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HEAT TRANSFER
Content
•   Modes of heat transfer?
•   Fourier Law of heat conduction
•   Convective heat coefficient
•   Radiant heat coefficient
•   Overall heat transfer coefficient
•   Hands-on example
Temperature
• A measure of energy due to level of heat
  – Freezing point of water is 0 ˚ C
  – Boiling point of water is 100 ˚ C
Common Temperature Scales
What is Heat?
Heat is the total internal kinetic energy due to
 molecular motion in an object
Quantity of heat is BTU or Kilo Joule (kJ)
  • One BTU is the amount of heat required to raise 1
    lb of water by 1 ˚ F
  • One calorie is required to raise 1 g of water by 1 ˚
    C
    1 cal = 4.187 J
  • 1 BTU= 1.055 kJ= 1055 J
Heat Vs Temperature
• Heat energy depends on mass. Temperature is
  independent of mass.
  – 2 litres of boiling water has more heat energy than
    1 litre of boiling water
• Temperature is not energy, but a measure of it
• Heat is energy
Heat is Energy
When heat (ie energy) goes into a substance,
  one of two things can happen:
1. Temperature goes up
2. Change of state
Temperature Goes Up
• Heat that causes a rise in temperature e.g.
  heating water before boiling
• The heat energy is used to increase the kinetic
  energy of the molecules in the substance
• This is also known as the sensible heat
Change Of State
• Heat that brings about a change in potential
  energy of the molecules (temperature remains
  constant). Also called the latent heat.
Specific Heat
• It is the heat required to the temperature of 1
  kg (lb) a substance by 1 ˚ K (F)
• Example:
  water’s specific heat is 1 btu/ lb F (4.2 kJ/kg K)
  air’s specific heat is 0.24 btu/ lb F (1.0 kJ/kg K)
Sizing Heating Capacity

Quantity of heat required  mass x specific heat x T

     Example:
     What is the heat required to raise air
     temperature from 15 ˚C to 25 ˚C at a
     flow rate of 2000 l/s?
Heat Transfer
• If there is a temperature difference in a
  system, heat will always move from higher to
  lower temperatures

           What is actually flowing?
Heat Transfer Modes


There are 3 modes
of heat transfer.
1. Conduction
2. Convection
3. Radiation
Conduction
• Heat transfer through a solid medium via
  direct contact
• Expressed by Fourier’s Law
Fourier’s Law
                                      T2       T1

        dT
q"  k
                                                    Q


        dx                                 X


k = thermal conductivity (W/ m K)
T = temperature (K)
q” = heat flux (W/m2)


  Heat flow rate = q” x area        (W)
Fourier’s law at steady state
         dT
q"   k            (Fourier Law)
          dx
         Tout  Tin
q"   k               (Steady State)
             L
       Tout  Tin
q"  
          L/k
Heat transfer rate
                                               q
Q  q" x Area of heat flow
                                                    T2
    T T
  out in                        T1
      L / kA
                                        R=L/k
                                        Unit thermal resistance
Example 1
• Temperature of 35 C and 22 C are maintained
  on opposite sides of a steel floor of 6mm
  thick. Compute the heat flux through the
  floor.
• Thermal conductivity for steel = 50 W/m K
Thermal Conductivity, k (W/m K)

Liquids              Common Metals
Water: 0.556         Copper: 385
Ammonia: 0.54        Aluminum: 221
Gases                Steel: 50
Air : 0.024          Non-metals
Water vapor: 0.021   Common brick: 0.6
                     Mineral wool: 0.04
                     Ceiling board: 0.06
Quiz
• Suppose a human could live for 2 h unclothed
  in air at 45 ˚F. How long could she live in water
  at 45 ˚F?
Electrical- Thermal Analogy
                                            q

                                                T2
Electrical (Ohm' s Law)       T1


             Voltage Potential     R=L/kA
Current, I 
               Re sis tan ce
Thermal
               Temperature difference
Heat flux, q 
                     Re sis tan ce
Composite Wall

                     Using the resistance concept,

                             T 2 T1
                        q" 
                             R1 R 2
                             x1
                        R1 
                             k1
                              x2
     R1   R2   T2       R2 
T1                            k2
           Q
Example 2
A wall of a Switchgear room consists the
  following:
                      6mm    100mm   25mm


