bar

150oC superheated steam

Specific heat

Specific heat

Specific heat

Latent heat

Latent heat


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Specific heat required to raise the temperature of ice from -20oCto 0oC= (2 kg) (2.06 kJ/kg oC) [0 - (-20)]oC = 82.4 kJ

Latent heat required to turn ice into water at 0oC= (2 kg) (334 kJ/kg) = 668 kJ

Specific heat required to raise the temperature of water from 0oC to 120.2oC

= (2 kg) (4.18 kJ/kg oC) [120.2 - 0)]oC = 1004.9 kJ


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Latent heat required to turn water into steam at 120.2oC and at 2 bar= (2 kg) (2202 kJ/kg) = 4404 kJ

[Latent heat of vapourization at 2 bar is 2202 kJ/kg as could be referred to from the Steam Table]

Specific heat required to raise the temperature of steam from 120.2oC to 150oC

= (2 kg) (2770 – 2707) kJ/kg = 126 kJ

[Enthalpy at 120.2oC and 2 bar is the saturated steam enthalpy of 2707 kJ/kg and the enthalpy at 150oC and 2 bar is 2770 kJ/kg as could be referred to from the Steam Table]


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Total amount of heat required

= 82.4 kJ + 668 kJ + 1004.9 kJ + 4404 kJ + 126 kJ

= 6285.3 kJ


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Application: Heat ExchangerIt is an industrial equipment in which heat is transferred from a hot fluid (a liquid or a gas) to a cold fluid (another liquid or gas) without the two fluids having to mix together or come into direct contact.

Hot fluid at TH,in Hot fluid

at TH,out

Cold fluid at TC,out

Cold fluid at TC,in

Heat lost by the hot fluid = Heat gained by the cold fluid


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Application: Heat Exchanger


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Heat Exchanger

mhot chot (TH,in – TH,out) = mcold ccold (TC,out – TC,in). .


mass flow rate of hot fluid

Specific heat of hot fluid

mass flow rate of cold fluid

Specific heat of cold fluid

Temperature decrease in the hot fluid

Temperature increase in the cold fluid


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Heat Exchanger

mhot chot (TH,in – TH,out) = mcold ccold (TC,out – TC,in). .


The above is true only under the following conditions:

(1) Heat exchanger is well insulated so that no heat is lost to the environment

(2) There are no phase changes occurring within the heat exchanger.


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Heat Exchanger


+ Heat lost to the environment

If the heat exchanger is NOT well insulated, then


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High pressure liquid water at 10 MPa (100 bar) and

30oC enters a series of heating tubes. Superheated

steam at 1.5 MPa (15 bar) and 200oC is sprayed over

the tubes and allowed to condense. The condensed

steam turns into saturated water which leaves the

heat exchanger. The high pressure water is to be

heated up to 170oC. What is the mass of steam

required per unit mass of incoming liquid water?

The heat is assumed to be well insulated (adiabatic).

Worked Example in Heat Exchanger


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Solution: High pressure (100 bar) water enters at 30oC and leaves at 198.3oC.Boiling point of water at 100 bar is 311.0oC. Therefore, no phase changes in the high pressure water that is getting heated up in the heater.

Heat gained by high pressure water

= ccold (TC,out – TC,in)

= (4.18 kJ/kg oC) x (170-30)oC

= 585.2 kJ/kg

[You could calculate the above by taking the difference in enthalpies at the 2 given states from tables available.]



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Solution continued: Superheated steam at 1.5 MPa (15 bar) and 200oC is sprayed over the tubes and allowed to condense. The condensed steam turns into saturated water which leaves the heat exchanger.

Heat lost by steam

= heat lost by superheated steam to become saturated

steam

+ latent heat of steam lost for saturated steam to turn into

saturated water

= Enthalpy at 15 bar and 200oC

– Enthalpy of saturated steam at 15 bar

+ Latent heat of vapourization at 15 bar

= (2796 kJ/kg – 2792 kJ/kg) + 1947 kJ/kg = 1951 kJ/kg



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Solution continued:

Since there is no heat loss from the heater,

Heat lost by steam = Heat gained by high pressure water

Mass flow of steam x 1951 kJ/kg

= Mass flow of water x 585.2 kJ/kg

Mass flow of steam / Mass flow of water

= 585.2 / 1951

= 0.30 kg stream / kg of water



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Give the design of a heat exchanger which has the most effective heat

transfer properties.

Group Assignment 1

Learning objectives:1) To be able to appreciate heat transfer applications in pharmaceutical

industry

2) To become familiar with the working principles of various heat exchangers

3) To get a mental picture of different heat exchangers so that solving heat transfer problems in class becomes more interesting


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Group Assignment 2 Steam enters a heat exchanger at 10 bar and 200oC and

leaves it as saturated water at the same pressure. Feed-water enters the heat exchanger at 25 bar and 80oC and leaves at the same pressure and at a temperature 20oC less than the exit temperature of the steam. Determine the ratio of the mass flow rate of the steam to that of the feed-water, neglecting heat losses from the heat exchanger.

If the feed-water leaving the heat exchanger is fed directly to a boiler to be converted to steam at 25 bar and 300oC, find the heat required by the boiler per kg of feed-water.

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R. Shanthini 10 May 2010_modified 1 PM3125 Content of Lectures 1 to 6: Heat transfer: Source of heat...

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