                                                   TNF panel
                             k2                    k = 0.02 W/m K

               35 C          q2             22 C
                      Q
                      Q
                                                   Q
Steel plate
                                                     Firebatt
k = 50 W/m K
                                                     k = 0.04 W/m K



      Determine Q, if the wall is 3m x 4m ?
Convection
• Energy transfer by fluid
  motion
• Two kinds of convection
  – Forced convection: Fluid is
    forced
  – Natural or free convection:
    fluid is induced by
    temperature difference
Convective Heat Transfer
                                         y   Ta
Newton's Law of cooling              q

q"  hc (Ts  Ta )        air flow

     (Ts  Ta )                                              Ts
q" 
         1
        hC                 where:
                           h c is convection coefficient (W/m2C),
     1                     Ts is surface temperature (C),
Rc                        T a is surrounding air temperature (C)
     hc
                           Rc= unit convective resistance.
Magnitude of Convection Coefficients
Arrangement          h, W/m2 K   Btu/(h.ft2.F)
Air, free (indoor)   10-30       1-5
Air, forced          30-300      5-50
(outdoor)
Oil, forced          60-1800     10-300
Water, forced        300-6000    50-1000
Steam, condensing 6000-120000    1000-20000
Example 3
The same as Example 2. Consider convection of
  the exposed surfaces, calculate Q.
                      6mm    100mm   25mm


                                                   TNF panel
                             k2                    k = 0.02 W/m K

               35 C          q2             22 C
                      Q
                      Q
                                                   Q
Steel plate
                                                     Firebatt
k = 50 W/m K
                                                     k = 0.04 W/m K
Radiation
• Energy emitted by object that is at any
  temperature above absolute zero
• Energy is in the form electromagnetic waves
• No medium needed and travel at speed of
  light

                            Example :
         Hot Body           Solar radiation
                            Radiator
Radiation
• Important mode of heat at high temperatures,
  e.g. combustion furnace
• At room temperature it may just be
  measurable.
• Intensity depends on body temperature and
  surface characteristics
Solar Radiation

• Solar radiation is the radiation emitted by the
  sun due to nuclear fusion reaction
• Solar Constant: The amount of solar energy
  arriving at the top of the atmosphere
  perpendicular to the sun’s rays.
• = 1375 W m-2
Solar Radiation Spectrum

        99% of solar radiation is between 0.3 to 3 µm.
Wien’s Law



             2900
        m       m
              T
Wien’s Law
The Black Body

              4
    E = AT

   • E =The amount of energy (W )
     emitted by an object
   •  = Stefan-Boltzmann constant =
     5.67 x 10-8 W m-2 K-4
   • T = Temperature (K)
   • A= area (m2)
The Grey Body

   For an actual body,
   E   Eb   A(T ) where
                      4



     emissitivity
      0.8 - 0.9 for common materials
      0.02 - 0.07 for polished metals
Net Radiant Heat


• If a hot object is radiating to a cold
  surrounding, the radiation loss is

         q   A(Th 4  Tc 4 )
Quiz
How much energy does human body radiate?
• Body temperature is 37 C
• Body area is 1.5 m2
• ε= 0.7
Radiant Heat Transfer
• Unit thermal resistance for radiation is written
  as q"  hr ( T)
             1
        Rc 
             hr

  Radiation coefficient is a function of
  temperature, radiation properties and
  geometrical arrangement of the enclosure
  and the body in question.
Combined convection and radiant
             Coefficient
• The heat transfer is combination of convection
  and radiation
  q"  qc  qr
 q"  ( hc  hr )(T )
 Combined thermal resistance,
           1
  R
       hc  hr
Combined Surface Coefficients
• Some practical values of surface coefficients:
(source: ASHRAE Fundamentals 1989)


    Air velocity           Emissivity, ε=0.9
    3.5 m/s                h = 22.7 W/m2 K
    7 m/s                  h = 35 W/m2 K
    Still air              h = 8.5 W/ m2 K
Combined modes
                                                                   Thot
                                         Thot

Outside
                                                      R3=1/hhot

                                    T3
                                                                      T3
    k2                      T2
    k1
                                                R2=L1/k1 + L2/K2
                       T1
Inside                                                               T1


                                                     R1=1/hcold
            Tcold

                                                T
                                                                     Tcold
  Resistance in parallel, R= R1 + R2 +R3
Compute
                                                                    Thot

R  R1  R 2  R 3
                                                        R3=1/hhot
       1      L1 L 2 1
R          / 
     hcold k 1 k 2 hhot
                    Thot  Tcold                                       T2
q"                                                R2=L1/k1 + L2/k2
     1 / hhot  1 / hcold  L1 / k 1  L 2 / k 2
     T1  Tcold
q"                                                                   T1
      1 / hcold
               T2  Tcold                              R1=1/hcold
q" 
     1 / hcold  L1 / k 1  L 2 / k 2
                                                                      Tcold
Overall Heat Transfer Coefficient
• Heat transfer processes includes conduction,
  convection and radiation simultaneously
• The total conduction heat transfer for a wall or
  roof is expressed as
   Q = A x U x ∆T where
   U is the overall heat transfer coefficient (or U-
  value)

      R  R1  R 2         R 3  .......
          1
      U 
          R
Example
• Find the overall heat
  transfer coefficient of
  a flat roof having the
  construction shown in
  the figure.
Solution
                T1


           R1

           R2

           R3


           R4

           R5

           R6



                T2
Solution
Resistance   Construction    Unit resistance (m2 K/ W)


R1           Outside air


R2           steel


R3           Mineral wool


R4           Air space


R5           Ceiling board


R6           Inside air

Total R
Solution

Overall heat transfer coefficien t
    1      1
U             0.40 W/m K 2

    R 2.48
Heat Transfer Loop
 in a DX System
Heat Exchanger Coil

            Heat is exchanged between
            2 fluids.
            Q= UA ∆T
            For cross flow,
            Q= UA (LMTD)
Heat Exchanger- Mean Temperature
           Difference


                 Heat Transfer, Q  U x Area x LMTD
                                 GTD - LTD
                 Q  U x Area x
                                     GTD
                                  Ln
                                     LTD
Heat transfer optimization
• We have the following relations for heat transfer:
   – Conduction: Q = k A ∆T /d
   – Convection: Q = A h c ∆T
   – Radiation: Q = A h r ∆T
• As a result, when equipment designers want to improve
  heat transfer rates, they focus on:
   – Increasing the area A, e.g. by using profiled tubes and ribbed
     surfaces.
   – Increasing T (which is not always controllable).
   – For conduction, increasing k /d.
   – Increase h c by not relying on natural convection, but
     introducing forced convection.
   – Increase hr, by using “black” surfaces.

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11 Heat Transfer

  • 2. Content • Modes of heat transfer? • Fourier Law of heat conduction • Convective heat coefficient • Radiant heat coefficient • Overall heat transfer coefficient • Hands-on example
  • 3. Temperature • A measure of energy due to level of heat – Freezing point of water is 0 ˚ C – Boiling point of water is 100 ˚ C
  • 5. What is Heat? Heat is the total internal kinetic energy due to molecular motion in an object Quantity of heat is BTU or Kilo Joule (kJ) • One BTU is the amount of heat required to raise 1 lb of water by 1 ˚ F • One calorie is required to raise 1 g of water by 1 ˚ C 1 cal = 4.187 J • 1 BTU= 1.055 kJ= 1055 J
  • 6. Heat Vs Temperature • Heat energy depends on mass. Temperature is independent of mass. – 2 litres of boiling water has more heat energy than 1 litre of boiling water • Temperature is not energy, but a measure of it • Heat is energy
  • 7. Heat is Energy When heat (ie energy) goes into a substance, one of two things can happen: 1. Temperature goes up 2. Change of state
  • 8. Temperature Goes Up • Heat that causes a rise in temperature e.g. heating water before boiling • The heat energy is used to increase the kinetic energy of the molecules in the substance • This is also known as the sensible heat
  • 9. Change Of State • Heat that brings about a change in potential energy of the molecules (temperature remains constant). Also called the latent heat.
  • 10. Specific Heat • It is the heat required to the temperature of 1 kg (lb) a substance by 1 ˚ K (F) • Example: water’s specific heat is 1 btu/ lb F (4.2 kJ/kg K) air’s specific heat is 0.24 btu/ lb F (1.0 kJ/kg K)
  • 11. Sizing Heating Capacity Quantity of heat required  mass x specific heat x T Example: What is the heat required to raise air temperature from 15 ˚C to 25 ˚C at a flow rate of 2000 l/s?
  • 12. Heat Transfer • If there is a temperature difference in a system, heat will always move from higher to lower temperatures What is actually flowing?
  • 13. Heat Transfer Modes There are 3 modes of heat transfer. 1. Conduction 2. Convection 3. Radiation
  • 14. Conduction • Heat transfer through a solid medium via direct contact • Expressed by Fourier’s Law
  • 15. Fourier’s Law T2 T1 dT q"  k Q dx X k = thermal conductivity (W/ m K) T = temperature (K) q” = heat flux (W/m2) Heat flow rate = q” x area (W)
  • 16. Fourier’s law at steady state dT q"   k (Fourier Law) dx Tout  Tin q"   k (Steady State) L Tout  Tin q"   L/k Heat transfer rate q Q  q" x Area of heat flow T2 T T   out in T1 L / kA R=L/k Unit thermal resistance
  • 17. Example 1 • Temperature of 35 C and 22 C are maintained on opposite sides of a steel floor of 6mm thick. Compute the heat flux through the floor. • Thermal conductivity for steel = 50 W/m K
  • 18. Thermal Conductivity, k (W/m K) Liquids Common Metals Water: 0.556 Copper: 385 Ammonia: 0.54 Aluminum: 221 Gases Steel: 50 Air : 0.024 Non-metals Water vapor: 0.021 Common brick: 0.6 Mineral wool: 0.04 Ceiling board: 0.06
  • 19. Quiz • Suppose a human could live for 2 h unclothed in air at 45 ˚F. How long could she live in water at 45 ˚F?
  • 20. Electrical- Thermal Analogy q T2 Electrical (Ohm' s Law) T1 Voltage Potential R=L/kA Current, I  Re sis tan ce Thermal Temperature difference Heat flux, q  Re sis tan ce
  • 21. Composite Wall Using the resistance concept, T 2 T1 q"  R1 R 2 x1 R1  k1 x2 R1 R2 T2 R2  T1 k2 Q
  • 22. Example 2 A wall of a Switchgear room consists the following: 6mm 100mm 25mm TNF panel k2 k = 0.02 W/m K 35 C q2 22 C Q Q Q Steel plate Firebatt k = 50 W/m K k = 0.04 W/m K Determine Q, if the wall is 3m x 4m ?
  • 23. Convection • Energy transfer by fluid motion • Two kinds of convection – Forced convection: Fluid is forced – Natural or free convection: fluid is induced by temperature difference
  • 24. Convective Heat Transfer y Ta Newton's Law of cooling q q"  hc (Ts  Ta ) air flow (Ts  Ta ) Ts q"  1 hC where: h c is convection coefficient (W/m2C), 1 Ts is surface temperature (C), Rc  T a is surrounding air temperature (C) hc Rc= unit convective resistance.
  • 25. Magnitude of Convection Coefficients Arrangement h, W/m2 K Btu/(h.ft2.F) Air, free (indoor) 10-30 1-5 Air, forced 30-300 5-50 (outdoor) Oil, forced 60-1800 10-300 Water, forced 300-6000 50-1000 Steam, condensing 6000-120000 1000-20000
  • 26. Example 3 The same as Example 2. Consider convection of the exposed surfaces, calculate Q. 6mm 100mm 25mm TNF panel k2 k = 0.02 W/m K 35 C q2 22 C Q Q Q Steel plate Firebatt k = 50 W/m K k = 0.04 W/m K
  • 27. Radiation • Energy emitted by object that is at any temperature above absolute zero • Energy is in the form electromagnetic waves • No medium needed and travel at speed of light Example : Hot Body Solar radiation Radiator
  • 28. Radiation • Important mode of heat at high temperatures, e.g. combustion furnace • At room temperature it may just be measurable. • Intensity depends on body temperature and surface characteristics
  • 29. Solar Radiation • Solar radiation is the radiation emitted by the sun due to nuclear fusion reaction • Solar Constant: The amount of solar energy arriving at the top of the atmosphere perpendicular to the sun’s rays. • = 1375 W m-2
  • 30. Solar Radiation Spectrum 99% of solar radiation is between 0.3 to 3 µm.
  • 31. Wien’s Law 2900 m  m T
  • 33. The Black Body 4 E = AT • E =The amount of energy (W ) emitted by an object •  = Stefan-Boltzmann constant = 5.67 x 10-8 W m-2 K-4 • T = Temperature (K) • A= area (m2)
  • 34. The Grey Body For an actual body, E   Eb   A(T ) where 4   emissitivity  0.8 - 0.9 for common materials  0.02 - 0.07 for polished metals
  • 35. Net Radiant Heat • If a hot object is radiating to a cold surrounding, the radiation loss is q   A(Th 4  Tc 4 )
  • 36. Quiz How much energy does human body radiate? • Body temperature is 37 C • Body area is 1.5 m2 • ε= 0.7
  • 37. Radiant Heat Transfer • Unit thermal resistance for radiation is written as q"  hr ( T) 1 Rc  hr Radiation coefficient is a function of temperature, radiation properties and geometrical arrangement of the enclosure and the body in question.
  • 38. Combined convection and radiant Coefficient • The heat transfer is combination of convection and radiation q"  qc  qr q"  ( hc  hr )(T ) Combined thermal resistance, 1 R hc  hr
  • 39. Combined Surface Coefficients • Some practical values of surface coefficients: (source: ASHRAE Fundamentals 1989) Air velocity Emissivity, ε=0.9 3.5 m/s h = 22.7 W/m2 K 7 m/s h = 35 W/m2 K Still air h = 8.5 W/ m2 K
  • 40. Combined modes Thot Thot Outside R3=1/hhot T3 T3 k2 T2 k1 R2=L1/k1 + L2/K2 T1 Inside T1 R1=1/hcold Tcold T Tcold Resistance in parallel, R= R1 + R2 +R3
  • 41. Compute Thot R  R1  R 2  R 3 R3=1/hhot 1 L1 L 2 1 R  /  hcold k 1 k 2 hhot Thot  Tcold T2 q"  R2=L1/k1 + L2/k2 1 / hhot  1 / hcold  L1 / k 1  L 2 / k 2 T1  Tcold q"  T1 1 / hcold T2  Tcold R1=1/hcold q"  1 / hcold  L1 / k 1  L 2 / k 2 Tcold
  • 42. Overall Heat Transfer Coefficient • Heat transfer processes includes conduction, convection and radiation simultaneously • The total conduction heat transfer for a wall or roof is expressed as Q = A x U x ∆T where U is the overall heat transfer coefficient (or U- value) R  R1  R 2  R 3  ....... 1 U  R
  • 43. Example • Find the overall heat transfer coefficient of a flat roof having the construction shown in the figure.
  • 44. Solution T1 R1 R2 R3 R4 R5 R6 T2
  • 45. Solution Resistance Construction Unit resistance (m2 K/ W) R1 Outside air R2 steel R3 Mineral wool R4 Air space R5 Ceiling board R6 Inside air Total R
  • 46. Solution Overall heat transfer coefficien t 1 1 U   0.40 W/m K 2 R 2.48
  • 47. Heat Transfer Loop in a DX System
  • 48. Heat Exchanger Coil Heat is exchanged between 2 fluids. Q= UA ∆T For cross flow, Q= UA (LMTD)
  • 49. Heat Exchanger- Mean Temperature Difference Heat Transfer, Q  U x Area x LMTD GTD - LTD Q  U x Area x GTD Ln LTD
  • 50. Heat transfer optimization • We have the following relations for heat transfer: – Conduction: Q = k A ∆T /d – Convection: Q = A h c ∆T – Radiation: Q = A h r ∆T • As a result, when equipment designers want to improve heat transfer rates, they focus on: – Increasing the area A, e.g. by using profiled tubes and ribbed surfaces. – Increasing T (which is not always controllable). – For conduction, increasing k /d. – Increase h c by not relying on natural convection, but introducing forced convection. – Increase hr, by using “black” surfaces.